You can Download Samacheer Kalvi 11th 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 11th Maths Solutions Chapter 2 Basic Algebra Ex 2.13

Choose the correct or the most suitable questions.

Question 1.
If |x + 2| ≤ 9, then x belongs to
(a) (-∞, -7)
(b) [-11, 7]
(c) (-∞, -7) ∪ [11, ∞)
(d)(-11, 7)
Solution:
(b) [-11, 7]
Hint:
-x – 2 ≤ 9 x + 2 ≤ 9
-x < 9 + 2 = 11 x ≤ 9 – 2 = 7
⇒ x ≥ -11
so x ∈ [-11, 7]

Question 2.
Given that x, y and b are real numbers x < y, b ≥ 0, then ……..
(a) xb < yb (b) xb > yb
(c) xb ≤ vb
(d) xlb ≥ ylb
Solution:
(a) xb < yb
Hint:
Samacheer Kalvi 11th Maths Solutions Chapter 2 Basic Algebra Ex 2.13 1

Question 3.
Samacheer Kalvi 11th Maths Solutions Chapter 2 Basic Algebra Ex 2.13 3
(a) [2, ∞]
(b) (2, ∞)
(c) (-∞, 2)
(d) (-2, ∞)
Solution:
(b) (2, ∞)
Hint:
Samacheer Kalvi 11th Maths Solutions Chapter 2 Basic Algebra Ex 2.13 4

Question 4.
The solution of 5x – 1 < 24 and 5x + 1 > -24 is …….
(a) (4, 5)
(b) (-5, -4)
(c) (-5, 5)
(d) (-5, 4)
Solution:
(c) (-5, 5)
Hint:
Samacheer Kalvi 11th Maths Solutions Chapter 2 Basic Algebra Ex 2.13 5

Samacheer Kalvi 11th Maths Solutions Chapter 2 Basic Algebra Ex 2.13

Question 5.
The solution set of the following inequality |x – 1| ≥ |x – 3| is …….
(a) [0, 2]
(b) (2, ∞)
(c) (0, 2)
(d) (-∞, 2)
Solution:
(b) (2, ∞)

Question 6.
Samacheer Kalvi 11th Maths Solutions Chapter 2 Basic Algebra Ex 2.13 6
(a) 16
(b) 18
(c) 9
(d) 12
Solution:
(b) 18
Hint:
Samacheer Kalvi 11th Maths Solutions Chapter 2 Basic Algebra Ex 2.13 7

Question 7.
Samacheer Kalvi 11th Maths Solutions Chapter 2 Basic Algebra Ex 2.13 8
(a) -2
(b) -8
(c) -4
(d) -9
Solution:
(c) -4
Hint:
Samacheer Kalvi 11th Maths Solutions Chapter 2 Basic Algebra Ex 2.13 9

Question 8.
Samacheer Kalvi 11th Maths Solutions Chapter 2 Basic Algebra Ex 2.13 10
(a) 0.5
(b) 2.5
(c) 1.5
(d) 1.25
Solution:
(a) 0.5
Hint:
Samacheer Kalvi 11th Maths Solutions Chapter 2 Basic Algebra Ex 2.13 11

Question 9.
Samacheer Kalvi 11th Maths Solutions Chapter 2 Basic Algebra Ex 2.13 12
(a) 2
(b) 1
(c) 3
(d) 4
Solution:
(b) 1
Hint:
Samacheer Kalvi 11th Maths Solutions Chapter 2 Basic Algebra Ex 2.13 13

Samacheer Kalvi 11th Maths Solutions Chapter 2 Basic Algebra Ex 2.13

Question 10.
If 3 is the logarithm of 343, then the base is ……
(a) 5
(b) 7
(c) 6
(d) 9
Solution:
(b) 7
Hint.
⇒ logx343 = 3 ⇒ 343 = x3
(.i.e.,) 73 = x3 ⇒ x = 7
⇒ x = 7

Question 11.
Find a so that the sum and product of the roots of the equation 2x2 + (a – 3)x + 3a – 5 = 0 are equal is ……..
(a) 1
(b) 2
(c) 0
(d) 4
Solution:
(b) 2
Hint:
Samacheer Kalvi 11th Maths Solutions Chapter 2 Basic Algebra Ex 2.13 14

