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Tamilnadu State Board New Syllabus Samacheer Kalvi 12th Maths Guide Pdf Chapter 12 தனிநிலைக் கணிதம் Ex 12.1 Textbook Questions and Answers, Notes.

TN Board 12th Maths Solutions Chapter 12 தனிநிலைக் கணிதம் Ex 12.1

கேள்வி 1.
கீழே கொடுக்கப்பட்டுள்ள கணங்களின் மீது வரையறுக்கப்பட்டிருக்கும் * ஓர் ஈருறுப்புச் செயலியா எனத் தீர்மானிக்க .
(i) ℝ-ன் மீது a * b = a . |b|
(ii) A = {1, 2, 3, 4, 5} – ன் மீது a * 5 = (a, b) -ல் சிறியது.
(iii) ℝ -ன் மீது (a*b) = a \(\sqrt{b}\)
தீர்வு:
(i) ℝ -ன் மீது a = a . |b|
கொடுக்கப்பட்ட ℝ -ன் மீது a* b = a • |b| a, b ∈ ℝ என்க
பிறகு a * b = a. |b| ∈ ℝ.
ஆதலால் a • |b| = ab, b> 0 எனில்
= -ab, b < 0 எனில்
∴ a * (b) = a . |b| ∈ ℝ
ஆம் * ஆனது ℝ-ன் மீதான ஓர் ஈருறுப்புச் செயலி ஆகும்.

(ii) A = {1, 2, 3, 4, 5} – ன் மீது a * b = (a, b) -ல் சிறியது.
a, b ∈ A என்க
பிறகு (a, b) -ல் சிறியது. = a அல்லது b மற்றும் a, b ∈ A
∴ a * b = (a,b)-ல் சிறியது ∈ A
ஆம் * ஆனது ℝ-ன் மீதான ஓர் ஈருறுப்புச் செயலி ஆகும்.

(iii) ℝ -ன் மீது (a * b) = a \(\sqrt{b}\)
a, b = ℝ என்க [∴ குறை எண்களின் வர்க்க மூலம் ℝ-ல் இல்லை]
a * b = a \(\sqrt{b}\) = ℝ, b < 0 எனில்
எனவே* ஆனது ℝ-ன் மீதான ஈருறுப்புச் செயலி அல்ல.

கேள்வி 2.
ℤ -ன் மீது ⓧ என்ற செயலி பின்வருமாறு வரையறுக்கப்பட்டுள்ளது. (m ⓧ n)=mⁿ + n^m: ∀m, I n ∈ ℤ. *ஆனது -ன் மீது அடைவுப் பண்பை பெற்றுள்ளதா?
தீர்வு: கொடுக்கப்பட்ட m ⦻ n = mⁿ + n^m ∀m, n ∈ ℤ m, n ∈ ℤ என்க .
m = -3, n = 2 எனக் கொள்க.
∴ m ⓧ n = (-3)² + 2^-3
= 9 + \(\frac{1}{8}\) = \(\frac{72+1}{8}\) = \(\frac{73}{8}\) ∉ ℤ
∴ ⓧஆனது, ℤ-ன் மீது அடைவு பெறவில்லை .

கேள்வி 3.
ℝ-ன் மீது * ஆனது (a*b) = a + b + ab – 7 என வரையறுக்கப்பட்டால் * ;ℝ – ன் மீது அடைவு பெற்றுள்ளதா? அவ்வாறெனில், 3 * (\(\frac{-7}{15}\)) காண்க.
தீர்வு:
கொடுக்கப்பட்ட a* b = a + b + ab – 7

கேள்வி 4.
A = {a + \(\sqrt{5}\) b: a,b ∈ ℤ} என்க. வழக்கமான பெருக்கல் A -ன் மீது ஓர் ஈருறுப்புச் செயல் ஆகுமா என பரிசோதிக்க.
தீர்வு:
கொடுக்கப்பட்ட A = {a + \(\sqrt{5}\)b, a, b ∈ z}
C = a + \(\sqrt{5}\) b என்க
B = c + \(\sqrt{5}\) d ∈ A
இங்கு a, b, c, d ∈ ℤ
∴ C . B = (a + \(\sqrt{5}\) b). (c + \(\sqrt{5}\) d)
= ac + \(\sqrt{5}\) ad + cb \(\sqrt{5}\) + 5bd
= (ac + 5 bd) + \(\sqrt{5}\) (ad + bc) = A [∵ ac + 5 bd ∈ ℤ மற்றும் ad + bc ∈ ℤ]
∴ C. B ∈ A Va, b, c, d, ∈ ℤ
∴ வழக்கமான பெருக்கல் A-ன் மீது ஓர் ஈருறுப்புச் செயலி ஆகும்.

கேள்வி 5.
(i) *என்ற ஓர் ஈருறுப்புச் செயலி ℚ -ன் மீது பின்வருமாறு வரையறுக்கப் படுகிறது. இந்த * ஆனது, அடைவுப் பண்பு, பரிமாற்றுப் பண்பு . சேர்ப்புப் பண்பு ஆகியவற்றை நிறைவு செய்கிறதா எனச் சோதிக்க
a*b=(\(\frac{a+b}{2}\)); ∀a, b ∈ ℚ.
(ii) *ஆனது, சமனிப் பண்பு மற்றும் எதிர்மறைப் பண்பு ஆகியவை, ℚ -ன் மீது உண்மையாகுமா எனச் சோதிக்க.
a*b=(\(\frac{a+b}{2}\)); ∀ a, b ∈ ℚ
தீர்வு:
கொடுக்கப்பட்ட a* b = \(\frac{a+b}{2}\) ∀a. b ∈ ℚ.
(i) அடைவுப் பண்பு :
a, b ∈ ℚ என்க
∴ a * b = \(\frac{a+b}{2}\) ∈ ℚ
[∵ கூட்டல் மற்றும் பெருக்கல் ℚ-ல் அடைவுப் பண்பு பெற்றுள்ளது]
ℚ-ல் * அடைவுப் பண்பு பெற்றுள்ளது.

(ii) பரிமாற்றுப் பண்பு
a, b = ℚ என்க.
பிறகு a * b = \(\frac{a+b}{2}\) = \(\frac{b+a}{2}\) = b * a
∴ a * b = b * a ∀a, b ∈ ℚ
∴ Qஇல் * பரிமாற்றுப் பண்புடையதாகும்.

சேர்ப்புப் பண்பு
a, b, c ∈ ℚ என்க
a * (b * c) = (a * b) * c
a = 2, b = 3, c =-5 என்க
∴ a * (b * c) = 2 * (3 * -5)
= 2* (\(\frac{3-5}{2}\))
= 2 * (-1) = \(\frac{2+(-1)}{2}\)
= \(\frac{1}{2}\) …..(1)

(1) மற்றும் (2)லிருந்து, a * (b * c) = (a * b) * c
∴ ℚ இல் * சேர்ப்புப் பண்பு இல்லை.

(ii) கொடுக்கப்பட்ட a * b = \(\frac{a+b}{2}\), இங்கு a, b ∈ ℚ
a, b ∈ ℚ என்க
a * e = e * a = a என்ற உறுப்பை பின்வருமாறு காண வேண்டும்.
a = 5 என்க, பிறகு 5 * e = 5

சமனி உறுப்பு ஒவ்வொரு உறுப்புக்கும் மாறுவதால், ℚ-வில் சமனி உறுப்பு இல்லை
∴ * க்கு ℚ -வில் சமனி பண்பு இல்லை .
∴ * க்கு ℚ- வில் எதிர்மறை பண்பு இல்லை .
எனவே சமனி மற்றும் எதிர்மறை பண்பு ஈருறுப்பு செயலி * க்கு இல்லை .

கேள்வி 6.
* என்ற ஈருறுப்புச் செயலி ஆனது A = {a, b, c} என்ற கணத்தின் மீது பரிமாற்று விதிக்கு கட்டுப்பட்டால் பின்வரும் பட்டியலைப் பூர்த்தி செய்க.

தீர்வு:
A இல் கொடுக்கப்பட்ட * பரிமாற்று பண்புடையது
கொடுக்கப்பட்ட b * a = c ⇒ a * b = c
கொடுக்கப்பட்ட c * a = a ⇒ a * c = a
கொடுக்கப்பட்ட b * c = a ⇒ c * b = a
எனவே

கேள்வி 7.
A = {a, b, c, d} என்ற கணத்தின் மீது * என்ற ஈருறுப்புச் செயலியை பின்வரும் பட்டியலுடன் கருதுக.

இது மாற்றுப்பண்பு மற்றும் சேர்ப்புப் பண்புகளைப் பெற்றுள்ளதா?
தீர்வு:
கொடுக்கப்பட்ட A = {a, b, c, d} மற்றும் * பின்வருமாறு வரையறுக்கப்படுகிறது.

அட்டவணையிலிருந்து
(i) a * b = C மற்றும் ba = d
⇒ A இல் * பரிமாற்று பண்பை பெறவில்லை .
(ii) a * (b * c) = (a * b) * C என்பதை சரிபார்க்க
⇒ a * (b) = c * c
⇒ c # a
∴ A இல் * ஆனது சேர்ப்பு பண்பை நிறைவு செய்யவில்லை.

கேள்வி 8.
A = \(\left(\begin{array}{llll}
1 & 0 & 1 & 0 \\
0 & 1 & 0 & 1 \\
1 & 0 & 0 & 1
\end{array}\right)\), B = \(\left(\begin{array}{llll}
0 & 1 & 0 & 1 \\
1 & 0 & 1 & 0 \\
1 & 0 & 0 & 1
\end{array}\right)\), C = \(\left(\begin{array}{llll}
1 & 1 & 0 & 1 \\
0 & 1 & 1 & 0 \\
1 & 1 & 1 & 1
\end{array}\right)\) என்பவைகள் ஒரே மாதிரியான வகையினை உடைய ஏதேனும் மூன்று பூலியன் அணிகள் எனில்,
(i) A ∨ B
(ii) A ∧ B
(iii) (A ∨ B) ∧ C
(iv) (A ∧ B)∨C
ஆகியவைகளைக் காண்க.
தீர்வு:
கொடுக்கப்பட்ட A = \(\left(\begin{array}{llll}
1 & 0 & 1 & 0 \\
0 & 1 & 0 & 1 \\
1 & 0 & 0 & 1
\end{array}\right)\),

கேள்வி 9.
(i) M = \(\left\{\left(\begin{array}{ll}
x & x \\
x & x
\end{array}\right): x \in \mathbb{R}-\{0\}\right\}\) என்க.
* என்பது அணிப் பெருக்கல் எனக் கொள்க. * ஆனது M-ன் மீது அடைவு பெற்றுள்ளதா எனத் தீர்மானிக்க. அவ்வாறெனில்,
* ஆனது M -ன் மீது பரிமாற்றுப் பண்பு, சேர்ப்புப் பண்புகளையும் நிறைவு செய்யுமா எனச் சோதிக்க.

(ii) M = \(\left\{\left(\begin{array}{ll}
x & x \\
x & x
\end{array}\right): x \in \mathbb{R}-\{0\}\right\}\)* என்பது அணிப் பெருக்கல் எனக் கொள்க.
* ஆனது M -ன் மீது அடைவு பெற்றுள்ளதா எனத் தீர்மானிக்க. அவ்வாறெனில்,
* ஆனது M -ன் மீது சமனிப்பண்பு, மற்றும் எதிர்மறைப் பண்புகளை நிறைவு செய்யுமா எனவும் சோதிக்க. மற்றும் * என்பது அணி பெருக்கல்
தீர்வு:

∴ M இல் * ஆனது அடைவுப் பண்புடையது.
பரிமாற்று பண்பு

(1) மற்றும் (2) லிருந்து, A * B = B * A
∴ M-ல் *க்கு பரிமாற்றுப் பண்பு உண்டு .
சேர்ப்புப் பண்பு



∴ M இல் அடைவுப் பண்பு நிறைவு செய்யப்படுகிறது.
சமனி 2 × 2 அணிகளின் சமனி I = \(\left(\begin{array}{ll}
1 & 0 \\
0 & 1
\end{array}\right)\) ∉ M
∴ M இல் *க்கு சமனி உறுப்பு இல்லை .
எதிர்மறை :
சமனி உறுப்பு இல்லை எனவே எதிர்மறை பண்பும் இல்லை .

கேள்வி 10.
(i) A = ℚ\{1} என்க. A-ன் மீது* பின்வ ருமாறு வரையறுக்கப்படுகிறது. xy = x + y – xy.
* ஆனது A-ன்மீது அடைவு பெற்றுள்ளதா? அவ்வாறெனில், A-ன் மீது
* ஆனது பரிமாற்று விதி மற்றும் சேர்ப்பு விதிகளை நிறைவு செய்யுமா எனச் சோதிக்க.

(ii) A = Q\{1} என்க. A-ன் மீது * பின்வ ருமாறு வரையறுக்கப்படுகிறது.xy = x + y – xy.
* ஆனது A -ன் மீது அடைவு பெற்றுள்ளதா? அவ்வாறெனில், A-ன் மீது
* ஆனது சமனிப்பண்பு மற்றும் எதிர்மறைப் பண்புகளை நிறைவு செய்யுமா எனச் சோதிக்க.
தீர்வு:
(i) கொடுக்கப்பட்ட A = {Q\ {1}}
x * y = x + y – xy
எனுமாறு A இல் வரையறுக்கப்படுகிறது.
x, y ≠ 1 என்க
∴ x * y = x + y – xy
இங்கு x + y – xy # 1
x + y -.xy = 1 என்க
x + y – xy – 1 = 0
(x – 1) – y(x – 1) = 0
(x – 1) (1 – y) = 0
x = 1 அல்லது y = 1 இது தவறாகும். [∵ x, y # 1]
∴ நமது அனுமானம் தவறு.
∴ x + y – xy # 1
A இல் * ஆனது ஒரு ஈருறுப்புச் செயலி.
பரிமாற்றுப் பண்பு
x, y ∈ A ⇒ x, y # 1 என்க .
∴ x * y = x + y – xy’
மற்றும் y * x = y + x – yx
⇒ x + y = y * x ∀x, y ∈ A .
*க்கு A இல் பரிமாற்றுப் பண்பு உண்டு.
சேர்ப்புப் பண்பு x, y, z ∈ A ⇒ x, y, z + 1 என்க .
கருது (x * y) * z = (x + y – xy) * z
= x + y – xy + z – (x + y – xy)z
= x + y – xy + z – xz – yz +xyz
= x + y + z – xy – yz – zx + xyz ………….. (1)
= x + y + z – yz – x (y + z – yz)
= x + y + z – yz – zy – xz + xyz …..(2)
(1) மற்றும் (2) லிருந்து, (x * y) * z = x * (y * z) A இல் *க்கு சேர்ப்புப் பண்பு உண்டு.

(ii) சமனிப் பண்பு
e ∈ A என்ற உறுப்பை பின்வருமாறு காண வேண்டும்.
a * e = e * a = a
⇒ a + e – ae = a
⇒ e – ae = 0
⇒ e(1 – a) = 0
⇒ e = \(\frac{0}{1-a}\) = 0 ∈ A
* க்கு A இல் சமனி உண்டு .

எதிர்மறை பண்பு
ஒவ்வொரு a ∈ Aக்கும் a’ ∈ A ஆனது பின்வருமாறு
உள்ள து a * d’ = a’ * a = e
⇒ a + a’ – aa’ = 0 [∵ e = 0]
⇒ a + a'(1 – a) = 0
⇒ a'(1 – a) = -a
a’ = \(\frac{-a}{1-a}\)
நிரூபிக்க \(\frac{-a}{1-a}\) ≠ 1
\(\frac{-a}{1-a}\) = 1 என்க
⇒ -a = 1 – a
⇒ -a – a + a = 1 ⇒ 0 ≠ 1
∴ நமது அனுமானம் தவறு.
⇒ \(\frac{-a}{1-a}\) ≠ 1
∴ x ∈ Aக்கு A இல் எதிர்மறை பண்பு உண்டு.

Tamilnadu State Board New Syllabus Samacheer Kalvi 12th Maths Guide Pdf Chapter 1 அணிகள் மற்றும் அணிக்கோவைகளின் பயன்பாடுகள் Ex 1.2 Textbook Questions and Answers, Notes.

TN Board 12th Maths Solutions Chapter 1 அணிகள் மற்றும் அணிக்கோவைகளின் பயன்பாடுகள் Ex 1.2

கேள்வி 1.
பின்வரும் அணிகளுக்கு சிற்றணிக்கோவையை பயன்படுத்தி அணித்தரம் காண்க:
(i) \(\left[\begin{array}{rr}
2 & -4 \\
-1 & 2
\end{array}\right]\)
(ii) \(\left[\begin{array}{rr}
-1 & 3 \\
4 & -7 \\
3 & -4
\end{array}\right]\)
(iii) \(\left[\begin{array}{rrrr}
1 & -2 & -1 & 0 \\
3 & -6 & -3 & 1
\end{array}\right]\)
(iv) \(\left[\begin{array}{rrr}
1 & -2 & 3 \\
2 & 4 & -6 \\
5 & 1 & -1
\end{array}\right]\)
(v) \(\left[\begin{array}{llll}
0 & 1 & 2 & 1 \\
0 & 2 & 4 & 3 \\
8 & 1 & 0 & 2
\end{array}\right]\)
தீர்வு:
(i) \(\left[\begin{array}{rr}
2 & -4 \\
-1 & 2
\end{array}\right]\)

A ஒரு 2×2 வரிசை அணி
∴ \(\rho\)(A) ≤ (2, 2) – மீச்சிறு = 2
A-ன் பூச்சியமற்ற சிற்றணிக் கோவைகளின்
உச்ச வரிசை 2 ஆகும்.
இது \(\left|\begin{array}{rr}
2 & -4 \\
-1 & 2
\end{array}\right|\) = 4 – 4 = 0
ஆகையால், \(\rho\)(A)<2
அடுத்து 1 வரிசையுடைய சிற்றணிக்
கோவையை தேர்வு செய்வோம் |2| = 2≠0
∴ \(\rho\)(A) = 1

(ii) \(\left[\begin{array}{rr}
-1 & 3 \\
4 & -7 \\
3 & -4
\end{array}\right]\)
A = \(\left[\begin{array}{rr}
-1 & 3 \\
4 & -7 \\
3 & -4
\end{array}\right]\) என்க .
A ஒரு 3 × 2 வரிசை அணி
∴ ρ(A) ≤ (3, 2) -ன் மீச்சிறு = 2
A -ன் பூச்சியமற்ற சிற்றணிக் கோவைகளின்
உச்ச வரிசை 2 ஆகும்.
அது \(\left|\begin{array}{cc}
-1 & 3 \\
4 & -7
\end{array}\right|\) = 7-12 =-5 ≠ 0
∴ ρ(A) = 2.

(iii) \(\left[\begin{array}{rrrr}
1 & -2 & -1 & 0 \\
3 & -6 & -3 & 1
\end{array}\right]\)
A = \(\left[\begin{array}{rrrr}
1 & -2 & -1 & 0 \\
3 & -6 & -3 & 1
\end{array}\right]\) என்க.
A ஒரு (2 × 4) வரிசை அணி
∴ ρ(A) ≤ (2, 4) -ன் மீச்சிறு = 2
A-ன்பூச்சியமற்ற சிற்றணிக்கோவைகளின்
உச்சவரிசை 2 ஆகும்.
அது \(\left|\begin{array}{ll}
1 & -2 \\
3 & -6
\end{array}\right|\) = – 6+6 =0

∴ ρ(A) = 2.

(iv) \(\left[\begin{array}{rrr}
1 & -2 & 3 \\
2 & 4 & -6 \\
5 & 1 & -1
\end{array}\right]\)
A = \(\left[\begin{array}{rrr}
1 & -2 & 3 \\
2 & 4 & -6 \\
5 & 1 & -1
\end{array}\right]\) என்க.
A ஒரு 3 × 3 வரிசை அணி
∴ ρ(A) ≤ (3, 3) – ன் மீச்சிறு = 3
A-ன் பூச்சியமற்ற சிற்றணிக்கோவைகளின்
உச்சவரிசை 3 ஆகும்.
அது, |1 -2 3)

[R₁.- ன் மூலம் விரிவுபடுத்தப்பட்டது]
= 1 (-4+ 6) + 2 (- 2 + 30) + 3 (2 – 20)
= 1 (2) + 2 (28) + 3 (- 18) = 2 + 56 – 54 = 58 – 54 = 4≠0
∴ ρ(A) = 3.

(v) \(\left[\begin{array}{llll}
0 & 1 & 2 & 1 \\
0 & 2 & 4 & 3 \\
8 & 1 & 0 & 2
\end{array}\right]\)
A = \(\left[\begin{array}{llll}
0 & 1 & 2 & 1 \\
0 & 2 & 4 & 3 \\
8 & 1 & 0 & 2
\end{array}\right]\) என்க.
A ஒரு 3 × 4 வரிசை அணி
∴ ρ(A) ≤ (3, 4)- ன் மீச்சிறு = 3
A-ன்பூச்சியமற்ற சிற்றணிக்கோவைகளின்
உச்ச வரிசை 3
=-8 (6 – 4) = – 8(2) =-16≠0
∴ ρ(A) = 3

கேள்வி 2.
பின்வரும் அணிகளுக்கு ஏறுபடி வடிவத்தைப் பயன்படுத்தி அணித்தரம் காண்க :
(i) \(\left[\begin{array}{rrrr}
1 & 1 & 1 & 3 \\
2 & -1 & 3 & 4 \\
5 & -1 & 7 & 11
\end{array}\right]\)
(ii) \(\left[\begin{array}{rrr}
1 & 2 & -1 \\
3 & -1 & 2 \\
1 & -2 & 3 \\
1 & -1 & 1
\end{array}\right]\)
(iii) \(\left[\begin{array}{rrrr}
3 & -8 & 5 & 2 \\
2 & -5 & 1 & 4 \\
-1 & 2 & 3 & -2
\end{array}\right]\)
தீர்வு:
(i) \(\left[\begin{array}{rrrr}
1 & 1 & 1 & 3 \\
2 & -1 & 3 & 4 \\
5 & -1 & 7 & 11
\end{array}\right]\)
A = \(\left[\begin{array}{cccc}
1 & 1 & 1 & 3 \\
2 & -1 & 3 & 4 \\
5 & -1 & 7 & 11
\end{array}\right]\) என்க

கடைசி சமான அணியானது நிரை ஏறுபடி வடிவத்தில் அமைந்துள்ளது. இரண்டு அபூச்சிய நிரைகளை உடையது.
∴ ρ(A) = 2.

(ii) \(\left[\begin{array}{rrr}
1 & 2 & -1 \\
3 & -1 & 2 \\
1 & -2 & 3 \\
1 & -1 & 1
\end{array}\right]\)
A = \(\left[\begin{array}{ccc}
1 & 2 & -1 \\
3 & -1 & 2 \\
1 & -2 & 3 \\
1 & -1 & 1
\end{array}\right]\) என்க.


கடைசி சமான அணியானது நிரை ஏறுபடி வடிவத்தில் அமைந்துள்ளது. மூன்று அபூச்சிய நிரைகளை உடையது.
∴ ρ(A) = 3

(iii) \(\left[\begin{array}{rrrr}
3 & -8 & 5 & 2 \\
2 & -5 & 1 & 4 \\
-1 & 2 & 3 & -2
\end{array}\right]\)
Let A = \(\left[\begin{array}{rrrr}
3 & -8 & 5 & 2 \\
2 & -5 & 1 & 4 \\
-1 & 2 & 3 & -2
\end{array}\right]\)


கடைசி சமான அணியானது நிரை ஏறுபடி வடிவில் அமைந்துள்ளது. மூன்று அப்பூச்சிய நிரைகளை உடையது.
∴ ρ(A) = 3

கேள்வி 3.
பின்வரும் அணிகளுக்கு காஸ்-ஜோர்டன் நீக்கல் முறையைப் பயன்படுத்தி நேர்மாறு காண்க:
(i) \(\left[\begin{array}{cc}
2 & -1 \\
5 & -2
\end{array}\right]\)
(ii) \(\left[\begin{array}{rrr}
1 & -1 & 0 \\
1 & 0 & -1 \\
6 & -2 & -3
\end{array}\right]\)
(iii) \(\left[\begin{array}{lll}
1 & 2 & 3 \\
2 & 5 & 3 \\
1 & 0 & 8
\end{array}\right]\)
தீர்வு:
(i) \(\left[\begin{array}{ll}
2 & -1 \\
5 & -2
\end{array}\right]\)

காஸ்-ஜோர்டன் முறையை பயன்படுத்த கிடைப்பது

(ii) \(\left[\begin{array}{rrr}
1 & -1 & 0 \\
1 & 0 & -1 \\
6 & -2 & -3
\end{array}\right]\)
A = \(\left[\begin{array}{rrr}
1 & -1 & 0 \\
1 & 0 & -1 \\
6 & -2 & -3
\end{array}\right]\) என்க.
காஸ்-ஜோர்டன் முறையை பயன்படுத்த கிடைப்பது

(iii) \(\left[\begin{array}{lll}
1 & 2 & 3 \\
2 & 5 & 3 \\
1 & 0 & 8
\end{array}\right]\)
A = \(\left[\begin{array}{lll}
1 & 2 & 3 \\
2 & 5 & 3 \\
1 & 0 & 8
\end{array}\right]\) என்க
காஸ்-ஜோர்டன் முறையை பயன்படுத்த கிடைப்பது

Tamilnadu State Board New Syllabus Samacheer Kalvi 12th Maths Guide Pdf Chapter 7 வகை நுண்கணிதத்தின் பயன்பாடுகள் Ex 7.2 Textbook Questions and Answers, Notes.

TN Board 12th Maths Solutions Chapter 7 வகை நுண்கணிதத்தின் பயன்பாடுகள் Ex 7.2

கேள்வி 1.
கொடுக்கப்பட்ட புள்ளிகளில் பின் வரும் வலை வரைகளுக்கும் தொடு கோட்டின் சாட்யினைக் பாண்க.
(i) y = x⁴ + 2x² – x, x = 1
(ii) x = a cos³ t, y = sin³ t, t = \(\frac{\pi}{2}\)
தீர்வு:
(i) y = x⁴ + 2x² – x, x = 1
கொழிக்கப்பட்ட y = x⁴ + 2x² – x
\(\frac{d y}{d x}\) = 4x³ + 4x – 1
x = 1 ம் தோற்கோட்டின் சாய்வு
m = \(\left(\frac{d y}{d x}\right)_{(x=1)}\)
= 4(1)³ + 4(1) – 1
= 4 +4 – 1 = 7
∴ m = 7

(ii) x = a cos³ t, y = sin³ t, t = \(\frac{\pi}{2}\)
கொடுக்கப்பட்டா x = a cos³ t; y = sin³ t
\(\frac{d x}{d t}\) = -3a cos² t sin t;
\(\frac{d y}{d t}\) = -3b sin² t cos t;
∴ \(\frac{d y}{d x}\) = \(\frac{\frac{d y}{d t}}{\frac{d x}{d t}}=\frac{3 b \sin ^{2} t \cos t}{-3 a \cos ^{2} t \sin t}=\frac{-b}{a} \tan t\)
t = \(\frac{\pi}{2}\) என்பது தொடுகோட்டின் சாய்வு
m = \(\)
= \(\frac{-b}{a}\) tan \(\frac{\pi}{2}\) = \(\frac{-b}{a}\) × ∞ = ∞
∴ m = ∞

கேள்வி 2.
y = x² – 5x + 4 என்ற வளைவரைக்கு எப்புள்ளிகளில் வரையப்படும் தொடுகோடு 3x + y = 7 என்ற கோட்டிற்கு இணையாக இருக்கம்?
தீர்வு:
கொடுக்கப்பட்ட பாரடி y = x² – 5x + 4 மற்றும் கோடு 3x+y=7
வாையரைக்கான தொாபோட்டின் சாய்வு
m₁ = \(\frac{d y}{d x}\) = 2x – 5
கோட்டின் சாய்வு = m₂ = \(\frac{d y}{d x}\) = -3

வளைவளை மற்றும் தொடுகோட்டின் சாய்வு சமம்
∴ m₁ = m₂
⇒ 2x – 5 = -3
⇒ 2x = 2
⇒ x = 1
x = 1 இக சாய்து
y = x² – 5x + 4 இடைட்டது
y = 1² – 5(1) + 4 = 0
∴ தேவையான புரிகள் (1, 0)

கேள்வி 3.
y = x³ – 6x² + x + 3 போன்ற வளை வரைக்கு எப்புள்ளிகளில் வரையப்படும் தொடுகோடு x + y = 1729 என்ற கோட்டிற்கு செங்குத்தாக இருக்கும்?
நீர்வு:
கொடுக்கப்பட்ட எனைவரை x³ – 6x² + x + 3
மற்றும் மோர் x + y = 1729
சளைகாரங்க தொர்கோட்டின் சாப்பு
\(\frac{d y}{d x}\) = 3x² – 12x + 1
வளைவறையின் நேர்க்கோட்டின் சாய்வு
m₁ = \(\frac{-1}{3 x^{2}-12 x+1}\)
நேர்க்கோட்டின் சாய்வு
m₂ = \(\frac{-1}{1}\) = -1
வளைவரைக்கான செங்கோடு மற்றும் நோக்கோடுகள்
m₁ = m₂
\(\frac{-1}{3 x^{2}-12 x+1}\) = – 1
3x² – 12x + 1 = 1
3x² – 12x = 0
3x(x – 4) = 0
x = 0 x = 4
x= 0 எனில், y = 0³ – 6(0)² + 0 + 3
y = 3 [1) விருந்து]
x = 4 எனில், y = 4³ – 6(4)² + 4 + 3
= 64 – 96 + 7 = -25
∴ (0, 3) மற்றும் (4.–25) தேவையான புள்ளிகள்

கேள்வி 4.
y² – 4xy = x² + 5 என்ற வளைவரைக்கு எப்புள்ளிகளில் வரையப்படும் தொடுகோடு கிடைமட்டமாக இருக்கும்?
தீர்வு:
கோழிக்கப்பட்ட வளைவரையின் சமன்பாடு
y² – 4xy = x² + 5 ………… (1)
‘x’ ஆல் வகைப்படுத்த கிடைப்பது

வரைவரைக்கான தொடுகோடு கடைமட்டம் ஆதலால்
⇒ \(\frac{d y}{d x}\) = 0
∴ \(\frac{x+2 y}{y-2 x}\) = 0
⇒ x + 2y = 0
⇒ x = -2y ……….. (2)
(2) and (1)ல் பிரதிட்ட கடைப்பது
⇒ y² – 4(-2y)y = (-2y)² + 5
⇒ y² + 8y² = 4y² + 5
⇒ 9y² = 4y² + 5
⇒ 5y² = 5
⇒ y² = 1
⇒ y = ±1
(2) விருந்து,
y = 1 எனில், x = -2
y = -1 எனில், x = 2
∴ தேவையான புள்ளிகள் (2, -1) மற்றும் (-2, 1)

கேள்வி 5.
கீழ்க்கண்ட வளை வரைகளின் மீது’ கொடுக்கப்பட்ட புள்ளிகளில் தொடுகோடு மற்றும் செய்கோடுகளின் சமன்பாடுகளைக் காண்க.
(i) y = x² – x⁴; (1, 0)
(ii) y = x⁴ + 2e^x; (0, 2)
(iii) y = x sin x; (\(\frac{\pi}{2}\) , \(\frac{\pi}{2}\))
(iv) x = cost, y = 2sin² t; t = \(\frac{\pi}{3}\)
தீர்வு:
(i) y = x² – x⁴; (1, 0)

தொடுக்காட்டின் சமன்பார் y – y₁ = m(x – x₁)
⇒ y – 0 = -2(x – 1)
⇒ y = -2x + 2
⇒ 2x + y = 2
செங்கோட்டின் சமன்பாடு)- y – y₁ = \(\frac{-1}{m}\)(x – x₁)
⇒ y – 0 = \(\frac{1}{2}\)(x – 1)
⇒ 2y = x – 1
⇒ x – 2y = 1

(ii) y = x⁴ + 2e^x; (0, 2)

தொடுப்பாட்டின் சாட்வு y – y₁ = m(x – x₁)
⇒ y – 2 = 2 (x – 0)
⇒ y – 2 = 2x
⇒ 2x – y = -2
செங்கோட்டின் சாய்வு y – y₁ = \(\frac{-1}{m}\)(x – x₁)
⇒ y – 2 = \(\frac{1}{2}\)(x – 0)
⇒ 2y – 4 = -x
⇒ x + 2y = 4

(iii) y = x sin x; (\(\frac{\pi}{2}\) , \(\frac{\pi}{2}\))
கோர்க்கப்பட்ட அனைவரையின் சமன்பாடு y = x sin x

(iv) x = cost, y = 2sin² t; t = \(\frac{\pi}{3}\)
கொடுக்கப்பட்ட போயாவரையின் சமன்பாடு
x = cos t; y = 3 sin² t

கேள்வி 6.
y = 1 + x³ என்ற வளைவரைக்கும் x + 12y = 12 என்ற கோட்டிக்கு செங்குத்தாக உள்ள தொடு கோடுகளின் சமன்பாடுகளைக் காண்க, .
தீர்வு:
வெறுக்கப்பட்ட வரைமின் சமன்பாடு
y = 1 + x³ மர்மம் கோர்ட் x + 12y = 12
வளைவரைபின் தொடுகோடின் சாய்வு
m₁ = \(\frac{d y}{d x}\) = 3x² மற்றும்
கோட்டின் சாய்வு = m₂

வளைவரைக்கான தொடுகோடு மற்றும் நேர்க்கோடு சொய்கத்து ஆதமாம் m₁ m₂ = -1
∴ 3x² (\(\frac{-1}{12}\)) = -1
⇒ \(\frac{x^{2}}{4}\) = 1
⇒ x² = 4
⇒ x = ±2
x = 2 எனில், y = 1 + 2³ = 9
x = -2 எனில், y = 1 + (-2)³
= 1 – 8 = -7
∴ (2, 9) ல் தொடுகோட்டின் சமன்பாடு
y – 9 = 12 (x – 2) [∵ m₁ = 3x² = 3(2)² = 12]
⇒ y – 9 = 12x – 24
⇒ 12x – y = 15
(-2, -7) -ல் தொடுகோட்டின் சமன்பார்
y + 7 = 12(x + 2)
⇒ y + 7 = 12x + 24
⇒ 12x – y = -17

கேள்வி 7.
y = \(\frac{x+1}{x-1}\) என்ற வளைவரைக்கு x + 2y = 6 என்ற கோட்டிக்கு இணையாக உள்ள தொடு கோடுகளின் சமன்பாடுகளைக் காண்க .
தீர்வு:
கொடுக்கப்பட்ட மாளவரைபின் சமன்பார்.
y = \(\frac{x+1}{x-1}\) மற்றும் கோடு x + 2y = 5 .
வளைவரைக்கான தொர்கோட்டின் சாப்பு

வளைவரைக்கான தொடுகோடு மற்றும் கோடுகள்
m₁ = m₂
⇒ \(\frac{-2}{(x-1)^{2}}\) = \(\frac{-1}{2}\)
⇒ 4 = (x + 1)²
⇒ x – 1 = ±2
⇒ x – 1 = 2 அல்லது x – 1 = -2
⇒ x = 3 அல்லது x = – 1
⇒ x = -1 எனில், y = \(\frac{3+1}{3-1}=\frac{4}{2}\) = 2
⇒ x = – 1 (அல்லது)
y = \(\frac{-1+1}{-1-1}=\frac{0}{-2}\) = 0
∴ (3, 2)-ல் தொடுகோட்டின் சமன்பாடு
y – y₁ = m(x – x₁)
⇒ y – 2 = \(\frac{-1}{2}\)(x – 3)
⇒ 2y – 4 = -x + 3
⇒ x + 2y = 7
(-1,0 ) தொடுக்காட்டின் சமன்பாற்
y – 0 = \(\frac{-1}{2}\)(x + 1)
⇒ 2y = -x – 1
x + 2y = -1

கேள்வி 8.
x = 7 cos t மற்றும் y = 2 sin t, t ∈ ℝ என்ற வளைவரைக்கு ஏதேகம் – புள்ளியில் வரையப்படும் தொடுபோடு மற்றும் செங்கோட்டின் சமன்பாடுகளைக் காண்க. தீர்வு:
கோர்க்கப்பட்ட வளைவரையின் சமன்பாடு

∴ வாைகரையில் எந்த பள்ளிக்கான தொட்கோட்டின்
சமன்பாடு y – 2 sin t = \(\bar{A}\) (x – 7 cos t)
⇒ (-7 sin t) y + 14 sin² t = (2 cos t)x – 14 cos² t
⇒ (2 cos t)x + (7 sin t)y
= 14(sin² t + cos² t)
= 14(1) = 14
⇒ (2 cos t)x + (7 sin t)y = 14
வளைவறையின் ஒத புsirefiதமான செங்கத்தின் சமன்பாடு y – 2 sin t = \(\frac{7 \sin t}{2 \cos t}\) (x – 7 cos t)
⇒ (2 cos t)y – 4 sin t cos t = (7 sin t)x – 49 sin t cos t
⇒ (7 sin t)x – (2 cos t)y = 49 sin t cos t – 4 sin t cos t
⇒ (7 sin t)x – (2 cos t)y = 45 sin t cos t

கேள்வி 9.
xy = 2 என்ற செவ்வக அதிபரவளையத்திற்கும் x² + 4y = 0 என்ற பரவளையத்திற்கும் இடைப்பட்ட கோணத்தினைக் காண்க.
தீர்வு:
செவ்வக அதிபரவளையத்தின் சமன்பாடு xy = 2
⇒ y = \(\frac{2}{x}\)
⇒ x . \(\frac{d y}{d x}\) + y (1) = 0
⇒ \(\frac{d y}{d x}\) = \(\frac{-y}{x}\)
வளைவரைக்கான தொடுகோட்டின் சாய்வு m₁ = \(\frac{-y}{x}\)
பரவளையத்தின் சமன்பாடு x² + 4y = 0 …… (1)
⇒ 2x + 4 \(\frac{d y}{d x}\) = 0
\(\frac{d y}{d x}\) = \(\frac{-2 x}{4}=\frac{-x}{2}\)
வளைவரைக்கான தொடுகோட்டின் சாய்வு m₂ = \(\frac{-x}{2}\)
(1) ஐ (2) ல் பிரதியிட கிடைப்பது,
x² + 4 (\(\frac{2}{x}\)) = 0 ⇒ x² + \(\frac{8}{x}\) = 0
⇒ x³ + 8 = 0
⇒ x = -8= (-2) ⇒ x = -2
⇒ x = -2, y = –\(\frac{-2}{2}\) = -1
செவ்வக அதிபரவளையத்திற்கும் மற்றும் பரவளையத்திற்கான வெட்டும் புள்ளி (-2, -1)
∴ m₁ = \(\frac{-y}{x}=\frac{-(-1)}{-2}=\frac{-1}{2}\)
m₂ = \(\frac{-x}{2}=\frac{-(-2)}{2}=1\)
அதிபரவளையம் மற்றும் செவ்வக அதிபரவளைத்திற்கான கோணம் θ என்க.

கேள்வி 10.
x² – y² = r² மற்றும் xy = c² என்ற வளைவரைகள் செங்குத்தாக வெட்டிக் கொள்ளும் எனக்காட்டுக. இங்கு c, r ஆகியவை மாறிலிகள்.
தீர்வு:
கொடுக்கப்பட்ட வளைவரையின் சமன்பாடுகள் x² – y² = r² மற்றும் xy = c²
x² – y² = r²
⇒ 2x – 2y \(\frac{d y}{d x}\) = 0 .
⇒ 2x = 2y\(\frac{d y}{d x}\),
⇒ \(\frac{d y}{d x}\) = \(\frac{2 x}{2 y}=\frac{x}{y}\)
வளைவரைகளின் வெட்டும் புள்ளி (x₁, y₂,) என்க.
∴ முதல் வளைவரைக்கான தொடுகோட்டின்
சாய்வு m₁ = \(\frac{x_{1}}{y_{1}}\) ……….. (1)
⇒ xy = c²
⇒ x . \(\frac{d y}{d x}\) + y (1) = 0
⇒ x \(\frac{d y}{d x}\) = – y
⇒ \(\frac{d y}{d x}\) = \(\frac{-y}{x}\)
∴ முதல் வளைவரைக்கான தொடுகோட்டின்
சாய்வு m₂ = \(\frac{-y_{1}}{x_{1}}\) ……….. (1)
கருது m₁m₂ = \(\left(\frac{x_{1}}{y_{1}}\right)\left(\frac{-y_{1}}{x_{1}}\right)\) = -1
ஆதலால் கொடுக்கப்பட்ட m₁m₂ = -1 வளை வரைகள் செங்குத்தாக வெட்டிக் கொள்ளும்.

Tamilnadu State Board New Syllabus Samacheer Kalvi 12th Maths Guide Pdf Chapter 1 அணிகள் மற்றும் அணிக்கோவைகளின் பயன்பாடுகள் Ex 1.1 Textbook Questions and Answers, Notes.