Question 12.
If a and b are the roots of the equation x2 – kx + 16 = 0 and satisfy a2 + b2 = 32, then the value of k is ……
(a) 10
(b) -8
(c) (-8, 8)
(d) 6
Solution:
(c) -8, 8
Hint:
a + b = k ….(1) ab = 16 ….(2)
a2 + b2 = (a + b)2 – 2ab = 32 .
k2 – 32 = 32 ⇒ k2 = 64 ⇒ k = ±8

Question 13.
The number of solutions of x2 + |x – 1| = 1 is ………
(a) 1
(b) 0
(c) 2
(d) 3
Solution:
(c) 2
Samacheer Kalvi 11th Maths Solutions Chapter 2 Basic Algebra Ex 2.13 15
We have two solutions 0, 1

Question 14.
The equations whose roots are numerically equal but opposite in sign to the roots of 3x2 – 5x – 7 = 0 is ……
(a) 3x2 – 5x – 7 = 0
(b) 3x2 + 5x – 7 = 0
(c) 3x2 – 5x + 7 = 0
(d) 3x2 + x – 7 = 0
Solution:
(b) 3x2 + 5x – 7 = 0
Hint:
Samacheer Kalvi 11th Maths Solutions Chapter 2 Basic Algebra Ex 2.13 16

Samacheer Kalvi 11th Maths Solutions Chapter 2 Basic Algebra Ex 2.13

Question 15.
If 8 and 2 are the roots of x2 + ax + c = 0 and 3, 3 are the roots of x2 + ax + b = 0, then the roots of the equation x2 + ax + b = 0 are …….
(a) 1, 2
(b) -1, 1
(c) 9, 1
(d) -1, 2
Solution:
(c) 9, 1
Hint:
Sum = 8 + 2 = 10 = -a ⇒ a = -10
Product = 3 × 3 = 9 = b ⇒ b = 9
Now the equation x2 + ax + b = 0
⇒ x2 – 10x + 9 = 0
⇒ (x- 9) (x – 1) = 0
x = 1 or 9

Question 16.
If a and b are the real roots of the equation x2 – kx + c = 0, then the distance
between the points (a, 0) and (b, 0) is ……..
Samacheer Kalvi 11th Maths Solutions Chapter 2 Basic Algebra Ex 2.13 17
Solution:
Samacheer Kalvi 11th Maths Solutions Chapter 2 Basic Algebra Ex 2.13 18
Hint:
a + b = k, ab = c
Samacheer Kalvi 11th Maths Solutions Chapter 2 Basic Algebra Ex 2.13 19

Question 17.
Samacheer Kalvi 11th Maths Solutions Chapter 2 Basic Algebra Ex 2.13 20
(a) 1
(b) 2
(c) 3
(d) 4
Solution:
(c) 3
Samacheer Kalvi 11th Maths Solutions Chapter 2 Basic Algebra Ex 2.13 21

Question 18.
Samacheer Kalvi 11th Maths Solutions Chapter 2 Basic Algebra Ex 2.13 22
(a) -1/2
(b) -2/3
(c) 1/2
(d) 2/3
Solution:
(a) -1/2
Hint:
Samacheer Kalvi 11th Maths Solutions Chapter 2 Basic Algebra Ex 2.13 23

Samacheer Kalvi 11th Maths Solutions Chapter 2 Basic Algebra Ex 2.13

Question 19.
The number of real roots of (x + 3)4 + (x + 5)4 = 16 is ……
(a) 4
(b) 2
(c) 3
(d) 0
Solution:
(a) 4
Hint:
The equation is (x + 3)4 + (x + 5)4 = 16
(x + 3)4 + (x + 5)4 = 24
This is biquadratic equation. It has 4 roots.

Question 20.
The value of log3 11 . log11 13 . log13 15 . log15 27 . log27 81 is …….
(a) 1
(b) 2
(c) 3
(d) 4
Solution:
(d) 4
Solution:
(d) 4
Hint.
Samacheer Kalvi 11th Maths Solutions Chapter 2 Basic Algebra Ex 2.13 50