TN Board 12th Maths Solutions Chapter 1 அணிகள் மற்றும் அணிக்கோவைகளின் பயன்பாடுகள் Ex 1.1

கேள்வி 1.
பின்வரும் அணிகளுக்குச் சேர்ப்பு அணி காண்க:
(i) \(\left[\begin{array}{cc}
-3 & 4 \\
6 & 2
\end{array}\right]\)
(ii) \(\left[\begin{array}{lll}
2 & 3 & 1 \\
3 & 4 & 1 \\
3 & 7 & 2
\end{array}\right]\)
(iii) \(\frac{1}{3}\left[\begin{array}{ccc}
2 & 2 & 1 \\
-2 & 1 & 2 \\
1 & -2 & 2
\end{array}\right]\)
தீர்வு:
(i) \(\left[\begin{array}{cc}
-3 & 4 \\
6 & 2
\end{array}\right]\)

[தன்மை மூலைவிட்ட உறுப்புகளை இடமாற்ற மற்றும் மூலைவிட்டமல்லாத உறுப்புகளின் குறியை மாற்றுக]

(ii) \(\left[\begin{array}{lll}
2 & 3 & 1 \\
3 & 4 & 1 \\
3 & 7 & 2
\end{array}\right]\)

(iii) \(\frac{1}{3}\left[\begin{array}{ccc}
2 & 2 & 1 \\
-2 & 1 & 2 \\
1 & -2 & 2
\end{array}\right]\)

∴ தேவையான அணியின் சேர்ப்பு

= \(\frac{3}{9}\left[\begin{array}{rrr}
2 & -2 & 1 \\
2 & 1 & -2 \\
1 & 2 & 2
\end{array}\right]\)
[ஒவ்வொரு வரிசையிலும் 3 ஐ பொதுவில் எடுக்க]
= \(\frac{1}{3}\left[\begin{array}{rrr}
2 & -2 & 1 \\
2 & 1 & -2 \\
1 & 2 & 2
\end{array}\right]\)

கேள்வி 2.
பின்வரும் அணிகளுக்கு நேர்மாறு (காண முடியுமெனில்) நேர்மாறு காண்க:
(i) \(\left[\begin{array}{rr}
-2 & 4 \\
1 & -3
\end{array}\right]\)
(ii) \(\left[\begin{array}{lll}
5 & 1 & 1 \\
1 & 5 & 1 \\
1 & 1 & 5
\end{array}\right]\)
(iii) \(\left[\begin{array}{lll}
2 & 3 & 1 \\
3 & 4 & 1 \\
3 & 7 & 2
\end{array}\right]\)
தீர்வு:
(i) \(\left[\begin{array}{rr}
-2 & 4 \\
1 & -3
\end{array}\right]\)
A= \(\left[\begin{array}{cc}
-2 & 4 \\
1 & -3
\end{array}\right]\)என்க
|A| = \(\left|\begin{array}{cc}
-2 & 4 \\
1 & -3
\end{array}\right|\) = 6 – 4 = 2 ≠ 0
A பூச்சியமற்றக் கோவை அணி ஆதலால் A^-1 காணலாம்.
A^-11 = \(\frac{1}{|\mathrm{~A}|}\)adj A
இங்கு adj A = \(\left[\begin{array}{rr}
-3 & -4 \\
-1 & -2
\end{array}\right]\)
[முதன்மை மூலைவிட்ட உறுப்புகளை இடமாற்றம் மற்றும் மூலைவிட்டத்தில் இல்லாத உறுப்புகளின் குறியை மாற்றுக)]
∴ A^-1 = \(\frac{1}{2}\left[\begin{array}{ll}
-3 & -4 \\
-1 & -2
\end{array}\right]\)

(ii) \(\left[\begin{array}{lll}
5 & 1 & 1 \\
1 & 5 & 1 \\
1 & 1 & 5
\end{array}\right]\)
A = \(\left[\begin{array}{lll}
5 & 1 & 1 \\
1 & 5 & 1 \\
1 & 1 & 5
\end{array}\right]\) என்க
R₁ மூலம் விரிவுபடுத்த,
|A| = 5\(\left|\begin{array}{ll}
5 & 1 \\
1 & 5
\end{array}\right|\) -1\(\left|\begin{array}{ll}
1 & 1 \\
1 & 5
\end{array}\right|\) + 1\(\left|\begin{array}{ll}
1 & 5 \\
1 & 1
\end{array}\right|\)
= 5(25 – 1) -1 (5- 1) + 1 (1- 5)
= 5(24) – 1 (4) + 1 (-4)
= 120-4-4 = 120- 8 = 112 ≠ 0
A ஒரு பூச்சியமற்றக் கோவை எனில் Aசாத்தியம்.

ஒவ்வொரு உறுப்பிலிருந்தும் 4 ஐ பொதுவில் எடுக்க,

(iii) \(\left[\begin{array}{lll}
2 & 3 & 1 \\
3 & 4 & 1 \\
3 & 7 & 2
\end{array}\right]\)
A = \(\left[\begin{array}{lll}
2 & 3 & 1 \\
3 & 4 & 1 \\
3 & 7 & 2
\end{array}\right]\) என்க.
R₁ மூலம் விரிவுபடுத்த கிடைப்பது,
|A| = 2\(\left|\begin{array}{ll}
4 & 1 \\
7 & 2
\end{array}\right|\) – 3\(\left|\begin{array}{ll}
3 & 1 \\
3 & 2
\end{array}\right|\) + 1\(\left|\begin{array}{ll}
3 & 4 \\
3 & 7
\end{array}\right|\)
= 2 (8-7) – 3 (6-3) +1 (21 – 12)
= 2 (1) – 3(3) + 1 (9)
= 2 – 9 + 9 = 2 ≠ 0
A ஒரு பூச்சியமற்றக் கோவை அணி ஆதலால்
A^-1 சாத்தியம்

கேள்வி 3.

தீர்வு:

F(α) ஒரு பூச்சியமற்றக் கோவை அணி ஆதலால்,

கேள்வி 4.
A = \(\left[\begin{array}{rr}
5 & 3 \\
-1 & -2
\end{array}\right]\) எனில், A² – 3A – 7I₂ = O₂, எனக்காட்டுக. இதன் மூலம் A^-1 காண்க.
தீர்வு:
கொடுக்கப்பட்ட A = \(\left[\begin{array}{rr}
5 & 3 \\
-1 & -2
\end{array}\right]\)

எனவே நிரூபிக்கப்பட்டது.
∴ A² – 3A – 7I₂ = 0
பின்புறமாக A^-1 ஆல் பெருக்க கிடைப்பது,
A². A^-1-3AA^-1 7I₂A^-1 = 0.A^-1
⇒ A(AA^-1) – 3 (AA^-1)-7(A^-1) = 0
[∵ I₂, A^-1 = A^-1 மற்றும் |(0)A^-1=0]
⇒ AI-3I – 7A^-1= 0 [∵AA^-1 = I]
⇒ AI – 3I = 7A^-1 [∵AI = A]

கேள்வி 5.
A=\(\frac{1}{9}\left[\begin{array}{rrr}
-8 & 1 & 4 \\
4 & 4 & 7 \\
1 & -8 & 4
\end{array}\right]\) எனில், A^-1=A^T நிறுவுக.
தீர்வு:
கொடுக்கப்பட்ட A =
\(\frac{1}{9}\left[\begin{array}{rrr}
-8 & 1 & 4 \\
4 & 4 & 7 \\
1 & -8 & 4
\end{array}\right]\)



(2) பிரதியிட கிடைப்பது,

(1) மற்றும் (3) லிருந்து கிடைப்பது, A^T = A^-1

கேள்வி 6.
A = \(\left[\begin{array}{rr}
8 & -4 \\
-5 & 3
\end{array}\right]\). எனில் A(adj A) = (adj A) A=|A| I₂ என்பதைச் சரிபார்க்க.
தீர்வு:
கொடுக்கப்பட்ட A = \(\left[\begin{array}{cc}
8 & -4 \\
-5 & 3
\end{array}\right]\)
adj A = \(\left[\begin{array}{ll}
3 & 4 \\
5 & 8
\end{array}\right]\)
[முதன்மை மூலைவிட்ட உறுப்புகளை இடமாற்ற மற்றும் மூலைவிட்டத்தில் இல்லாத உறுப்புகளின் குறியை மாற்ற]
|A| = 24 – 20 = 4

(1), (2) மற்றும் (3) லிருந்து,
A (adj A) = (adj A) A = |A|I₂
எனவே நிரூபிக்கப்பட்டது.

கேள்வி 7.
A = \(\left[\begin{array}{ll}
3 & 2 \\
7 & 5
\end{array}\right]\) மற்றும் B= \(\left[\begin{array}{rr}
-1 & -3 \\
5 & 2
\end{array}\right]\) என (AB)^-1 = B^-1A^-1 என்பதைச் சரிபார்க்க.
தீர்வு:

|AB| = -77+90=13+0 ⇒ (AB)^-1 காணலாம்.
|A| = 15 – 14 = 1≠0 ⇒ A^-1 காணலாம்
|B| = -2 + 15 = 13+0 ⇒ B^-1 காணலாம்

(1) மற்றும் (2) லிருந்து
(AB)^-1 = B^-1A^-1. எனவே நிரூபிக்கப்பட்டது.

கேள்வி 8.
adj (A) = \(\left[\begin{array}{rrr}
2 & -4 & 2 \\
-3 & 12 & -7 \\
-2 & 0 & 2
\end{array}\right]\), எனில் A – ஐ காண்க .
தீர்வு:

= 2 (24-0) + 4 (-6- 14) + 2 (0 + 24)
= 2 (24) + 4 (- 20 ) + 2 (24) = 48 – 80 + 48 )
= 96 – 80 = 16 …. (2)
இங்கு , adj (adj A)


(2) மற்றும் (3) ஐ (1)ல் பிரதியிட கிடைப்பது,

கேள்வி 9.
adj (A) = \(\left[\begin{array}{rrr}
0 & -2 & 0 \\
6 & 2 & -6 \\
-3 & 0 & 6
\end{array}\right]\) எனில் A^-1 -ஐ காண்க.
தீர்வு:

கேள்வி 10.

தீர்வு:

கேள்வி 11.

தீர்வு:

[முதன்மை மூலைவிட்ட உறுப்புகளை இடமாற்ற மற்றும் மூலைவிட்டத்தில் இல்லாத உறுப்புகளின் குறியை மாற்ற]

கேள்வி 12.
A = \(\left[\begin{array}{rr}
5 & 3 \\
-1 & -2
\end{array}\right]\) = \(\left[\begin{array}{rr}
14 & 7 \\
7 & 7
\end{array}\right]\)
தீர்வு:

கேள்வி 13.
AXB = C எனில், X என்ற அணியைக் காண்க.
தீர்வு:
கொடுக்கப்பட்ட A = \(\left[\begin{array}{rr}
1 & -1 \\
2 & 0
\end{array}\right]\), B = \(\left[\begin{array}{rr}
3 & -2 \\
1 & 1
\end{array}\right]\), C = \(\left[\begin{array}{ll}
1 & 1 \\
2 & 2
\end{array}\right]\), மேலும், AXB = C
A^-1 ஆல் முன்புறம் பெருக்க கிடைப்பது,
(A^-1A) X B = A^-1C
⇒ XB = A^-1C. [∵ A^-1A = I]
B^-1 ஆல் பின்புறம் பெருக்க கிடைப்பது
(XB) B^-1 = (A^-1C) B^-1
⇒ X = (A^-1C) B^-1

கேள்வி 14.
A=\(\left[\begin{array}{lll}
0 & 1 & 1 \\
1 & 0 & 1 \\
1 & 1 & 0
\end{array}\right]\) எனில் A^-1= \(\frac{1}{2}\left(A^{2}-3 I\right)\) எனக்காட்டுக.
தீர்வு:
கொடுக்கப்பட்ட A = \(\left[\begin{array}{lll}
0 & 1 & 1 \\
1 & 0 & 1 \\
1 & 1 & 0
\end{array}\right]\)


(1) மற்றும் (2)லிருந்து, A^-1= \(\frac{1}{2}\left[\mathrm{~A}^{2}-3 \mathrm{I}\right]\) எனவே நிரூபிக்கப்பட்டது.

கேள்வி 15.
\(\left[\begin{array}{rr}
-1 & -1 \\
2 & 1
\end{array}\right]\) என்ற அணியை பிந்தையப் பெருக்கல் சங்கேத மொழியாக்க அணியாகக் கொண்டு [2 -3] [20 4] என்ற பெறப்பட்ட \(\left[\begin{array}{rr}
-1 & -1 \\
2 & 1
\end{array}\right]\)-ன நோமாறு அணியின் பிந்தையப் பெருக்கற் சாவியாகக் கொண்டு சங்கேத மொழி மாற்றம் செய்க. இங்கு ஆங்கில எழுத்துகள் A – Z -க்கு முறையே எண்க ள் 1 – 26 ஐயும், காலியிடத்திற்கு எண் 0 ஐயும் பொருத்தி சங்கேத மொழியாக்கம் மற்றும் மொழிமாற்றம் செய்க.
தீர்வு:
சங்கேத மொழியாக்குதலுக்கான A=\(\left[\begin{array}{rr}
-1 & -1 \\
2 & 1
\end{array}\right]\) என்க.

ஆகையால் பெருக்கற் சாவி அணி \(\left[\begin{array}{rr}
1 & 1 \\
-2 & -1
\end{array}\right]\)

சங்கேத மொழி மாற்றம் செய்யப்பட்ட நிரை அணிகளின் வரிசை பின்வருமாறு
[8 5], [12 16]

Tamilnadu State Board New Syllabus Samacheer Kalvi 12th Maths Guide Pdf Chapter 7 வகை நுண்கணிதத்தின் பயன்பாடுகள் Ex 7.1 Textbook Questions and Answers, Notes.

TN Board 12th Maths Solutions Chapter 7 வகை நுண்கணிதத்தின் பயன்பாடுகள் Ex 7.1

கேள்வி 1.
ஆதிப்புள்ளியிலிருந்து t வினாடிகளுக்குப் பிறகு ஒரு துகள் உள்ள தூரத்தின் அளவு s = 2t² + 3t மீட்டர் எனும்படி நேர்க்கோட்டில் ஒரு துகள் நகர்கிறது.
(i) t = 3 மற்றும் t = 6 வினாடிகளுக்கிடையே டள்ள சராசரி திசைவேகம் என்ன?
(ii) t = 3 மற்றும் t = 6 வினாபாத்திடையே உள்ள கணப்பொழுது திசைவேகம் என்ன?
தீர்வு:
(i) கொடுக்கப்பட்ட s = 2t² + 3t
s(3) = 2 × 3² + 3(3)
= 2 × 9 + 9
= 27 மீ …(1)
s(6) = 2 × 6² + 3(6)
= 72 + 18 = 90மி …(2)
சராசரி திசைபோம் = \(\frac{s(6)-s(3)}{6-3}=\frac{90-27}{3}\)
= \(\frac{63}{3}\) = 21 மீ/வினாடி

(ii) கணப்பொழுது திசைவேகம்
V(t) = \(\frac{d s}{d t}\) = 4t + 3
t = 3 இல் கணப்பொழுது திசைமேகம்
= V(3) = 15 மீ/வினாடி [ (1) இலிருந்து]
t = 6 இம் காப்பொழுது திாைபேகம்
= V(6) = 27 மீ/வினாடி [ (2) இலிருந்து]

கேள்வி 2.
400 அடி உயர மலை உச்சி முகட்டிலிருந்து தவாதயாக ஒரு புகைப்படக் கருவி வீழுகியது. t வினாடிகளில் புகைப்படக் கருவி விடும் தூரம் s = 16t² ஆகும்,
(i) தரையைத் தொடும் முன்னர் புகைப்படக் கருவி விடி எடுத்துக்கொண்ட நேரம் என்ன?
(ii) இடி விழுந்த இறுதி 2 வினாடிகளில் புகைப்படக் கருவியின் சரபரி திசைவேகம் என்ன?
(iii) தரையைத் தொடும் போது புகைப்படக் கருவியின் கணப்பொழுது திசைவேகம் என்ன ?
தீர்வு :
(i) கொர்க்கப்பட்ட s(t) = 16t²
உயரம் – 400 அடி
16t² = 400
⇒ t² = \(\frac{400}{16}=\frac{100}{4}\)
t² = 25
t = 5 வினாடி

(ii) சராளி நிலாபேகம் = \(\frac{d s}{d t}\) = 32t
இறுதி t = 2 வினாடிகளில்

(iii) கணப்பொழுது திசைவேகம்
= \(\frac{d s}{d t}=\) = 32t
இக்கா t = 5 வினாடி
திலைபேகம் = \(\frac{d s}{d t}=\) = 32(5)
= 160 அடிவினாடி

கேள்வி 3.
s(t) = 2t³ – 9t² + 12t – 4, இங்கு t > equal 0 எனும் விதிப்படி ஒரு கோட்டில் ஒரு துகள் நகர்கிறது.
(i) எந்நேரங்களில் துகளின் திசைமாறுகின்றது?
(ii) முதல் 4 வினாடிகளில் துகள் பயணித்த தூரம் என்ன?
(iii) திசைவேகம் பூச்சிய மதிப்பை அடையும் தேரங்காய் பால்காம் துகளின் முடுக்கம் கான்க?
தீர்வு :
கொடுக்கப்பட்ட s(t) = 2t³ – 9t² + 12t – 4, t > equal 0.
(i) வகைப்படுத்த கூடப்பது,
V(t) = 6t² – 18t + 12 …(1)
= 6(t²– 3t + 2)
= 6(t – 1)(t – 2)
இங்கு V(t) = 0
⇒ 6(t – 1)(t – 2) = 0
⇒ t = 1, 2
V(t) யின் தறி மாறும் பொழுது துகளின் திசை மாறுகின்றது.
0 ≤ t < 1 எனில், (t – 1) மற்றும் (t – 2) இரண்டும் < 0 ⇒ V(t) > 0
1 < t < 2 னில், (t – 1) > 0 மற்றும் (t – 2) < 0
⇒ V(t) < 0 t > 2 யில், both (t – 1) மாறும் (t – 2) அன்ற ம் > 0
⇒V(t) > 0
∴ t = 1 மற்றும் t = 2 வினாடியாரில் பயான் திசை மாறன்ற து.

(ii) முகம் 4 கோடிகளில் சகன் யணித்த பம்
|s(0) – s(1)| + |s(1) – s(2)| + |s(2) – s(4)|
s(0) = -4
s(1) = 2(1)³ – 9(1)² + 12(1) – 4
= 2 – 9 + 12 – 4 = 1
s(2) = 2 x 2³ – 9 x 2² + 12 x 2 – 4
= 16 – 36 + 24 – 4 = 0
s(4) = 2(4)³ – 9(4)² + 12(4) – 4
= 128 – 144 + 48 – 4 = 28
∴ |s(0) – s(1)| + |s(1) – s(2)| + |s(2) – s(4)|
= |-4 – 1| + |1 – 0| + |0 – 28|
= |-5| + |1| + |0 – 28|
= 5 + 1 + 28 = 34 மீ

(iii) முடுக்கம் A = 12t – 18 [வடுக்கம் = \(\frac{d v}{d t}\)]
t = 1 எனில்,
மாதகம் = 12 (1) – 18 = -6 மீ/வினாடி²
t = 2 எனில்,
முடுக்கம் – 12 (2) – 18 = 6 மீ/வினாடி²

கேள்வி 4.
x பக்க அளவு கொண்ட ஒரு கன சதுரத்தின் கன அளவு v = x³ பாலில் x = 5 கலகள் எனம் போது x -அப் பொறுத்து கன அளவு மாறுவிதம்
தீர்வு :
கொடுக்கப்பட v = x³
x பொறுத்து வகைப்படுத்த கிடைப்பது,
\(\frac{d v}{d x}\) = 3x²

கேள்வி 5.
x நீளமுள்ள (மீட்டரில்) ஒரு மெல்லிய கோலின் நிறை m(x) ( கிலோகிராமில்), m(x) = \(\) பானக் கொடுக்கப்பட்டுள்ளது ானில், x = 3 மற்றும் x = 27 மீட்டர் எனும் போது நீளத்தைப் பொறுத்து நிறையின் மாறுபாட்டு வீதத்தை காண்க.
தீர்வு :
கொடுக்கப்பட்ட m(x) = \(\sqrt{3 x}\)=\(\sqrt{3}\) . x^{\({\frac{1}{2}}\)}
x பொறுத்து வகைப்படுத்த கிடைப்பது,

கேள்வி 6.
ஒரு குளத்தில் விழுந்த கல்லினால் பொது மைய வட்டங்களின் வடிவத்தில் சிலைகள் ஏற்படுகின்றது. வெளிப்பு சிந்தமையின் ஆரம் r வினாடிக்கு 2 செ மீவீதம் அதிகரிக்கிறது. ஆரம்
5 செ.மீ. பனும் போது கலங்கும் நீரின் பரப்பாவு மாறுவீதம் என்ன?
தீர்வு:
சிற்றலையின் ஆரம் r மற்றும் பரப்பு A கொ.
டுக்கப்பட்ட \(\frac{d r}{d t}\) = 2 செ.மீ/ வினாடி மற்றும்
r = 5 2 செ.மீ …(1)
A = πr² என்பது

கேள்வி 7.
கடற்கரையிலிருந்து 5 கி.மீ தூரத்தில் கப்பல் நங்கூரமிடப்பட்டுள்ளது. கலங்கரை விளக்கத்தின் ஒரு விளக்கு ஒவ்வொரு 10 வினாடிகளுக்கு ஒரு முறை சுற்றுகிறது. கலங்கரை விளக்கத்தின் ஒளிக்கற்றை கடற்கரையுடன் 45° கோணத்தை ஏற்படுத்தும் போது கடற்கரையில் ஒளிக்கற்றை எவ்வளவு வேகமாக நகரும்?
தீர்வு:
கலங்கரை விளக்கத்தின் ஒருவாக்கும்பொரு 10 வினாடிக்கு (360°) இம் சுற்றுவதால்

கேள்வி 8.
தலை கீழாக வைக்கப்பட்ட ஒரு நேர்வட்ட கூம்பின் வடிவில் உள்ள ஒரு நீர்நிலைத் தொட்டியின் ஆழம் 12 மீட்டர் மற்றும் மேலுள்ள வட்டத்தின் பாரம் 5 மீட்ட ளன்க, நிமிடத்திற்கு 10 கன மீட்டர் வேகத்தில் நீர் பாய்ச்சப்படுகிறது எனில், 8 மீட்டர் ஆழத்தில் நீர் இருக்கும் போது நீரின் ஆழம் அதிகரிக்கும் வேகம் என்ன?
தீர்வு:
கொடுக்கப்பட்ட h = 12 மீ
r = 5 மீ

V என்பது கூம்பின் கன அளவு
பாத் உச்சிக் கோணம் α

கேள்வி 9.
17 மீட்டர் நீளமுள்ள ஒரு ஏணி செங்குத்தான சுவரில் சாய்த்து வைக்கப்பட்டுள்ளது. ரணியின் அடிப்பக்கம் சுவற்றிலிருந்து விலகிச் செல்லும் விதம் வினாடிக்கு 5 மீட்டர் எனில் ரணியின் அடிப்பக்கம் சுவற்றிலிருந்து 8 மீட்டர் தொலைவில் இருக்கும் போது,
(i) அதன் உச்சி என்ன வீதத்தில் கீழ்நோக்கி இயங்கும் என்பதைக் காண்க.
(ii) எந்த விதத்தில், ஏணி, சுவர் மற்றும் தரை ஆகியவத்மால் உருவாகும் முக்கோணத்தின் பரப்பளவு மாறுகிறது?
தீர்வு:
(i) OA = x பாம் OB = y வருமாறு காமம் t மில் ஏணி ABமின் நிமையாகும்.

எனவே OA² + OB² = AB²
⇒ x² + y² =17² …(1)
கொடுக்கப்பட்ட \(\) = 5 மற்றும் x = 8
x = 8 எனில், 8² + y² = 17²
⇒ y² = 289 – 64 = 225
⇒ = 15
‘t’ யை பொறுத்து (1) யை பாகப்படுத்தக்கூடப்பது,

∴ வணியின் உச்சி கீழ் நோக்கி இறங்கும் விதம் \(\frac{-8}{3}\)மீ/வினாடி.

(ii) ஏணி, கார் மற்றும் தரை ஆகியவற்றால் உருவாகும் வாங்கோண முக்கோணம்
∴ ப்படிப்பு = \(\frac{1}{2}\)xy
‘t’ யை பொறுத்து வகையீட கிடைப்பது.

கேள்வி 10.
வடதிசையிலிருந்து ஒரு செங்கோண சந்திப்பை அரும் ஒரு காவல்துறை வாகனம் வேகமாகச் சென்று திரும்பி கிழக்கு நோக்கிச் செல்லும் ஒரு மகிழுத்தை காத்துகிறது. சாலை சந்திப்பின் வடக்கே 0.6 கி.மீ நொணயலில் காவல்துறையின் வாகனமும் கிழக்கே 0.8 கி.மீ தொலைவில் மகிழுந்தும் உள்ள பொழுது, மின்காந்த அலைக் காலியின் துணைகொண்டு பாவங்கனை தங்களது வாகனத்திற்கும் மகிழுத்துக்கும் இடைப்பட்ட தூரம் மணிக்கு 20 கி.மீ வீதத்தில் அதிகரிக்கிறது எனத் தீர்மானிக்கின்றனர். காவல்துறை வாகனம் மணிக்கு 60 கி.மீ வேகத்தில் நகர்கிறது எனில் மகிழுத்தின் வேகம் என்ன?
தீர்வு:

x குறிப்பது மகிழ்ந்து கடந்த தூரம் y குறிப்பது காவல்துறை கடாக வாகனம் மற்றும் s குறிப்பது பாகனம் மற்றும் மகிழுந்து இடையேயான தூரம் அரும்.
∴ கொடுக்கப்பட்ட = x = 0.8 கி.மீ, y = 0.6 கி.மீ,

Tamilnadu State Board New Syllabus Samacheer Kalvi 12th Maths Guide Pdf Chapter 12 தனிநிலைக் கணிதம் Ex 12.3 Textbook Questions and Answers, Notes.

TN Board 12th Maths Solutions Chapter 12 தனிநிலைக் கணிதம் Ex 12.3

சரியான அல்லது மிகவும் ஏற்புடைய விடையினை | கொடுக்கப்பட்ட நான்கு மாற்று விடைகளிலிருந்து தேர்ந்தெடுக்கவும் :

கேள்வி 1.
ஓர் ஈருறுப்புச் செயலி S என்ற ஒரு கணத்தின் மீது ஒரு சார்பாக பின்வருவனவற்றிலிருந்து பெறப்படுகிறது
(1) S → S
(2) (S × S) → S
(3) S →(S × S)
(4) (S× S) → (S × S)
விடை:
(2) (S × S) → S

கேள்வி 2.
கழித்தலின் கீழ் பின்வரும் கணம் அடைவு பெறவில்லை .
(1) ℝ
(2) ℤ
(3) ℕ
(4) ℚ
விடை:
(3) ℕ

கேள்வி 3.
பின்வருபவைகளில் எது ℕ-ன் மீது ஓர் ஈருறுப்புச் செயலி ஆகும்.
(1) கழித்த ல்
(2) பெருக்கல்
(3) வகுத்தல்
(4) அனைத்தும்
விடை:
(2) பெருக்கல்

கேள்வி 4.
மெய் எண்க ளின் கணம் ℝ – ன் மீது ‘*’ பின்வருமாறு வரையறுக்கப்படுகிறது. இதில் எது ℝ-ன் மீது ஈருறுப்புச் செயலி அல்ல?
(1) a * b = min (a.b)
(2) a * b = max (a, b)
(3) a * b = a
4) a * b = a^b
விடை:
(4) a * b = a^b
குறிப்பு : a = 0, b = 0 என்க, = 0⁰ ∉ R. (4) a * b = a^b

கேள்வி 5.
என்ற ஈருறுப்புச் செயலி a * b = \(\frac{ab}{7}\) என வரையறுக்கப்படுகிறது. * எதன் மீது ஈருறுப்புச் செயலி ஆகாது?
(1) ℚ⁺
(2) ℤ
(3) ℝ
(4) ℂ
விடை:
(3) ℤ
குறிப்பு :a= 3, b = 2 என்க.
⇒ a * b = 3 * 2 = \(\frac{3(2)}{7}=\frac{6}{7}\) ∉ z

கேள்வி 6.
ℚ என்ற கணத்தில் a◉b = a + b + ab. என வரையறு பின்ன ர் 3◉(y◉5) =7?
(1) y = \(\frac{2}{3}\)
(2) y = \(\frac{-2}{3}\)
(3) y = \(\frac{-3}{2}\)
(4) y = 4
விடை:
(2) y = \(\frac{-2}{3}\)
குறிப்பு : ⓧ b=a + b + ab
∴ 3 ⓧ [y ⓧ 5) =7 = 3 ⓧ (y + 5 + 5y) = 7
⇒ 3 + y + 5 + 5y + 3[y + 5 + 5y) = 7
⇒ 8 + 6y + 3y +15 + 15y = 7
⇒ 23 + 24y = 7 ⇒ 24y = 7- 23 = -16
⇒ y = \(\frac{-16}{24}=\frac{-2}{3}\)

கேள்வி 7.
ℝ-ன் மீது a * b = \(\sqrt{a^{2}+b^{2}}\) ? எனில், *ஆனது
(1) பரிமாற்று விதிக்கு கட்டுப்படும் ஆனால் சேர்ப்பு விதியை நிறைவு செய்யாது.
(2) சேர்ப்பு விதிக்கு கட்டுப்படும் ஆனால் பரிமாற்று விதியை நிறைவு செய்யாது.
(3) பரிமாற்று விதி மற்றும் சேர்ப்பு விதிகளை நிறைவு செய்யும்.
(4) பரிமாற்று விதி மற்றும் சேர்ப்பு விதிகளை நிறைவு செய்யாது.
விடை:
(3) பரிமாற்று விதி மற்றும் சேர்ப்பு விதிகளை நிறைவு செய்யும்.

குறிப்பு : a * b = \(\sqrt{a^{2}+b^{2}}\) = \(\sqrt{b^{2}+a^{2}}\) = b * a
மேலும் a * (b * c) = a * \(\sqrt{b^{2}+c^{2}}\) = \(\sqrt{a^{2}+b^{2}+c^{2}}\)
(a * b) * c = \(\sqrt{a^{2}+b^{2}}\) = \(\sqrt{a^{2}+b^{2}+c^{2}}\)

கேள்வி 8.
பின்வரும் கூற்றுகளில் எது T மெய்மதிப்பை பெற்றிருக்கும்?
(1) sin.x ஓர் இரட்டைச் சார்பு.
(2) ஒவ்வொரு சதுர அணியும் பூச்சியமற்ற கோவை அணி ஆகும்.
(3) ஒரு கலப்பெண் மற்றும் அதன் இணை எண்ணின் பெருக்கற்பலன் முற்றிலும் கற்பனை.
(4) \(\sqrt{5}\) ஒரு விகிதமுறா எண்
விடை:
(4) \(\sqrt{5}\) ஒரு விகிதமுறா எண்

கேள்வி 9.
பின்வருபவைகளில் எது மெய்மதிப்பு F ஐ பெற்றிருக்கும்?
(1) சென்னை இந்தியாவில் உள்ளது அல்லது \(\sqrt{2}\) ஒரு முழு எண்
(2) சென்னை இந்தியாவில் உள்ளது அல்லது \(\sqrt{2}\) ஒரு விகிதமுறா எண்
(3) சென்னை சீனாவில் உள்ளது அல்லது \(\sqrt{2}\) ஒரு முழு எண்
(4) சென்னை சீனாவில் உள்ளது அல்லது 1/2 ஒரு விகிதமுறா எண்
விடை:
(3) சென்னை சீனாவில் உள்ளது அல்லது \(\sqrt{2}\) ஒரு முழு எண்

கேள்வி 10.
ஒரு கூட்டுக் கூற்றில் 3 தனிக் கூற்றுகள் உட்படுத்தப்பட்டிருந்தால் அம்மெய்மை அட்டவணையின் நிரைகளின் எண்ணிக்கை
(1) 9
(2) 8
(3) 6
(4) 3
விடை:
(2) 8
குறிப்பு : நிரைகளின் எண்ணிக்கை = 2³ = 8

கேள்வி 11.
(p ∨ q) → (p ∧ q)-ன் எதிர்மறை கூற்று எது?
(1) (p ∧ q) → (p ∨ q)
(2) ¬(p ∨ q) → (p ∧ q)
(3) (¬p ∨ -q) → (¬p ∧ ¬q)
(4) (¬p ∧ ¬q) → (¬p ∨ ¬q)
விடை:
(4) (¬p ∧ ¬q) → (¬p ∨ ¬q)
குறிப்பு : (p ∨ q) → (p ∧ q)
¬[(p ∨ q) → (p ∧ q)] → (¬p ∧ ¬q) → (¬p ∨ ¬q)

கேள்வி 12.
(p ∨ q) + r -ன் நேர்மாறுக் கூற்று எது
(1) ¬r → (¬p ∧ -q)
(2) ¬r → (p ∨ q)
(3) r → (p ∧ q)
(4) p → (q ∨ r)
விடை:
(1) ¬r → (¬p ∧ -q)
குறிப்பு : (p ∨ q) → r
நேர்மாறுக் கூற்று ¬r → (¬p ∧ ¬q)

கேள்வி 13.
(p ∧ q] ∨ ¬q -ன் மெய்மை அட்டவணை கீழே தரப்பட்டுள்ளது.

விடை:
(3) T T FT
குறிப்பு:

கேள்வி 14.
(p ∨ ¬q)ன் மெய்மை அட்டவணையில் கடைசி நிரலில் வரும் மெய் மதிப்பு ‘F’ விளைவுகளின் எண்ணிக்கை
(1) 1
(2) 2
(3) 3
(4) 4
விடை:
(3) 3
குறிப்பு:

கேள்வி 15.
பின்வருபவைகளில் எது சரியல்ல ? p மற்றும் q ஏதேனும் இரு கூற்றுகளுக்கு பின்வரும் தர்க்க சமானமானவைகள் பெறப்படுகிறது.
(1) ¬(p ∨ q) ≡ ¬p ∧ ¬q
(2) ¬(p ∧ q) ≡ ¬p ∨ ¬q
(3) ¬(p ∨ q) ≡ ¬p ∨ ¬q
(4) ¬(¬p) ≡ p
விடை:
(3) ¬(p ∨ q) ≡ ¬p ∨ ¬q
குறிப்பு : ¬(p ∨ q) = ¬p ∨ ¬q [-(p ∨ q) = ¬p ∧ ¬q

கேள்வி 16.

விடை:
(2) F T T T
குறிப்பு:

கேள்வி 17.
¬(p ∨ q) ∨ [p ∨ (p∧ ¬ r)) -ன் இருமம்
(1) ¬(p ∧ q] ∧ [p ∨ [p ∧ ¬r)]
(2) (p ∧ q] ∧ [p ∧ (p ∨ ¬r)]
(3) ¬(p ∧ q] ∧ [p ∧ (p ∧ r)]
(4) ¬(p ∧ q) ∧ [p ∧ (p ∨¬r)]
விடை:
(4) ¬(p ∧ q) ∧ [p ∧ (p ∨¬r)]

கேள்வி 18.
p ∧ (¬p ∨ q) என்ற கூற்று
(1) ஒரு மெய்மம்
(2) ஒரு முரண்பாடு
(3) p ∧ q -க்கு தர்க்க சமானமானவை
(4) p ∨ q -க்கு தர்க்க சமானமானவை
விடை:
(3) p ∧ q -க்கு தர்க்க சமானமானவை
குறிப்பு:

கேள்வி 19.
பின்வரும் ஒவ்வொரு கூற்றிற்கும் அதன் மெய் மதிப்பை தீர்மானிக்க.
(a) 4 + 2 = 5 மற்றும் 6 + 3 = 9
(b) 3 + 2 = 5 மற்றும் 6 + 1 = 7
(c) 4 + 5 = 9 மற்றும் 1 + 2 = 4
(d) 3 + 2 = 5 மற்றும் 4 + 7 = 11

விடை:
(1) F T F T
குறிப்பு :
(1) 4 + 2 = 5 மற்றும் 6 + 3 = 9 (F ∧ T)
(2) 3 + 2 = 5 மற்றும் 6 + 1 = 7 (T ∧ T) = T
(3) 4 + 5 = 9 மற்றும் 1 + 2 = 4 (T ∧ F) = F
(4) 3 + 2 = 5 மற்றும் 4 + 5 = 11 (T ∧ T) = T

கேள்வி 20.
பின்வருபவைகளில் எது உண்மையல்ல ?
(1) ஒருகூற்றின்மறுப்பின்மறுப்பு அக்கூற்றேயாகும்.
(2) ஒரு மெய்மை அட்டவணையில் இறுதி நிரல் முழுவதும் T எனில் அது ஒரு மெய்மமாகும்.
(3) ஒரு மெய்மை அட்டவணையில் இறுதி நிரல் முழுவதும் F எனில் அது ஒரு முரண்பாடாகும்.
(4) p மற்றும் q ஏதேனும் இரு கூற்றுகள் எனில் p ↔ q என்பது ஒரு மெய்மாகும்
விடை:
(4) p மற்றும் பு ஏதேனும் இரு கூற்றுகள் எனில் p ↔ q என்பது ஒரு மெய்மாகும்
குறிப்பு:
p மற்றும் q ஏதேனும் இரண்டு தனி கூற்றுகள்
எனில் p ⇔ q ஒரு மெய்மம்.
p ⇔ q ஒரு நிச்சயமின்மை என அறிவோம்.

You can Download Samacheer Kalvi 9th Maths Book Solutions Guide Pdf, Tamilnadu State Board help you to revise the complete Syllabus and score more marks in your examinations.

Tamilnadu Samacheer Kalvi 9th Maths Solutions Chapter 3 Algebra Ex 3.9

9th Maths Exercise 3.9 Question 1.
Find the GCD for the following:
(i) p⁵, p¹¹, p⁹
(ii) 4x³, y³, z³
(iii) 9 a² b² c³, 15 a³ b² c⁴
(iv) 64x⁸, 240x⁶
(v) ab² c³, a² b³ c, a³ bc²
(vi) 35x⁵ y³ z⁴, 49x² yz³, 14xy² z²
(vii) 25 ab³ c, 100 a² bc, 125 ab
(viii) 3abc, 5xyz, 7pqr
Solution:
(i) p⁵, p¹¹, p⁹
p⁵ = p⁵
p⁹ = p⁵ × p⁴
p¹¹ = p⁵ × p⁶
G.C.D. of p⁵, p¹¹, p⁹ = p⁵

(ii) 4x³, y³, z³
G.C.D. of 4x³ = 1 × 4x³
y³ = 1 × y³
z³ = 1 × z³
∴ G.C.D. = 1

(iii) 9 a² b² c³, 15 a³ b² c⁴
9 a² b² c³ = 3 × 3a² b² c³
15 a³ b² c⁴ = 3 × 5a³ b² c⁴
G.C.D. = 9 a² b² c³, 15 a³ b² c⁴ = 3 × a² b² c³ = 3 a² b² c³

(iv) 64x⁸, 240x⁶
64x⁸ = 2 × 2 × 2 × 2 × 2 × 2 × x⁶ × x⁸
240x⁶ = 2 × 2 × 2 × 2 × 3 × 5 x⁶
G.C.D. of 64x⁸, 240x⁶ = 2 × 2 × 2 × 2 x⁶ = 16x⁶

(v) ab² c³, a² b³ c, a³ bc²
ab² c³ = a × b × b × c × c × c
a² b³ c = a × a × b × b × b × c
a³ bc² = a × a × a × b × c × c
G.C.D. of ab² c³, a² b³ c, a³ bc² = a × b × c = abc

(vi) 35x⁵ y³ z⁴, 49x² yz³, 14xy² z²
35x⁵ y³ z⁴ = 5 × 7 x⁵ y³ z⁴
49x² yz³ = 7 × 7 x² y z³
14xy² z² = 2 × 7 x y² z²
G.C.D. is = 7 x y z²

(vii) 25 ab³ c, 100 a² bc, 125 ab
25 ab³ c = 5 × 5 ab³c
100 a² bc = 2 × 5 × 2 × 5 a² b c
125 ab = 5 × 5 × 5 ab
G.C.D is = 5 × 5 ab = 25ab

(viii) 3abc, 5xyz, 7pqr
3abc = 1 × 3 a bc
5xyz = 1 × 5 x y z
7pqr = 1 × 7 p q r
G.C.D is 1

Samacheer Kalvi 9th Maths Chapter 3 Question 2.
Find the GCD of the following
(i) (2x + 5), (5x + 2)
(ii) a^{m + 1}, a^{m + 2}, a^{m + 3}
(iii) 2a² + a, 4a² – 1
(iv) 3a², 5b³, 7c⁴
(v) x⁴ – 1, x² – 1
(vi) a³ – 9ax², (a – 3x)²
Solution:
(i) (2x + 5), (5x + 2)
(2x + 5) = 1 × (2x + 5)
(5x + 2) = 1 × (5x + 2)
∴ G.C.D = 1

(ii) a^{m + 1}, a^{m + 2}, a^{m + 3}
a^{m + 1} = a^m × a¹
a^{m + 2} = a^m × a¹ × a¹
a^{m + 3} = a^m × a¹ × a¹ × a¹
G.C.G = a^m × a¹ = a^{m + 1}

(iii) 2a² + a, 4a² – 1
2a² + a = a (2a + 1)
4a² – 1 = (2a)² – 1² = (2a + 1) (2a -1)
G.C.D = (2a + 1)

(iv) 3a², 5b³, 7c⁴
3a² = 1 × 3a × a
5b³ = 1 × 5 b × b × b
7c⁴ = 1 × 7 × c × c × c × c
∴ G.C.D = 1

(v) x⁴ – 1, x² – 1
x⁴ – 1 = (x²)² – 1² = (x² + 1) (x² – 1)
= (x² + 1) (x² – 1²) = (x² + 1) (x + 1 ) (x – 1)
x² – 1 = x² – 1² = (x + 1) (x – 1)
G.C.D = (x + 1) (x – 1) = x² – 1

(vi) a³ – 9ax², (a – 3x)²
a³ – 9ax² = a (a² – (3x)²) = a (a + 3x) (a – 3x)
(a – 3x)² = (a – 3x) (a – 3x)
G.C.D = (a – 3x)

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Tamilnadu Samacheer Kalvi 10th Social Science History Solutions Chapter 8 Nationalism: Gandhian Phase

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Nationalism: Gandhian Phase Textual Exercise

I. Choose the correct answer.

Question 1.
Who was arrested during the anti-Rowlatt protests in Amritsar?
(a) Motilal Nehru
(b) Saifuddin Kitchlew
(c) Mohamed Ali
(d) Raj Kumar Shukla
Answer:
(b) Saifuddin Kitchlew

Question 2.
In which session of the Indian National Congress was Non-Cooperation approved?
(a) Bombay
(b) Madras
(c) Lucknow
(d) Nagpur
Answer:
(d) Nagpur

Question 3.
Which among the following was declared as ‘Independence Day’?
(a) 26th January 1930
(b) 26th December 1929
(c) 16th June 1946
(d) 15th January 1947
Answer:
(a) 26th January 1930

Question 4.
When was the first Forest Act enacted?
(a) 1858
(b) 1911
(c) 1865
(d) 1936
Answer:
(c) 1865

Question 5.
On 8 January 1933 which day was observed …………..
(a) Temple Entry Day
(b) Day of Deliverance
(c) Direct Action Day
(d) Independence Day
Answer:
(a) Temple Entry Day

Question 6.
Which Act introduced Provincial Autonomy?
(a) 1858 Act
(b) Indian Councils Act, 1909
(c) Government of India Act, 1919
(d) Govemment of India Act, 1935
Answer:
(d) Govemment of India Act, 1935

Question 7.
Who defeated Pattabhi Sitaramaya, Gandhi’s candidate, and became the President of the Congress in 1939?
(a) Rajendra Prasad
(b) Jawaharlal Nehru
(c) Subash Chandra Bose
(d) Maulana Abul Kalam Azad
Answer:
(c) Subash Chandra Bose

Question 8.
Where was Gandhi when India attained independence on 15th August 1947?
(a) New Delhi
(b) Ahmedabad
(c) Wardha
(d) Noakhali
Answer:
(d) Noakhali

II. Fill in the blanks.

1. Gandhi was thrown out of the first-class compartment in ………….. station.
2. Gandhi regarded ……………. as his political guru.
3. Khilafat Movement was led by …………….
4. Government of India Act of 1919 introduced …………….. in the provinces.
5. The Civil Disobedience Movement in North West Frontier Province was led by …………….
6. Ramsay Macdonald announced ……………….. which provided separate electorates to the minorities and the depressed classes.
7. ………….. established Congress Radio underground during the Quit India Movement.
8. …………….. coined the term ‘Paksitan’.
Answers:
1. Pietermaritzburg railway
2. Gopal Krishna Gokhale
3. AH Brothers
4. Dyarchy
5. Khan Abdul Ghaffar Khan
6. Communal Award
7. Usha Mehta
8. Choudhry Rahmat Ali

III. Choose the correct statement.

Question 1.
(i) The Communist Party of India was founded in Tashkent in 1920.
(ii) M. Singaravelu was tried in the Kanpur Conspiracy Case.
(iii) The Congress Socialist Party was formed by Jayaprakash Narayan, Acharya Narendra Dev and Mino Masani.
(iv) The Socialists did not participate in the Quit India Movement.
(a) (i) and (ii) are correct
(b) (ii) and (iii) are correct
(c) (iv) is correct
(d) (i) (ii) and (iii) are correct
Answer:
(d) (i) (ii) and (iii) are correct

Question 2.
(i) Hindustan Republican Army was formed in Kanpur in 1924.
(ii) Ram Prasad Bismil was tried in the Kakori Conspiracy Case.
(iii) Hindustan Socialist Republican Association was formed by Surya Sen.
(iv) Chittagong Armoury Raid was carried out by B.K. Dutt.
(a) (i) and (ii) are correct
(b) (i) and (iii) are correct
(c) (iii) is correct
(d) (iii) and (iv) are correct.
Answer:
(a) (i) and (ii) are correct

Question 3.
Assertion: The Congress attended the First Round Table Conference.
Reason: Gandhi-lrwin Pact enabled the Congress to attend the Second Round Table Conference.
(a) Both A and R are correct but R is not the correct explanation .
(b) A is correct but R is wrong
(c) A is wrong but R is correct
(d) Both A and R are correct and R is the correct explanation
Answer:
(c) A is wrong but R is correct

Question 4.
Assertion: The Congress Ministries resigned in 1939.
Reason: The Colonial government of India entered the war without consulting the elected Congress ministries.
(a) Both A and R are correct but R is not the correct explanation
(b) A is correct but R is wrong
(c) Both A and R are wrong
(d) Both A and R are correct and R is the correct explanation
Answer:
(d) Both A and R are correct and R is the correct explanation

IV. Match the following.

Answer:
1. (e)
2. (a)
3. (b)
4. (c)
5. (d)

V. Answer the following briefly.

Question 1.
Describe the Jallianwala Bagh Massacre.
Answer:

1. To protest against the Rowlatt Act and the arrest of the two prominent local leaders Dr. Saifuddin kitchlew and Dr. Sathyapal at Amritsar a public meeting was arranged on 13^th April 1919 at Jallianwalla Bagh in Amritsar.
2. Thousands of villagers assembled there.
3. General Dyer heard about the gathering, surrounded the place with his troops and an armoured vehicle.
4. The only entrance to the park was blocked.
5. without any warning firing took place for ten minutes till the troops ran out of ammunition.
6. Nearly 379 were killed and more than thousands injured due to stampede.
7. After this incident martial law was declared in Punjab especially in Amritsar.
8. The brutality enraged Indians. This incident made Rabindranath Tagore and Gandhi to renounce and surrender their titles and medal.

Question 2.
Write a note on the Khilafat Movement.
Answer:
After World War I, the Caliph of Turkey, who was considered the head of Muslims all over the world, was given a very harsh treatment. The Khilafat Movement started in support of the Caliph. It was led by Maulana Mohamed Ali and Maulana Shaukat Ali, popularly known as the Ali brothers. It aimed to restore the prestige and power of the Caliphate. Mahatma Gandhi supported the movement and saw it an opportunity to unite the Hindus and the Muslims.

Question 3.
Why did Gandhi withdraw the Non-Cooperation Movement?
Answer:
On February 5^th 1922 a mass procession was took over by the nationalists and the peasants.

1. Gandhiji advised them not to indulge in any violence. Provoked by the police the people turned in to violence. The angry mob burnt the police station killing 22 policemen.
2. Gandhiji was upset and immediately withdrew the movement.

Question 4.
What was the conflict between the Swarajists and no-changers?
Answer:
In due course of time the Congress got divided into two groups—pro-changers (swarajists) and no-changers. Some of the Congressmen led by Motilal Nehru and C. R. Das wanted to contest the elections and enter the legislature. They argued that the national interest could be promoted by working in the Legislative Councils under Dyarchy and weakening the colonial government from within. These Congressmen were called the pro-changers. On the other hand, no-changers like Vallabhbhai Patel, C Rajagopalachari and other followers of Gandhi wanted to continue non-cooperation with the government.

Question 5.
Why was Simon Commission boycotted?
Answer:
On 8 December 1927, the British Government announced Indian statutory commission to super-wise and bring changes in the functioning of the Government in India, (to review the working of the Government of India Act of 1919 and to further suggest reforms in the administration)

1. The committee composed of seven members headed by Sir John Simon, widely known as “Simon Commission”.
2. No Indian members were there in the committee, Indians felt denial of their right to decide their own constitution. So all sections of India including congress and Muslim league decided to boycott the Simon commission.
3. When the Simon commission came to India they were greeted with flag marches with slogan “Go back Simon” and protest wherever they went.

Question 6.
What is Poorna Swaraj?
Answer:
Some of the Congressmen were not satisfied with dominion status of India and wanted to demand complete independence. In the Congress Session held in Lahore in December 1929 with Jawaharlal Nehru as the President, Poorna Swaraj was declared as the goal. Subsequently, 26 January 1930 was declared as the Independence Day and a pledge was taken all over the country to attain Poorna Swaraj without using any kind of violence.

Question 7.
Write a note on Bhagat Singh.
Answer:

1. Bhagat Singh, Sukhdev and their comrades reorganized the ‘Hindustan Republican Army’ (HRA) in Punjab.
2. By the influence of socialistic ideals they named it as “Hindustan Socialist Republican Association” in 1928.
3. Bhagat Singh was held responsible for the assassination of ‘Sanders’ a British police officer who lathi charged Lala Laj pat Rai that led to his death.
4. Secondly he along with B. K. Dutt threw a smoke bomb in to the central assembly in 1929 and threw pamphlets shouting Inquilab Zindabadh.
5. He along with Rajaguru was arrested and sentenced to death at the age of 23.
6. Bhagat Singh’s daring and courage inspired many youths across India.

Question 8.
What are the terms of the Poona Pact?
Answer:
The main terms of the Poona Pact were:
(i) The principle of separate electorates was abandoned. Instead, the principle of joint electorate was accepted with reservation of seats for the depressed classes.

(ii) Reserved seats for the depressed classes were increased from 71 to 147. In the Central Legislature 18 per cent of the seats were reserved.

VI. Answer all the questions given under each caption.

Question 1.
Gandhi and Mass Nationalism

(a) Which incident is considered a turning point in the life of Gandhi?
Answer:
The racial discrimination Gandhi had personally in South Africa was a turning point.

(b) Name the works that influenced Gandhi?
Answer:
He was deeply influenced by the works of Tolstoy “The Kingdom of God is within you” Ruskins ‘Unto this last’ and Thoreau’s ‘Civil Disobedience’.

(c) How did Gandhi use satyagraha as a strategy in South Africa?
Answer:
Gandhiji used the strategy of Satyagraha for fighting the issues of immigration and racial discrimination.

(d) What do you know about the Champaran Satyagraha?
Answer:
Champaran Satyagraha ended the oppression of the peasants by the Indigo planters. It gave the object of ‘Civil Disobedience’. The success of champaran Satyagraha made Gandhiji as a leader of mass struggle.

Question 2.
Constructive Programme of Gandhi
(a) What is constructive programme?
Answer:
Programmes that aimed at Khadi promotion, Hindu-Muslim unity and the abolition of untouchability are called constructive programmes.

(b) What did Gandhi exhort the Congressmen to do?
Answer:
He exhorted the Congressmen to go throughout their districts and spread the message of Khaddar, the message of Hindu-Muslim unity, the message of anti-untouchability and take up in hand the youth of the country and make them the real soldiers of Swaraj.

(c) How did Gandhi try to bring about Hindu-Muslim unity?
Answer:
Gandhi tried to bring about Hindu-Muslim unity to strengthen the cause of Swaraj.

(d) What is the contribution of Gandhi towards abolition of untouchability?
Answer:
Gandhiji wanted to abolish untouchability from the country. He undertook an all-India tour called the Harijan Tour. He started the Harijan Sevak Sangh to work for the removal of discriminations. He worked to promote education, cleanliness and hygiene and giving up of liquor among the depressed class. He also launched the Temple Entry Movement.

Question 3.
Subhas Chandra Bose and Ina

(a) How did Subhas Chandra Bose reach Japan?
Answer:
Subhas Chandra Bose made his way and reached Japan on a Submarine.

(b) Who headed the women wing of Indian National Army?
Answer:
The women wing of Indian National Army was headed by captain Lakshmisahgal.

(c) How did Subhas Chandra Bose reorganize the INA?
Answer:
Subhas Chandra Bose reorganized INA in to three brigades: Gandhi Brigade, Nehru Brigade and a women brigade named after Rani of Jhansi.

(d) Name the slogan provided by Subhas Chandra Bose.
Answer:
Subhas Chandra Bose gave the Slogan‘Dilli Chalo’.

VII. Answer in detail.

Question 1.
Examine the factors that led to the transformation of Gandhi into a mass leader.
Answer:

1. Gandhi was a person dedicated to the cause of poorest of the poor instantly gained the goodwill of the masses.
2. He visited Champaran (Bihar) for the cause of getting the solution for the peasants and the people suffering under the exploitation of indigo planters.
3. On reaching Champaran he was asked by the police to return back but he refused.
4. He was summoned for trial.
5. The news spread like wildfire and people in thousands swarmed the place in support of Gandhi.
6. Eventually a committee was formed with Gandhi as a member recommended the abolition of the “tinkathia system”. Thus ending the oppression of the peasants by the Indigo planters.
7. His fruitful intervention in Ahmadabad mill strike and kheda Satyagraha helped Gandhi to establish as a leader of mass struggle.
8. His ability to mobilise the common people across the country through truth and Non- violence transformed Gandhi into a mass leader.

Question 2.
Critically examine the Civil Disobedience Movement as the typical example of Gandhian movement.
Answer:
Programmes such as no-base campaigns caught the imagination of the peasants. Gandhi announced a no-tax campaign in Bardoli in February 1922. These movements greatly enhanced Gandhi’s reputation as a national leader, especially the peasants. Gandhi made a nation-wide tour. Wherever he visited there was a bonfire of foreign clothes. Thousands left government jobs, students gave up their studies in large numbers and the lawyers gave up thriving practices. Boycott of British goods and institutions were effective.

The boycott of the Prince of Wales’ visit to India was successful. During this boycott trade unions and workers participated actively. However, Gandhi suddenly withdrew the movement because of the Chauri Chaura incident. On 5 February 1922 a procession of the nationalists in Chauri Chaura, a village near Gorakhpur in present-day Uttar Pradesh provoked by the police turned violent. The mob burnt the police station 22 policemen lost their lives. Gandhi immediately withdrew the movement. Gandhi was arrested and was released only in 1924.

Question 3.
Discuss the reasons behind the partition of India.
Answer:

1. Muslim League was formed mainly to fight for the political rights of the Indian Muslims.
2. Jinnah revived the Muslim League in 1934 with the determination of demanding separate state for Muslims.
3. By 1940 he was demanding a separate nation for Muslims arguing that in Independent India Muslims would lose all political power to the Hindus.
4. The Muslim league dubbed the congress as a Hindu organisation.
5. The British policy of Divide and rule had encouraged the vested interests of the Muslims to exploit the religious differences.
6. Cripps mission declared that it would provide a federal Government and the provinces were divided in to three groups namely.
7. Non – Muslim majority provinces, Muslim majority provinces in the North west and in the North East.
8. This proposal was agreed by both the parties but interpreted it differently.
9. The congress wanted the division temporary but the Muslim league wanted to be permanent.
10. Differences arose between the congress and the Muslim League led to the Hindu – Muslim conflicts bringing the communal violence.
11. Finally Mountbatten plan – Two Nation theory – dividing India in to two states India and Pakistan.
12. Partition of India was the ultimate outcome to split the unity of Independent India.

VIII. Activity

Question 1.
Students can be asked to mark the important places of Gandhian Movement in a map and write a sentence or two about what happened there.

• Amritsar and Lahore: The anti-Rowlatt protest was intense in Punjab, especially in Amritsar and Lahore.
• Delhi: All India Khilafat Conference was held at Delhi in November 1919.
• Calcutta: The Indian National Congress approved the non-cooperation movement in a special session held in Calcutta on September 1920.
• Gorakhpur: On 5 February 1922 a procession of the nationalists in Chauri Chaura, a village near Gorakhpur in present-day Uttar Pradesh provoked by the police turned violent.
• Sabarmati Ashram: At the break of dawn on 12 March 1930 Gandhi set out from Sabarmati Ashram with 78 of its inmates.
• Dandi: At the age of 61 Gandhi covered a distance of 241 miles in 24 days to reach Dandi at sunset on 5 April 1930.
• Vedaranyam: In Tamil Nadu, C. Rajaji led a similar salt march from Tiruchirappalli to Vedaranyam.

Question 2.
Students can be divided into groups and asked to debate the views of Gandhi, Jinnah, B.R. Ambedkar, Revolutionaries and Communists.
Answer:
Do it yourself.

Nationalism: Gandhian Phase Additional Questions

I. Choose the correct answer.

Question 1.
The unification of the country was brought by the British ……………
(a) Imperialism
(b) Politics
(c) Conquerts
Answer:
(a) Imperialism

Question 2.
Gandhi sailed to England to study.
(a) law
(b) Politics
(c) business
(d) Philosophy
Answer:
(a) law

Question 3.
The religious and social reformers prepared the ground for the rise of …………..
(a) Nationalism
(b) Revolution
(c) Mutiny
Answer:
(a) Nationalism

Question 4.
In South Africa ……………… were treated as coolies.
(a) Gujarathi’s
(b) Indians
(c) South African people
(d) English people
Answer:
(b) Indians

Question 5.
Home – Rule league in Bombay was formed by ………….
(a) Nehru
(b) Tilak
(c) Bharathi
Answer:
(b) Tilak

Question 6.
Towards the end of 19th ……………… century synthetic dyes had forced indigo out of the market.
(a) British
(b) Chinese
(c) German
(d) French
Answer:
(c) German

Question 7.
The slogan adopted during Swadeshi movement was ………….
(a) Go back to Vedas
(b) Vande Mataram
(c) Swaraj is my birth right
Answer:
(b) Vande Mataram

Question 8.
………………… returned his knighthood after the Jallianwala Bagh tragedy for the brutality by the British.
(a) Maulana Mohammed Ali
(b) Mrs. Annie Besant
(c) Motilal Nehru
(d) Rabindranath Tagore
Answer:
(d) Rabindranath Tagore

Question 9.
The first session of the Indian National Congress was chained by …………..
(a) Tilak
(b) A.O. Hume
(c) W.C. Bannerjee
Answer:
(c) W.C. Bannerjee

Question 10.
Khilafat movement came to an end with the abolition of caliphate in:
(a) Isreal
(b) Arabia
(c) Turkey
(d) India
Answer:
(c) Turkey

Question 11.
Dr. Annie Besant was an …………..
(a) English lady
(b) Indian lady
(c) Irish lady
Answer:
(c) Irish lady

Question 12.
In Tamil Nadu C. Rajaji led the salt March from ………………… to vedaranyam
(a) Tanjore
(b) Madurai
(c) Thirunelveli
(d) Tiruchirapalli
Answer:
(d) Tiruchirapalli

Question 13.
Rowlatt Act was passed in …………
(a) 1919
(b) 1917
(c) 1918
Answer:
(a) 1919

Question 14.
Gandhi attended the ………………… held at London in 1931 after Gandhi – Irwin pact was signed.
(a) First Round Table Conference
(b) Second Round Table Conference
(c) Third Round Table Conference
(d) Cabinet mission
Answer:
(b) Second Round Table Conference

Question 15.
C. R. Das and Motilal Nehru formed ……………… party.
(a) Khadar
(b) DMK
(c) Swarajya
Answer:
(c) Swarajya

Question 16.
To form the interim Government Nehru sought the help of ……………
(a) Abdul Kalam Azad
(b) Jinnah
(c) Salimullah Khan
Answer:
(b) Jinnah

Question 17.
Separate state for Muslims was demanded by ……………
(a) Netaji
(b) Jinnah
(c) Ali brothers
Answer:
(b) Jinnah

Question 18.
In which year, Ahmedabad mill strike took place?
(a) 1916
(b) 1917
(c) 1918
Answer:
(c) 1918

Question 19.
Anti-Rowlatt protest was intense in ……………
(a) Punjab
(b) Maharashtra
(c) Haryana
Answer:
(a) Punjab

Question 20.
The Khilafat Committee meeting was held in ………….
(a) Lucknow
(b) Allahabad
(c) Amritsar
(d) Kanpur
Answer:
(b) Allahabad

Question 21.
The Poona Pact took place between Mahatma Gandhi and …………….
(a) Ambedkar
(b) Jawaharlal Nehru
(c) Vallabhai Patel
(d) M. N. Roy
Answer:
(a) Ambedkar

Question 22.
Who was sent as Viceroy to India with the specific task of transfer of power?
(a) Sir John Simon
(b) Pethick Lawrence
(c) Sir Strafford Cripps
(d) Lord Mountbatten
Answer:
(d) Lord Mountbatten

II. Fill in the blanks :

1. The Indian National Congress was founded in ………………
2. The congress became divided as …………. and …………….
3. The Moderates and the Extremists joined in the Lucknow session in …………..
4. In the …………… session Jawaharlal Nehru met Gandhiji for the first time.
5. ‘Nethaji’ means …………….
6. The All India Muslim League was formed by a group of Muslim …………… and ……………
7. The Rowlatt Act curbed …………… rights such as the freedom of expression and strengthened powers.
8. Mahatma Gandhi abruptly called off the ………………. movement when it took violent turn.
9. The congress resolved to fight for Puma Swaraj in 1929 under the presidentship of ………………
10. The Quit India Movement started in ………………
11. The programme of Non-cooperation included boycott of foreign goods and spreading the doctrine of ……………….
12. During 1902 the Hindu Mahasabha was gaining popularity under ………………. and the Muslim League under Ali Brothers.
13. In the Congress session held in Lahore in December 1929 with Jawaharlal Nehru as the President, …………….. was declared as the goal.
14. Gandhiji started the Harijan Sevak Sangh to work for the removal of ……………..
15. The All India Congress Committee that met at ………….. on 8 August, 1942 passed the Quit India Resolution demanding immediate ending of the British mle in India.
Answers:
1. 1885
2. Extremist, Moderates
3. 1916
4. Lucknow
5. Leader
6. landlords, nawabs
7. Fundamental
8. Non-cooperation
9. Jawaharlal Nehru
10. 1942
11. Swadeshi
12. Madan Mohan Malaviya
13. Pooma Swaraj
14. discriminations
15. Bombay

III. True or false:

1. Subash Chandra Bose was a moderate nationalist.
2. The Jallianwala Bagh Massacre occurred in Amritsar on Baisaki day.
3. The Swadeshi Movement started after the partition of Bengal.
4. Maulan Azad became the major spokes person for the demand for Pakistan.
5. Khan Abdul Ghaffar Khan also known as Badshah Khan founded the Khudai Khidmatgar.
Answer:
1. False
2. True
3. True
4. False
5. True

IV. Choose the correct statement.

Question 1.
(i) The Wavell Plan was announced in June 1945.
(ii) It provided for an interim government, with an equal number of Hindus and Muslims in the Viceroy’s Executive Council.
(iii) All portfolios, including war portfolio, was to be held by Indian ministers.
(iv) However, in Shimla Conference, the Congress and the Muslim League could not come to an agreement.
(a) (i) and (ii) are correct
(b) (i) (ii) and (iii) are correct .
(c) (ii) (iii) and (iv) are correct
(d) (i) (ii) and (iv) are correct
Answer:
(d) (i) (ii) and (iv) are correct

Question 2.
Assertion: After the First World War the Caliph of Turkey, who was considered the head of Muslims all over the world, was given a harsh treatment.
Reason: The Khilafat Movement was started in support of the Caliph.
(a) Both A and R are correct and R is the right explanation.
(b) A is right but R is wrong.
(c) Both A and R are wrong.
(d) Both A and R are correct but R is not the right explanation
Answer:
(a) Both A and R are correct and R is the right explanation.

V. Match the following.

Answer:
1. (c)
2. (a)
3. (d)
4. (e)
5. (b)

Answer:
1. (b)
2. (a)
3. (d)
4. (e)
5. (c)

Answer:
1. (d)
2. (e)
3. (c)
4. (b)
5. (a)

Answer:
1. (b)
2. (c)
3. (d)
4. (e)
5. (a)

VI. Answer briefly:

Question 1.
Write a brief note on Gandhi’s early life.
Answer:
Mohandas Karam Chand Gandhi was bom in a well to do family on 2nd October 1869 at Porbandar.

1. His father was Kaba Gandhi served as Diwan of Porbandar and Rajkot.
2. Mother was putlibai, a devout vaishavite influenced the young Gandhi.
3. After passing matriculation Gandhi sailed to England to study law in 1888.
4. After becoming barrister Gandhi returned to India in June 1891.
5. He strongly believed in British sense of justice and fair play till he experienced racial discrimination by himself.
6. A Gujarati firm sought his service for assistance in a law suit in South Africa, and he left in April 1893 to South Africa.

Question 2.
Name some of the important moderate leaders.
Answer:

• Dadabai Naoroji
• Surendranath Banarjee
• Pheroze Sha Mehta
• Gopala Krishna Gokhale
• M. G. Ranade

Question 3.
What influenced Gandhi to get trained in the path of Satyagraha?
Answer:

1. Gandhi ideas were formed due to a blend of Indian and Western thoughts.
2. He was greatly influenced by western thinkers and was highly critical of western civilisation and industrialisation.
3. He was inspired by writings of Ruskin and established the phoenix settlements and the Tolstoy Farm.
4. These settlements had equality, community living and dignity of labour and formed as training grounds for the Satyagraha.

Question 4.
When and by whom was the Indian National Congress founded?
Answer:
The Indian National Congress was founded in 1885 by Allan Octavian Hume, a retiree L civil servant.

Question 5.
Write a note on Pro – changers and no – changers of group of congress.
Answer:
In 1923 there was a split in congress namely prochangers and no changers after the suspension of Non – cooperation movement by Gandhi in 1922.

Pro – Changers: The congressmen led by Mothilal Nehru and C.R Das wanted to contest the elections and enter the legislature.

They had the notion that national interest could be promoted by working in the legislative councils under Dyarchy and wreck the colonial Government within.

They effectively used the legislature as a platform for propagation of nationalist ideas.

No. Changers: Staunch followers of Gandhi like Vallabhbhai Patel. C. Rajaji and others who wanted to continue non – cooperation with the Government.

Question 6.
Why was Khilafat Movement started?
Answer:

1. After the defeat of Germany in the first world war, the Turkish empire was broken up.
2. Its territories were shared by British and France.
3. The Sultan of Turkey was humiliated.
4. The Sultan was also the caliph or the religious leader of the Muslims.
5. So the Muslims started the Khilafat Movement.
6. The Ali brothers Mohammad Ali and Shaukat Ali started the Khilafat Movement in India.

Question 7.
Write a note on Direct Action Day call by Muslims.
Answer:

1. Differences arose between congress and Muslim league.
2. When the congress nominated a Muslim member the league argued it was to be sole representative of the Muslim and withdrew its approval.
3. Jinnah declared 16th August 1946 as the “Direct Action Day”.
4. Hartals, and demonstrations took place which soon turned in to Hindu – Muslim conflict.
5. It spread to other districts of Bengal. The worst affected district was ‘ Noakhali.
6. Gandhi left for the worst affected regions bringing the communal violence under control and spread the message of peace and non – violence.

Question 8.
Write about Swaraj party.
Answer:
(i) In order to lead the national movement a section of the nationalist leaders like C.R. Das and Motilal Nehru formed the Swaraj party in 1923.

(ii) Instead of boycotting the Assemblies there leaders wanted to oppose the British Government from within the legislature.

(iii) It passed the resolution demanding the establishment of a responsible Government in India,

(iv) After the death of C. R. Das the Swaraj party was dissolved.

Question 9.
Who were the members of the Cabinet Mission?
Answer:

1. Pethick Lawrence
2. A.V. Alexander
3. Sir Stafford Cripps

Question 10.
Explain the Communal Award and Poona Pact of 1932.
Answer:

• At the end of the Second Round Table Conference the British Prime Minister Ramsay MacDonald announced a scheme known as the communal Award.
• It provided separate electorates for the minorities and the depressed classes.
• Dr. Ambedkar accepted it but Gandhiji protested against this and went on a fast into death.
• After the Poona Pact in 1932 Gandhiji’s ended his fast.
• The depressed communities agreed to have joint electorates with adequate representation.

Question 11.
How India was partitioned?
Answer:

• The new state Pakistan comprised of west Punjab, Sind, north west frontier provinces.
• All the remaining provinces remained with the Indian dominion.

Question 12.
Inspired by Ruskin, Gandhiji established two settlements. Write their names and features.
Answer:
Inspired by Ruskin Gandhiji established the Phoenix Settlements in 1905 and the Tolstoy Farm in 1910. Equality, community living and dignity of labour were inculcated in the settlements. They were also the training grounds for the satyagrahis.

Question 13.
Why did Gandhiji support the Khilafat Movement?
Answer:
Gahdhiji supported the Khilafat Movement as he saw it as an opportunity to unite the Hindus and the Muslims.

Question 14.
The Non-cooperation Movement got nation-wide support. Support the statement with valid points.
Answer:
The Non-cooperation Movement was supported by the people of all sections. They boycotted foreign goods and spread the doctrine of Swadeshi. Thousands left government jobs, students gave up their studies in large numbers and the lawyers gave up thriving practices. They also boycotted the Prince of Wales’ visit to India. The trade unions and workers also participated actively.

Question 15.
What were the recommendations of the Nehru Report?
Answer:

1. Dominion status for India
2. Elections of the Central Legislature and the Provincial Legislatures on the basis of joint and mixed electorates
3. Reservation of seats for the Muslims in Central Legislature and in provinces where they are in a minority and for the Hindus in North West Frontier Province where they were in a minority
4. Provision of fundamental rights, and universal adult franchise.

Question 16.
Jinnah was hailed as ambassador of Hindu-Muslim unity. What made him change his stand?
Or
Under what circumstances did Jinnah begin to espouse the cause of separate nation for Muslims?
Answer:
Jinnah demanded one-third of seats be reserved for Muslims. But it was rejected in the All Party Conference. Later he proposed a resolution which came to be known as Jinnah’s Fourteen Points. However, it was also rejected. Thereafter, he changed his stand and began to espouse the cause of separate nation for Muslims.

Question 17.
Why did the negotiations between the Cripps Mission and the Congress fail? What did the Cripps Mission offer?
Answer:
The negotiations between the Cripps Mission and the Congress failed because Britain was not willing to transfer of effective power immediately. The Cripps Mission offered:

1. Grant of Dominion Status after the War
2. Indian Princes could sign a separate agreement with the British implying the acceptance for the demand of Pakistan.
3. British control of defence during the War.

VI. Answer all the questions given under each caption:

Question 1.
Factors leading to the rise of National Movement
(a) How did the national leaders inspire the people?
Answer:
They inspired the people with the ideas of self-respect and self-confidence.

(b) When was the Vernacular Press Act passed?
Answer:
The Vernacular Press Act was passed in 1878.

(c) What was the policy of the British?
Answer:
The British followed the policy of “Divide and Rule”.

(d) How did the British consider the Indians?
Answer:
The British considered the Indians as inferior and uncivilized.

Question 2.
Role of socialists

(a) Who provided the leadership for the Quit India movement when the leaders of congress were in jail?
Answer:
The socialists provided the leadership for the movement in the absence of congress leaders.

(b) Who escaped from the jail and what they did?
Answer:
Jayaprakash Narayan and Ramanand Misra escaped from the prison and organised underground movement.

(c) Who was the women activists who played a heroic role?
Answer:
Aruna Asaf Ali was the woman activists who played a heroic role.

(d) What Gandhi did to stop the atrocities done by the British Government?
Answer:
Gandhi commenced a twenty one day fast in February 1943 which nearly threatened his life.

Question 3.
Extremists
(a) Name the extremists leaders:
Answer:

1. Lokmanya Bala Gangadhar Tilak
2. Bipin Chandra Pal
3. Lala Lajpat Rai
4. Arabind Ghosh

(b) What did Tilak declare?
Answer:
Tilak declared, “Swaraj is my birth right and I shall have it”.

(c) Name the festivals revived by Tilak?
Answer:
Tilak revived the celebration of “Ganapathi and “Shivaji” festivals.

(d) What was the desire of the militant nationalists?
Answer:
The Militant Nationalists desired to change the aim of the congress and the means to attain it.

Question 4.
Royal indian Navy Revolt

(a) When and where the Royal Indian Navy ratings revolt?
Answer:
In February 1946 at Bombay the Royal Indian Navy ratings revolted.

(b) Where was similar strikes occurred?
Answer:
Strikes occurred in the Indian Air Force and the Indian signal corps Jabalpur.

(c) What was big blow to the imperial power?
Answer:
British surrender in South – East Asia to the Japanese was a big blow to imperial prestige.

(d) What was the effect of this revolt?
Answer:
All political leaders were released and ban on congress was lifted.

Question 5.
The Mount Batten Plan
(a) Who became the Governor General of India in 1947?
Answer:
Lord Mount Batten became the Governor General of India in 1947.

(b) Who was the last British Governor General?
Answer:
Lord Mount Batten was the last British Governor General.

(c) What was Mount Batten Plan?
Answer:
India would be divided into two independent countries namely Indian Union and the Pakistan Union.

(d) What was the reaction of the Congress and Muslim League?
Answer:
Both the Congress and the Muslim League accepted this plan.

Question 6.
Direct Action Day call by Muslim League
(a) What led to a difference between Congress and Muslim League?
Answer:
The nomination of a Muslim member by the Congress led to a difference between Congress and Muslim League.

(b) What was the League’s argument?
Answer:
The League argued it was to be the sole representative of the Muslims and so withdrew its approval.

(c) What happened on the Direct Action Day?
Answer:
Hartals and demonstrations took place which soon turned into Hindu-Muslim communal conflict.

(d) Which district of Bengal was the worst affected? What did Gandhiji do to control the situation?
Answer:
The district of Noakhali was the worst affected. Gandhiji toured the worst affected regions on bare foot spreading the message of peace and non-violence.

Question 7.
Independence and Partition.
(a) Which Act gave effect to the Mount Batten Plan?
Answer:
The Indian Independence Act gave effect to the Mount Batten Plan.

(b) When did the Act come into being?
Answer:
The Act came into being on 18 July 1947.

(c) What changes came with the enactment of the Act?
Answer:
The Act abolished the sovereignty of the British Parliament over India. India was partitioned into two dominions—India and Pakistan.

VII. Answer the following in detail.

Question 1.
Narrate how the tribal groups were affected by the Forest Acts enacted by the British? Who attained martyrdom for the cause of forest dwellers?
Answer:

1. The First Forest Act was enacted by the British in 1865.
2. This act restricted the access of the forest dwellers to the forest areas to collect firewood, cattle fodder and other minor forest produce such as honey seeds, nuts, medicinal herbs.
3. Indian Forest Act of 1878.
4. Claimed that original ownership of forests was with the state.
5. Waste lands and fallow lands were included as forests.
6. Shifting cultivation practiced by the tribal people was prohibited.
7. Alienation of forests from local control was stiffly resisted by the aggrieved tribals and the nationalists.
8. Uprising of adivasis (1922 – 24) organised by Alluri Sitarama Raju in Rampa.
9. He made Adivasi areas – the forest area along the Godawari district Vishakapatnam (Eastern ghats) his home.
10. The Adivasis lived in utter poverty and were harassed by police, forest and revenue officials.
11. The efforts of Raju against corrupt officials to protect the interests of Rampa tribals altered the British to target his life.
12. A special team of Malabar police was sent to suppress the uprising of Rampa Adivasis in 1922 – 24.
13. For the cause of forest dwellers Alluri Sitarama Raju attained martyrdom.

Question 2.
Write a short note on Salt Satyagraha. Causes for the Salt Satyagraha:
Answer:

1. The British Government levied tax on common salt used by millions of people.
2. It hit the poor hard. So Gandhiji started the civil disobedience movement on 12th March 1930
3. This movement is known as Salt Satyagraha or the civil disobedience movement.

Dandi March:

1. Gandhi had 78 chosen followers including Sarojini Naidu left Sabarmathi Ashram to Dandi.
2. It covered nearly a distance of 400 km. Thousands of Indians joined the March.
3. They reached Dandi on 6th April. The slogan “Vande Mathara”, echoed every where Gandhiji broke the salt laws on the same day by preparing salt from sea water.

Results:

1. Gandhiji was arrested and put into the prison.
2. In Tamil Nadu Rajagopalachari organized a march from Trichy to Vedaranyam on Tanjore coast to break the salt laws.

Question 3.
Write a paragraph on Quit India Movement:
Answer:
Quit India Movement – 1942:

1. The failure of Cripps mission brought about a change in Gandhi’s attitude.
2. He felt that non-violent methods so far followed did not yield the desired effect. !*‘) Therefore he asked for the complete withdrawal of the British from India.

Resolution:

1. During the Second World War Japan got victory over victory.
2. The Congress leaders felt that the presence of English in India would naturally invite Japan to invade India.
3. So the congress working committee passed a resolution on 8th August 1942 demanding the immediate withdrawal of the British from India.

Gandhi’s memorable speech:
I am not going to be satisfied with anything short of complete freedom. We shall do or die. We shall either free India or die in the attempt.
Results:

• Gandhiji, Nehru, Abul Kalam Azad and other prominent leaders of the congress were arrested.
• Due to lack of proper leadership violent riots took place everywhere.
• At the end of the Second World War, labour party under Clement Atlee came to power in England. He was the supporter of Indian freedom struggle.
• He withdraw all the prohibitory orders imposed on the Congress by the British and also deputed a mission to find a solution for India’s problem.

Question 4.
Throw light on the Round Table Conferences. How did they disappoint the Congress leaders?
Answer:
The First Round Table Conference was held at London in November 1930 in the midst of the Civil Disobedience Movement. Ramsay MacDonald, the British Prime Minister, proposed a federal government with provincial autonomy. There was a deadlock over the question of separate electorates for the minorities. The Congress did not attend this conference as all its leaders were in jail. So, the conference closed without any result. It was clear that without
‘ Congress participation the discussions were of no value. Gandhiji was released from the jail unconditionally.

The Viceroy Lord Irwin held talks with Gandhiji on 5 March 1931. The British agreed to the demand of immediate release of all political prisoners not involved in violence, return of confiscated land and lenient treatment of the government employees who had resigned. It also permitted the people of coastal villages to make salt and non-violent picketing. The Congress agreed to suspend the Civil Disobedience Movement and attend the Second Round Table Conference. Gandhiji attended this conference which began on 7 September 1931 but refused to accept separate electorates for the minorities. As a result, the second conference also failed.

On returning to India on 28th December 1931, Gandhiji revived the Civil Disobedience Movement. This time the government was prepared to meet the resistance. So, it enforced martial law and arrested Gandhiji on 4th January 1932. Soon all the Congress leaders were also arrested. Protests and picketing by people were suppressed with force. The national st press was completely banned. In the meantime, the Third Round Table Conference was he id from 17 November to 24 December 1932. The Congress did not participate in the confers ce as it had revived the Civil Disobedience Movement.
IMPORTANT EVENTS AND YEARS:

We think the data given here clarify all your queries of Chapter 8 and make you feel confident to attempt all questions in the examination. So, practice more & more from Tamilnadu State Board solutions for 10th Social Science History Chapter 8 Nationalism: Gandhian Phase Questions and Answers & score well. Need any information regarding this then ask us through comments & we’ll give the best possible answers very soon.

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Tamilnadu Samacheer Kalvi 12th Computer Science Solutions Chapter 13 Python and CSV Files

Samacheer Kalvi 12th Computer Science Python and CSV Files Text Book Back Questions and Answers

PART – I
I. Choose The Correct Answer

Csv File Questions Class 12 Question 1.
A CSV file is also known as a
(a) Flat File
(b) 3D File
(c) String File
(d) Random File
Answer:
(a) Flat File

Csv Files In Python Class 12 Questions Question 2.
The expansion of CRLF is ………………………
(a) Control Return and Line Feed
(b) Carriage Return and Form Feed
(c) Control Router and Line Feed
(d) Carriage Return and Line Feed
Answer:
(d) Carriage Return and Line Feed

Questions On Csv Files In Python Question 3.
Which of the following module is provided by Python to do several operations on the CSV files?
(a) py
(b) xls
(c) csv
(d) os
Answer:
(c) csv

A Csv File Is Also Known As A 3d File Question 4.
Which of the following mode is used when dealing with non-text files like image or exe files?
(a) Text mode
(b) Binary mode
(c) xls mode
(d) csv mode
Answer:

A Csv File Is Also Known As A Flat File Question 5.
The command used to skip a row in a CSV file is ……………………….
(a) next( )
(b) skip( )
(c) omit( )
(d) bounce( )
Answer:
(b) skip( )

Question 6.
Which of the following is a string used to terminate lines produced by writer( )method of csv module?
(a) Line Terminator
(b) Enter key
(c) Form feed
(d) Data Terminator
Answer:
(a) Line Terminator

Question 7.
What is the output of the following program?
import csv
d=csv.reader(open(‘c:\PYPRG\chl3\city.csv’))
next(d)
for row in d:
print(row)
if the file called “city.csv” contain the following details
chennai,mylapore
mumbai,andheri
(a) chennai,mylapore
(b) mumbai,andheri
(c) chennai, mumbai
(d) chennai,mylapore,mumbai,andheri
Answer:
(b) mumbai,andheri

Question 8.
Which of the following creates an object which maps data to a dictionary?
(a) listreader( )
(b) reader( )
(c) tuplereader( )
(d) DictReader( )
Answer:
(d) DictReader( )

Question 9.
Making some changes in the data of the existing file or adding more data is called
(a) Editing
(b) Appending
(c) Modification
(d) Alteration
Answer:
(c) Modification

Question 10.
What will be written inside the file test.csv using the following program import csv
D = [[‘Exam’],[‘Quarterly’],[‘Halfyearly’]]
csv.register_dialect(‘M’,lineterminator = ‘\n’)
with open(‘c:\pyprg\chl3\line2.csv’, ‘w’) as f:
wr = csv.writer(f,dialect=’M’)
wr.writerows(D)
f.close( )
(a) Exam Quarterly Halfyearly
(b) Exam Quarterly Halfyearly
(c) Q H
(d) Exam, Quarterly, Halfearly
Answer:
(d) Exam, Quarterly, Halfearly

PART – II
II. Answer The Following Questions

Question 1.
What is CSV File?
Answer:
A CSV file is a human readable text file where each line has a number of fields , separated by commas or some other delimiter. A CSV file is also known as a Flat File. Files in the CSV format can be imported to and exported from programs that store data in tables, such as Microsoft Excel or OpenOfficeCalc.

Question 2.
Mention the two ways to read a CSV file using Python?
Answer:
Read a CSV File Using Python
There are two ways to read a CSV file.

1. Use the csv module’s reader function
2. Use the DictReader class.

Question 3.
Mention the default modes of the File?
Answer:
You can specify the mode while opening a file. In mode, you can specify whether you want to read ‘r’, write ‘w’ or append ‘a’ to the file. You can also specify “text or binary” in which the file is to be opened.
The default is reading in text mode. In this mode, while reading from the file the data w’ould . be in the format of strings.

Question 4.
What is use of next( ) function?
Answer:
# skipping the first row(heading)
Example: next( reader)

Question 5.
How will you sort more than one column from a csv file? Give an example statement?
Answer:
To sort by more than one column you can use itemgetter with multiple indices: operator .itemgetter (1,2).
#using operator module for sorting multiple columns
sortedlist = sorted (data, key=operator.itemgetter(1))

PART – III
III. Answer The Following Questions

Question 1.
Write a note on open( ) function of python. What is the difference between the two methods?
Answer:
Python has a built-in function open() to open a file. This function returns a file object, also called a handle, as it is used to read or modify the file accordingly.
For Example
>>> f = openf’sample.txt”) bopen file in current directory andf is file object
>>> f = open(‘c:\ \pyprg\ \chl3sample5.csv’) #specifyingfull path
You can specify the mode while opening a file. In mode, you can specify whether you want to read ‘r’, write ‘w’ or append ‘a’ to the file, you can also specify “text or binary” in which the file is to be opened.
The default is reading in text mode. In this mode, while reading from the file the data would be in the format of strings.
On the other hand, binary mode returns bytes and this is the mode to be used when dealing with non-text files like image or exe files.
f = open(“test.txt”) # since no mode is specified the default mode it is used
#perform file operations
f.close( )
The above method is not entirely safe. If an exception occurs when you are performing some operation with the file, the code exits without closing the file. The best way to do this is using the “with” statement. This ensures that the file is closed when the block inside with is exited. You need not to explicitly call the close() method. It is done internally.

Question 2.
Write a Python program to modify an existing file?
Answer:
import csv
row= [‘3’, ‘Meena’, ‘Bangalore’]
with open(‘student.csv’, ‘r’) as readFile:
reader= csv.reader(readFile)
lines =list(reader) # list( ) – to store each row of data as a list
lines[3] =row
with open(‘student.csv’, ‘w’) as writeFile:
# returns the writer object which converts the user data with delimiter
writer= csv.writer(writeFile)
#writerows( )method writes multiple rows to a csv file
writer, writerows(lines)
readFile.close( )
writeFile.close( )
When we Open the student.csv file with text editor, then it will show:

Question 3.
Write a Python program to read a CSV file with default delimiter comma (,)?
Answer:
CSV file with default delimiter comma(,)
The following program read a file called “sample l.csv” with default delimiter cpmma(,) and print row by row.
#importing csv
import csv
#opening the csv fde which is in different location with read mode
with open(‘c:\ \pyprg\\sample l.csv’, V) as F:
#other way to open the file is f = (‘c:\\pyprg\\sample l.csv’, ‘r’)
reader = csv.reader(F)
Sprinting each line of the Data row by row print(row)
F.close( )
OUTPUT
[‘SNO’, ‘NAME’, ‘CITY’]
[12101’,’RAM’, ‘CHENNAI’]
[‘12102′,’LAVANYA’,’TIRUCHY’]
[‘12103′,’LAKSHMAN’,’MADURA’]

Question 4.
What is the difference between the write mode and append mode?
Answer:
Append mode write the value of row after the last line of the “student.csv file:”
The ‘w’ write mode creates a new file. If the file is already existing ‘w’ mode over writs it. Where as ‘a’ append mode add the data at the end of the file if the file already exists otherwise creates a new one.

Question 5.
What is the difference between reader( ) and DictReader( ) function?
Answer:
Reading CSV File Into A Dictionary:
To read a CSV file into a dictionary can be done by using DictReader class of csv module which works similar to the reader( ) class but creates an object which maps data to a dictionary. The keys are given by the fieldnames as parameter. DictReader works by reading the first line of the CSV and using each comma separated value in this line as a dictionary key.

The columns in each subsequent row then behave like dictionary values and can be accessed with the appropriate key (i.e. fieldname). The main difference between the csv.reader( ) and DictReader( ) is in simple terms csv. reader and csv.writer work with list/tuple, while csv.DictReader and csv.DictWriter work ‘ with dictionary. csv.DictReader and csv.DictWriter take additional argument fieldnames that are used as dictionary keys.

PART – IV
IV. Answer The Following Questions

Question 1.
Differentiate Excel file and CSV file?
Answer:
The difference between Comma-Separated Values (CSV) and eXceL Sheets(XLS) file formats is
Answer:
Excel:

1. Excel is a binary file that holds information about all the worksheets in a file, including both content and formatting
2. XLS files can only be read by applications that have been especially written to read their format, and can only be written in the same way.
3. Excel is a spreadsheet that saves files into its own proprietary format viz. xls or xlsx
4. Excel consumes more memory while importing data

CSV:

1. CSV format is a plain text format with a series of values separated by commas.
2. CSV can be opened with any text editor in Windows like notepad, MS Excel, OpenOffice, etc.
3. CSV is a format for saving tabular information into a delimited text file with extension .csv
4. Importing CSV files can be much faster, and it also consumes less memory

Question 2.
Tabulate the different mode with its meaning?
Python File Modes:
Answer:

Question 3.
Write the different methods to read a File in Python?
Answer:
Read a CSV File Using Python
There are two ways to read a CSV file.

1. Use the csv module’s reader function
2. Use the DictReader class.

CSV Module’s Reader Function:
You can read the contents of CSV file with the help of csv.reader( )method. The reader function is designed to take each line of the file and make a list of all columns. Then, you just choose the column you want the variable data for. Using this method one can read data from csv files of different formats like quotes (” “),pipe (|) and comma(,).
The syntax for csv.reader( ) is
csv. reader (fileobject, delimiter,fmtparams)
where
file object:- passes the path and the mode of the file
delimiter:- an optional parameter containing the standard dilects like, I etc can be omitted
fmtparams:- optional parameter which help to override the default values of the dialects like skipinitialspace,quoting etc. Can be omitted

CSV file with default delimiter comma(,)
The following program read a file called “sample l.csv” with default delimiter comma(,) and print row by row.
#importing csv
import csv
#opening the csv file which is in different location with read mode
with open(‘c:\ \pyprg\\sample l.csv’, ‘r’) as F:
#other way to open the file is f= (‘c:\\pyprg\\sample l.csv’, ’r)
reader = csv.reader(F)
#printing each line of the Data row by row
print( row)
F.close( )
OUTPUT
[‘SNO’, ‘NAME’, ‘CITY’]
[‘12101′,’RAM’,’CHENNAI’]
[‘12102’, ‘LAVANYA’, ‘TIRUCHY’]
[‘12103’, ‘LAKSHMAN’, ‘MADURAI’]
CSV files- data with Spaces at the beginning
Consider the following file “sample 2.csv” containing the following data when opened through notepad

The following program read the file through Python using “csv.reader( )”.
import csv
csv.register_dialect(‘myDialect’,delimiter = ‘,’,skipimtialspace=True)
F=open(‘c:\ \pyprg\ \sample 2.csv’,’r’)
reader= csv.reader(F, dialect=’myDialect’)
for row in reader:
print( row)
F.close( )
OUTPUT
[‘Topic 1’, ‘Topic 2’, ‘Topic 3′]
[!one’, ‘two’, ‘three’]
[‘Example 1’, ‘Example 2’, ‘Example 3’]
As you can see in “sample 2.csv” there are spaces after the delimiter due to which the output is also displayed with spaces.
These whitespaces can be removed, by registering new dialects using csv.register_dialect( ) class of csv module. A dialect describes the format of the csv file that is to be read. In dialects the parameter “skipinitialspace” is used for removing whitespaces after the delimiter.

CSV File-Data With Quotes
You can read the csv file with quotes, by registering new dialects using csv.register_dialect( ) class of csv module.
Here, we have quotes.csv file with following data.
SNO,Quotes
(a) “The secret to getting ahead is getting started.”
(b) “Excellence is a continuous process and not an accident.”
(c) “Work hard dream big never give up and believe yourself.”
(d) “Failure is the opportunity to begin again more intelligently.”
(e) “The successful warrior is the average man, with laser-like focus.”
The following Program read “quotes.csv” file, where delimiter is comma (,)but the quotes are within quotes (“”). import csv
csv.register_dialect(‘myDialect’,delimiter = ‘,’,quoting=csv.QUOTE_ALL,
skipinitialspace=True)
f=open(’c:\\pyprg\ \quotes.csv’,’r’)
reader= csv.reader(f, dialect-myDialect’)
for row in reader:
print (row)
OUTPUT
[‘SNO’, ’Quotes’]
[(a), ’The secret to getting ahead is getting started.’]
[(b), ’Excellence is a continuous process and not an accident.’]
[(c), ’Work hard dream big never give up and believe yourself.’]
[(d), ’Failure is the opportunity to begin again more intelligently.’]
[(e), ’The successful warrior is the average man, with laser-like focus. ’]
In the above program, register a dialect with name myDialect. Then, we used csv. QUOTE_ ALL to display all the characters after double quotes.
CSV files with Custom Delimiters
You can read CSVfile having custom delimiter by registering a new dialect with the help of csv.register_dialect( ).
In the following file called “sample 4.csv”,each column is separated with | (Pipe symbol)

The following program read the file “sample4.csv” with user defined delimiter “|”
import csv
csv.register_dialect(‘myDialect’, delimiter ‘|’)
with open(‘c:\\pyprg\\sample 4.csv’, ‘r’) as f:
reader= csv.reader(f, dialect-myDialect’)
for row in reader:
print(row)
f.close( )
OUTPUT
[‘RollNo’, ‘Name’, ‘City’]
[‘12101’, ‘Arun’, ‘Chennai’]
[‘12102’, ‘Meena’, ‘Kovai’]
[T21031,’Ram’,’Nellai’]

Reading CSV File Into A Dictionary:
To read a CSV file into a dictionary can be done by using DictReader class of csv module which works similar to the reader() class but creates an object which maps data to a dictionary. The keys are given by the fieldnames as parameter. DictReader works by reading the first line of the CSV and using each comma separated value in this line as a dictionary key. The columns in each subsequent row then behave like dictionary values and can be accessed with the appropriate key (i.e. fieldname).

If the first row of your CSV does not contain your column names, you can pass a fieldnames parameter into the DictReader’s constructor to assign the dictionary keys manually. The main difference between the csv.reader( ) and DictReader( ) is in simple terms csv. reader and csv.writer work with list/tuple, while csv.DictReader and csv.DictWriter work with dictionary. csv.DictReader and csv.DictWriter take additional argument fieldnames that are used as dictionary keys.

For Example:
Reading “sample 8.csv” file into a dictionary
import csv
filename= ‘c:\ \pyprg\ \sample 8.csv’
input_file =csv.DictReader(open(filename;’r’))
for row in input_file:
print(dict(row))
print (data(row)) #dict( ) to print data
OUTPUT
{‘ItemName ‘^Keyboard’, ‘Quantity’: ’48’}
{‘ItemName VMonitor’, ‘Quantity’: ’52’}
{‘ItemName VMouse’, ‘Quantity’: ’20’}
In the above program, DictReader( ) is used to read “sample 8.csv” file and map into a dictionary. Then, the function dict( ) is used to print the data in dictionary format without order. Remove the dict( ) function from the above program and use print(row). Check you are getting
the following output
OrderedDict([(‘ItemName Keyboard’), (‘Quantity’, ’48’)])
OrderedDict([(‘ltemName ‘,’Monitor’), (‘Quantity’, ’52’)])
OrderedDict([(‘ItemName ‘,’Mouse’), (‘Quantity’, ’20’)])

Question 4.
Write a Python program to write a CSV File with custom quotes?
CSV File with quote characters
Answer:
You can write the CSV file with custom quote characters, by registering new dialects using csv.register_dialect( ) class of csv module,
import csv
csvData = [[‘SNO’,Items’], [‘l’,’Pen’], [‘2′,’Book’], [‘3′,’Pencil’]]
csv.register_dialect(‘myDialect’, delimiter = ‘|’,quotechar = “”,
quoting=csv.QUOTE_ALL)
with open(‘c:\\pyprg\ \chl3\\quote.csv’, ‘w’) as csvFile:
writer= csv.writer(csvFile, dialect-myDialect’)
writer, write rows(csvData)
print(“writing completed”)
csvFile.close( )
When you open the “quote.csv” file in notepad, we get following output:

In the above program, myDialect uses pipe (|) as delimiter and quotechar as doublequote “” to write inside the file.

Question 5.
Write the rules to be followed to format the data in a CSV file?
Answer:
Rules to be followed to format data in a CSV file:
(i) Each record (row of data) is to be located on a separate line, delimited by a line break by pressing enter key. For example:
xxx,yyy
denotes enter Key to be pressed

(ii) The last record in the file may or may not have an ending line break. For example:
PPP, qqq
yyy,xxx

(iii) There may be an optional header line appearing as the first line of the file with the same format as normal record lines. The header will contain names corresponding to the fields in the file and should contain the same number of fields as the records in the rest of the file. For example: field_ name 1,field_name 2,field_name_3 aaa,bbb,ccc
zzz,yyy,xxx CRFF( Carriage Return and Line feed)

(iv) Within the header and each record, there may be one or more fields, separated by commas. Spaces are considered part of a field and should not be ignored. The last field in the record must not be followed by a comma. For example: Red, Blue

(v) Each field may or may not be enclosed in double quotes. If fields are not enclosed with double quotes, then double quotes may not appear inside the fields. For example: “Red”,”Blue”,”Green” #Field data with double quotes
Black,White,Yellow #Field data without double quotes

(vi) Fields containing line breaks (CRLF), double quotes, and commas should be enclosed in double-quotes. For example:
Red, “;:Blue CRLF #comma itself is a field value, so it is enclosed with double quotes Red, Blue, Green

(vii) If double-quotes are used to enclose fields, then a double-quote appearing inside a field must be preceded with another double quote. For example:
“Red,” “Blue1: “Green”, #since double quotes is a field value it is enclosed with another double quotes,, White

Practice Programs

Question 1.
Write a Python program to read the following Namelist.csv file and sort the data in alphabetically order of names in a list and display the output

import csv.operator
data = csv.reader(open(‘c:\\PYPRG\\NameList.scv’))
next(data)
sorted list = sorted(data, key = operator.itemgetter(1))
for row in sorted list:
print(row)
Output:

Question 2.
Write a Python program to accept the name and five subjects mark of 5 students. Find the total and store all the details of the students in a CSV file?
Answer:
import csv
csvData = [[‘student’, ‘ml Vm2′,’m3′,’m4′,’m5′,’total’],
[‘Ram’, ’90’,’90’,”90′,”90′,”90′,”450′],
[‘Hari’,’100′,’100′,’100′,’10’,’90’,’490′],
[‘Sai’, ’90’,’90’,’ 100′,’ 100′,’ 100′,’480′],
[‘Viji’, ’ 100′,’90’,’90’,’90’,’ 100′,’470′],
[‘Raja’, ’80’,’’80’,”80′,’ 100′,’ 100′,’440′]]
with open(‘c:\\pyprg\\chl3\\st.csv’,’w’)as CF:
writer = csv.writer(CF) writer. writerows(csvData)
CF.close( )
Output:

Samacheer kalvi 12th Computer Science Python and CSV Files Additional Questions and Answers

PART – 1
I. Choose The Correct Answer

Question 1.
CSV means ……………………… files
(a) common server values
(b) comma separated values
(c) correct separator values
(d) constructor separated value
Answer:
(b) comma separated values

Question 2.
The file extension to save excel files are
(a) xls Civdsx
(b) XL
(c) exc or XL
(d) XL or xlx
Answer:
(a) xls Civdsx

Question 3.
csv files cannot be opened with ………………………..
(a) notepad
(b) MS Excel
(c) open office
(d) html
Answer:
(d) html

Question 4.
Identify the wrong statement
(a) Excel is a binary file
(b) csv is a plain text
(c) Excel is a plain text
(d) csv has tabular information
Answer:
(c) Excel is a plain text

Question 5.
Identify the statement which is correct.
(a) csv consumes less memory and faster
(b) Excel consumes less memory and slower
Answer:
(a) csv consumes less memory and faster

Question 6.
Find the wrong statement.
(a) csv files can be opened with any text editor
(b) Excel files can be opened with any text editor
Answer:
(b) Excel files can be opened with any text editor

Question 7.
…………………… file is used to store tabular data such as spreadsheet or database.
Answer:
csv

Question 8.
How will you open a new file in Notepad?
(a) File → New
(b) Ctrl + N
(c) both a and b
(d) shift + N
Answer:
(c) both a and b

Question 9.
If the fields of data in csv file has commas, then it should be given with …………………..
(a) ,
(b) ”
(c) ‘
(d) :
Answer:
(b) ”

Question 10.
Any field containing a newline as part of its data should be given in ……………………..
(a) quotes
(b) double colon
(c) colon
(d) double quotes
Answer:
(d) double quotes

Question 11.
If the fields contains double quotes as part of the data, the internal quotation marks need to be
(a) same
(b) quarter
(c) doubled
(d) tripled
Answer:
(c) doubled

Question 12.
The line // white indicates
(a) the first two fields of the row are empty
(b) It can be deleted
(c) comma not necessary
(d) only one field is there and , can be deleted
Answer:
(a) the first two fields of the row are empty

Question 13.
Find the correct statement
(I) The last record in the file may or may not have an ending line break
(II) Header is must with same format as record lines.
(a) (I) is true, (II) is False
(b) (I) is False, (II) – True
(c) (I), (II) – both are true
(d) (I), (II) – both are false
Answer:
(a) (I) is true, (II) is False

Question 14.
Identify the wrong statement from the following.
(a) Each field may or may not be enclosed in double quotes.
(b) If the fields are not enclosed with double quotes, then double quotes may not appear inside the fields
(c) Fields containing line breaks, double quotes and commas should be enclosed in single quotes.
(d) the last field in the record must not be followed by a comma
Answer:
(c) Fields containing line breaks, double quotes and commas should be enclosed in single quotes.

Question 15.
There are ……………………. ways to read a csv file.
(a) 1
(b) 2
(c) 3
(d) 4
Answer:
(b) 2

Question 16.
In open command, file name can be represented in ………………………
(a) ” ”
(b) ”
(c) $
(d) both a & b
Answer:
(d) both a & b

Question 17.
open( ) returns a file called ………………………… which is used to read or modify the file accordingly.
Answer:
handle

Question 18.
The default reading mode is ………………….. mode.
Answer:
text

Question 19.
The default mode when you open a file is
(a) r
(b) w
(c) x
(d) a
Answer:
(a) r

Question 20.
In text mode, while reading from the file the data would be in the format of ……………………..
(a) int
(b) float
(c) char
(d) strings
Answer:
(d) strings

Question 21.
What will happen when you open a file for writing and file already exists there?
(a) creates a new file
(b) truncates the file
(c) overwrite the file
(d) append the contents
Answer:
(b) truncates the file

Question 22.
To open the file updating data, click ……………………
(a) a
(b) b
(c) t
(d) +
Answer:
(d) +

Question 23.
…………………… opens a file for exclusive creation.
(a) r
(b) w
(c) x
(d) +
Answer:
(c) x

Question 24.
………………….. opens the file for read and write in binary mode.
(a) r
(b) b
(c) x + b
(d) r + b
Answer:
(d) r + b

Question 25.
Python has a ……………………… collector to clean up unreferenced objects.
Answer:
garbage

Question 26.
closing a file will free up the resources that were tied with the file and is done by ……………………. method.
(a) Exit
(b) close
(c) Quit
(d) None of these
Answer:
(b) close

Question 27.
Which format is not allowed to read data from cav files?
(a) quotes
(b) pipe
(c) comma
(d) Asterisk
Answer:
(d) Asterisk

Question 28.
How many arguments are there in csv.reader( ) functions?
(a) 2
(b) 3
(c) 4
(d) 5
Answer:
(b) 3

Question 29.
Which one of the following cannot be omitted in cav. reader?
(a) file object
(b) delimiter
(c) fmtparams
(d) space
Answer:
(a) file object

Question 30.
A ……………………. describes the format of the csv file that is to be read.
Answer:
dialect

Question 31.
In dialects, the parameter …………………… is used for remaining whitespaces after the delimiter.
Answer:
skipintialspace

Question 32.
By default, what will be the value of skipinitial space?
(a) True
(b) False
(c) 0
(d) 1
Answer:
(b) False

Question 33.
A ………………….. is a class of csv module which helps to define paramters for reading and writing csv.
Answer:
dialect

Question 34.
We can register for new dialects using class of csv module.
Answer:
csv.register-dialects

Question 35.
Which of the following is used to display all the characters after double quotes.
(a) Quote
(b) Quote-all
(c) double quotes
(d) single quotes
Answer:
(b) Quote-all

Question 36.
Which one of the following is used to add the elements in the list.
(a) add
(b) insert
(c) append
(d) update
Answer:
(c) append

Question 37.
Which one of the following cannot be used as a column separator?
(a) delimiter
(b) pipe
(c) comma
(d) #
Answer:
(d) #

Question 38.
List literals are written using ………………………..
(a) [ ]
(b) ( )
(c) { }
(d) <>
Answer:
(a) [ ]

Question 39.
An ordered sequence of elements which are mutable or changeable are called ……………………..
(a) object
(b) tuple
(c) list
(d) dictionary
Answer:
(c) list

Question 40.
…………………….. command arranges a list value in ascending order.
Answer:
sort( )

Question 41.
……………………… is used to arrange a list in descending order.
Answer:
sort(reverse)

Question 42.
To sort by more than one column, we can use ………………………. with multiple indices.
Answer:
itemgetter

Question 43.
To sort second column which option have to be selected?
(a) itemgetter(0)
(b) itemgetter(1)
(c) itemgetter(2)
(d) itemgetter(3)
Answer:
(b) itemgetter(1)

Question 44.
(I) csv.writer work with list/tuple
(II) csv.Dictwriter work with dictionary
(III) csv.DictReader work with list/tuple/dictionary.
(a) (I),(II) – True (III) – False
(b) (I) – True (II), (III) – False
(c) (I),(II),(III) – True
(d) (I),(II),(III) – False
Answer:
(a) (I),(II) – True (III) – False

Question 45.
The additoinal argument fieldnames that are used with csv.DictReader and csv. Dictwriter are called as …………………………
Answer:
dictionary keys

Question 46.
Which function is used to print the data in dictionary format without order?
(a) dictionary
(b) print( )
(c) dict( )
(d) dictprint( )
Answer:
(c) dict( )

Question 47.
Which is a dictionary subclass that saves the order in whcih its contents are added?
(a) orderedDist
(b) SortDist
(c) DistSort
(d) Sorting
Answer:
(a) orderedDist

Question 48.
……………………. is used to remove the ordered Diet.
Answer:
Dist( )

Question 49.
…………………. method writes a row of data into the specified file.
Answer:
writerow( )

Question 50.
The number of parameters in csv.writer( ) …………………….
(a) 2
(b) 3
(c) 4
(d) 5
Answer:
(b) 3

Question 51.
Identify the wrong statement.
(a) The writerow( ) writes one row at a time
(b) The writerows( ) writes all the data at once
(c) No such writerows( ) function in csv
Answer:
(c) No such writerows( ) function in csv

Question 52.
Identify the true statement.
(a) writerow( ) takes 1 dimensional data
(b) writerows( ) takes 2 dimensional data
(c) both are true
(d) both are false
Answer:
(c) both are true

Question 53.
By default, csv files open automatically in ……………………..
Answer:
Excel.

PART – II
II. Answer The Following Questions

Question 1.
What is the syntax for csv.reader( )?
Answer:
The syntax for csv.reader( ) is
where csv.reader(fileobject,delimiter,fmtparams)
file object – passes the path and the mode of the file
delimiter – an optional parameter containing the standard dilects like, | etc can be omitted
fmtparams – optional parameter which help to override the default values of the dialects like skipinitialspace,quoting etc. Can be omitted

PART – III
III. Answer The Following Questions

Question 1.
How will you create a csv file?
Answer:
Creating CSV Normal File
To create a CSV file in Notepad, First open a new file using
File → New or Ctrl +N.
Then enter the data you want the file to contain, separating each value with a comma and each row with a new line.
For example consider the following details
Topic 1,Topic 2,Topic 3
one,two,three
Example 1,Example 2,Example 3
Save this content in a file with the extension .csv . You can then open the same using Microsoft Excel or any other spreadsheet program. Here we have opened using Microsoft Excel. It would create a table of data similar to the following:

Question 2.
How will you create csv file that contains comma with data?
Answer:

To retain the commas in “Address” column, you can enclose the fields in quotation marks.
For example:
RollNo, Name, Address
12101, Nivetha, “Mylapore, Chennai”
12102, Lavanya, “Adyar, Chennai”
12103, Ram, “Gopalapuram, Chennai”
As you can see, only the fields that contain commas are enclosed in quotes. If you open this in MS Excel, It looks like as follows

Question 3.
How will you create csv file that contains double quotes with data?
Answer:
Creating CSV File That contains Double Quotes With Data
If your fields contain double-quotes as part of their data, the internal quotation marks need to be doubled so that they can be interpreted correctly. For Example, given the following data:
Answer:

It should be written in csv file as RollNo, Name, FavoriteSports, Address
12101,Nivetha””” Cricket’”‘”, FootballMylapore chennai 12102, Lavanya,””” Basketball Cricket “””, Adyar chennai 12103, Ram,””” Soccer”””,”” Hockey”””, Gopalapuram chennai
The output will be

Question 4.
How will you create csv file using MS-Excel?
Answer:
Create A CSV File Using Microsoft Excel:
To create a CSV file using Microsoft Excel, launch Excel and then open the file you want to save in CSV format. For example, below is the data contained in our sample Excel worksheet:

Item Name, Cost-Rs, Quantity, Profit
Keyboard,480, 12,1152 ,
Monitor, 5200, 10, 10400
Mouse,200,50,2000
Total Profit = 13552

Question 5.
What are the different formats to create csv files?
Answer:

1. CSV file – data with default delimiter comma (,)
2. CSV file – data with Space at the beginning
3. CSV file – data with quotes
4. CSV file – data with custom Delimiters

Question 6.
Write a program create csv files data with sapces at the beginning?
Answer:
import csv
csv.register_dialect(‘myDialect’,delimiter = 7,skipinitialspace=True)
F=open(‘c:\ \pyprg\ \sample2.csv’,’r’)
reader= csv.reader(F, dialect=’myDialect’)
for row in reader:
print( row)
F.close( )
OUTPUT
[‘Topic 1’, ‘Topic2’, ‘Topic3’]
[‘one’, ‘two’, ‘three’]
[‘Example 1’, ‘Example2’, ‘Example3’]

Question 7.
Write a program to read csv files with custom delimiters?
Answer:
import csv
csv.register_dialect(‘myDialect’, delimiter ‘|’)
with open(‘c:\\pyprg\\sample4.csv’, ‘r’) as
f: reader= csv.reader(f, dialect=’myDialect’)
for row in reader: print(row)
F.close( )
Output
[‘RollNo’, ‘Name’, ‘City’]
[‘12101’, ‘Arun’, ‘Chennai’]
[‘12102’, ‘Meena’, ‘Kovai’]
[‘12103’, ‘Ram’, ‘Nellai’]

Question 8.
Give the syntax for csv.writer( )
Answer:
The syntax for csv.writer( ) is
csv. writerffileobject, delimiter,fmtparams)
where
fileobject : passes the path and the mode of the file.
delimiter : an optional parameter containing the standard dilects like , | etc can be omitted.
fmtparams : optional parameter which help to override the default values of the dialects like skipinitialspace,quoting etc. can be omitted.

Question 9.
Give the program to add new row to the csv file?
Answer:
import csv
row= [‘6’, ‘Sajini’Madurai’]
with open(‘student.csv’, ‘a’) as CF: # append mode to add data at the end
writer= csv.writer(CF)
writer.writerow(row) # writerow( ) method write a single row of data in file
CF.close( )
Output

Question 10.
Give a program for csv file with a line terminator?
import csv
Answer:
Data= [[‘Fruit’, ‘Quantity’], [‘Apple’, ‘5’], [‘Banana’, ‘7’], [‘Mango’, ‘8’]] csv.register_dialect(‘myDialect’, delimiter= ‘|’, lineterminator = ‘\n’) with open(‘c:\\pyprg\ \chl3\\line.csv’, ‘w’) as f:
writer= csv.writer(f, dialect=’myDialect’) writer.writerows(Data)
f.close( )
Output

PART – IV
IV. Answer The Following Questions

Question 1.
Write a program to read a specific column in a file?
Answer:
Read a specific column In a File:
To get the specific columns like only Item Name and profit for the “sampleS.csv” file. Then you have to do the following:
import csv
#opening the csv file which is in different location with read mode
f=open(“c:\ \pyprg\ \chl3sample5.csv”,’r’)
#reading the File with the help of csv.reader( )
readFile=csv.reader(f)
#printing the selected column for col in readFile :
print col[0],col[3]
f.close( )

Question 2.
Write a python program to read a csv file and store it in a list?
Answer:
Read A CSV File And Store It In A List
In this topic you are going to read a CSV file and the contents of the file will be stored as a list. The syntax for storing in the List is
list = [ ] # Start as the empty list
list.append(element) # Use append( ) to add elements
For example all the row values of “sample.csv” file is stored in a list using the following
program
import csv
# other way of declaring the filename
inFile= ‘c:\ \pyprg\\sample.csv’
F=open(inFile,’r’)
reader= csv.reader(F)
# declaring array
arrayValue = [ ]
# displaying the content of the list
for row in reader:
array Value, appendfrow)
print(row)
F.close( )

Question 3.
Write a python program to read a csv file and store a column value in a list for sorting?
Answer:
python file
F=open(inFile;’r’)
# reading the File with the help of csv.reader( )
reader = csv.reader(F)
# skipping the first row(heading) next( reader)
# declaring a list array Value = [ ]
a= int(input (“Enter the column number 1 to 3:-“))
# sorting a particular column-cost for row in reader:
array Value. append(row[a]) array Value.sorif) for row in array Value: print (row)
F.close( )
OUTPUT
Enter the column number 1 to 3:- 2
50
12
10

Question 4.
Write a python program to get data at runtime and write it in a csv file?
Answer:
import csv
with open(‘c:\ \pyprg\ \chl3\\dynamicfile.csv’, ‘w’) as f:
w = csv. writer (f)
ans=’y’
while (ans= =’y’):
name= input(“Name?: “)
date = input(“Date of birth: “)
place = input(“Place: “) w.writerow([name, date, place])
ans=input(“Do you want to enter more y/n?: “)
F=open(‘c:\ \pyprg\ \chl3\\dynamiefde.csv,’r’)
reader = csv.reader(F)
for row in reader:
print(row)
F.close( )
OUTPUT
Name?: Nivethitha
Date of birth: 12/12/2001
Place: Chennai
Do you want to enter more y/n?: y
Name?: Leena
Date of birth: 15/10/2001
Place: Nagercoil
Do you want to enter more y/n?: y
Name?: Padma
Date of birth: 18/08/2001
Place: Kumbakonam
Do you want to enter more y/n?: n
[‘Nivethitha’, ’12/12/2001′, ‘Chennai’]
[ ]
[’Leena’, ’15/10/2001′, ‘Nagercoil’]
[ ]
[‘Padma’, ’18/08/2001′, ‘Kumbakonam’]

You can Download Samacheer Kalvi 9th Social Science Book Solutions Guide Pdf, Tamilnadu State Board help you to revise the complete Syllabus and score more marks in your examinations.

Tamilnadu Samacheer Kalvi 9th Social Science Civics Solutions Chapter 4 Forms of Government

Forms of Government Textual Exercise

I. Fill in the blanks.
1. ……… are the few examples for unitary form of government.
2. The Parliamentary government is also known as ……..
3. In the parliamentary form of government ….. is the leader of majority party.
Answers:
1. England, France
2. cabinet government
3. Prime Minister

II. Fill in the blanks.

9th Social Forms Of Government Question 1.

Answer:

III. Distinguish Between.

Forms Of Government And Democracy Class 9 Samacheer Kalvi Question 1.
Unitary and federal forms of government.
Answer:

Civics Chapter 4 Question 2.
Parliamentary and presidential form of government.
Answer:

IV. Give short note on:

Class 9 Chapter 4 Civics Question 1.
Unitary form of government
Answer:
A unitary system of government or unitary state, is a sovereign state governed as a single entity. The central government is supreme and the administrative divisions exercise only powers that the central government has delegated to them. England, France, Japan and SriLanka are examples of Unitary Form of governments. In a Unitary form of government, all the authority and power is vested in a single centre, whereas in a federal form of government authority and power is distributed between centre and the constituent units. Even in a Unitary form of Government, there might be a lot of decentralisation of authority, but we cannot claim it as a federal system.

V. Answer the following.

Civics Class 9 Chapter 4 Question Answer Question 1.
List out the types of constitution.
Answer:

4 Forms Of Government Question 2.
What are the merits of a federal government?
Answer:
Merits of federal form of government

• Reconciliation of local autonomy with national unity.
• Division of power between centre and states leads to administrative efficiency.
• It gives rise to big states
• Distribution of powers check the despotism of central government.
• More suitable for bigger countries.
• It is good for economic and cultural progress.

Question 3.
Write down the differences between unitary form of government and federal form of
government.
Answer:

VI. Answer in detail.

Question 1.
Write about the merits of unitary form of government.
Answer:
Merits of unitary form of government

• Suitable for small countries.
• There is no conflict of authority and responsibility.
• A unitary government will make prompt decisions and take speedy action.
• A unitary government is less expensive.
• Amendments to the constitution are easy.
• There is unity, uniformity of law, policy and administration.

Question 2.
Write about the presidential form of government and what is the difference between presidential and parliamentary forms of government.
Answer:
The Presidential Form Of Government is also known as non-responsible or non-parliamentary or fixed executive system of government, basically built on the principle of separation of power and is prevalent in the USA, Brazil, Russia and Sri Lanka among others.

The American President is both the head of the State and the head of government. As the head of State, he occupies a ceremonial position. As the head of government, he leads the executive organ of the government.

The President is elected by an electoral college for a fixed tenure of four years. He cannot be removed by the Congress, except by impeachment for a grave unconstitutional act.

The President governs with the help of a cabinet or a smaller body called ‘Kitchen Cabinet’. It is only an advisory body and consists of non-elected departmental secretaries. They are selected and appointed by him, are responsible only to him and can be removed by him any time.

The President and his secretaries are not responsible to the Congress for their acts. They neither possess membership in the Congress, nor attend its sessions.

Differences between presidential and parliamentary forms of government are:

Forms of Government Additional Questions

I. Fill in the blanks.

1. ……. is the main agency of the state.
2. The three organs in government are …….., ……… and ……….
3. ……… is the oldest form of government in the United Kingdom.
4. An example of Fedral form of Government ……..
5. The …… system of government is the one in which the executive is responsible to the legislature for its policies and acts.
6. The …… form of government is prevalent in U.S.A.
7. The President governs with the help of a cabinet (or) a small body called …… in Presidential form of government.
8. An unprecedented development forced the ……… to step down and paved the way for Democracy.
9. Gross National Happiness was first mentioned in the constitution of Bhutan, which was enacted on ……
10. …… and …….. are synonyms, both denoting the exercise of authority in an organization, institution (or) state.
Answers:
1. Government
2. legislature, executive, judiciary
3. Monarchy
4. Argentina
5. Parliamentary
6. Presidential
7. Kitchen Cabinet
8. King Gyanendra.
9. 18^th July 2008
10. Government, Governance

II. Fill up.

Answer:

III. Distinguish the following:

Question 1.
Monarchy and Democracy
Answer:

IV. Answer the following.

Question 1.
What is the meaning of Government?
Answer:
‘Government’ refers to the executive functions of the state. It denotes a body having authority to make and enforce laws applicable to the civil, corporate, religious, academic of other groups.

Question 2.
From where did the term Government was derived?
Answer:
The term Government is derived from Old French ‘governer’, derived from Latin ‘gubernare’ to direct, rule, guide, govern”.

Question 3.
Mention the demerits of Unitary form of Government.
Answer:

• It is not suitable for big countries.
• The central government will have to tackle so many complex problems that lead to administrative delay
• The central government will not concentrate on local problems, local interest and initiative.
• The concentration of powers may pave way for the despotism of the central government.

Question 4.
State the feature of Parliamentary form of governance.
Answer:
Features of parliamentary form of government

• Nominal and Real Executives
• Majority Party Rule
• Collective Responsibility
• Dual Membership
• Leadership of the Prime Minister

Question 5.
State the merits of the Presidential system of government.
Answer:
Merits of the presidential system of government

• Democratic
• Effective Control by the President
• Facilitate decision-making
• State government

Question 6.
Write down the characteristics of good governance.
Answer:
Characteristics of good governance:

• Participation
• Rule Of Law
• Transparency
• Responsiveness
• Consensus Orientation
• Equity
• Effectiveness And Efficiency
• Accountability

V. Answer in detail.

Question 1.
Explain the Federal form of Government.
Answer:
The classification of governments into unitary and federal is based on the nature of relations between the national and the regional governments.

A federal government is one in which powers are divided between the national government and the regional governments by the Constitution itself and both operate in their respective jurisdictions independently. U.S.A, Switzerland, Australia, Canada, Russia, Brazil, Argentina have federal form of governments. In a federal model, the national government is known as the Federal government or the Central government or the Union government and the regional government is known as the state government or the provincial government.

Merits of federal form of government

• Reconciliation of local autonomy with national unity
• Division of power between centre and states leads to administrative efficiency
• It gives rise to big states
• Distribution of powers check the despotism of central government
• More suitable for bigger countries
• It is good for economic and cultural progress

De-merits of federal form of government

• Federal government is weaker when compared to the unitary government.
• Federal government is more expensive
• Provincial tendencies are very common
• Lack of uniformity in Administration
• Threat to national unity
• Distribution of powers between centre and states lead to conflicts
• Double Citizenship
• Rigid constitution cannot be mended easily for changing needs
• The state governments sometimes place hindrances in the foreign policy.

Federal features of the Indian constitution

• Dual Government
• Written Constitution
• Division of Powers
• Supremacy of the Constitution. The Constitution is the supreme law of the land. The laws enacted by the Centre and the states must confirm to its provisions.
• Rigid Constitution
• Independent Judiciary
• Bicameralism

Question 2.
Explain Gross National Happiness.
Answer:
Gross National Happiness is a developing philosophy as well as an ‘index’ which is used to measure the collective happiness in any specific nation.The concept was first mentioned in the constitution of Bhutan, which was enacted on 18 July 2008.

The term ‘Gross National Happiness’ was coined by the fourth king of Bhutan, Jigme Singye Wangchuck, in the 1970s. The GNH’s central tenets are: “Sustainable and equitable socio-economic development; environmental conservation; preservation and promotion of culture; and good governance”. GNH is distinguishable by valuing collective happiness as the goal of governance and by emphasising harmony with nature and traditional values.