Students can download 12th Business Maths Chapter 5 Numerical Methods Ex 5.3 Questions and Answers, Samacheer Kalvi 12th Business Maths Book Solutions Guide Pdf helps you to revise the complete Tamilnadu State Board New Syllabus and score more marks in your examinations.

Tamilnadu Samacheer Kalvi 12th Business Maths Solutions Chapter 5 Numerical Methods Ex 5.3

Choose the correct answer.

Question 1.
2 y0 = ______
(a) y2 – 2y1 + y0
(b) y2 + 2y1 – y0
(c) y2 + 2y1 + y0
(d) y2 – y1 + 2y0
Answer:
(a) y2 – 2y1 + y0
Hint:
2 y0 = ∆(∆y0) = ∆(y1 – y0) = ∆y1 – ∆y0
= (y2 – y1) – (y1 – y0)
= y2 – 2y1 + y0

Question 2.
∆f(x) = _______
(a) f(x + h)
(b) f(x) – f(x + h)
(c) f(x + h) – f(x)
(d) f(x) – f(x – h)
Answer:
(c) f(x + h) – f(x)
Hint:
∆f(x) = f(x + h) – f(x)

Samacheer Kalvi 12th Business Maths Solutions Chapter 5 Numerical Methods Ex 5.3

Question 3.
E = ______
(a) 1 + ∆
(b) 1 – ∆
(c) 1 + ∇
(d) 1 – ∇
Answer:
(a) 1 + ∆
Hint:
E = 1 + ∆

Question 4.
If h = 1, then ∆(x2) = ________
(a) 2x
(b) 2x – 1
(c) 2x + 1
(d) 1
Answer:
(c) 2x + 1
Hint:
∆(x2) = (x + h)2 – x2 = (x + 1)2 – x2 = 2x + 1

Samacheer Kalvi 12th Business Maths Solutions Chapter 5 Numerical Methods Ex 5.3

Question 5.
If c is a constant then ∆c = ______
(a) c
(b) ∆
(c) ∆2
(d) 0
Answer:
(d) 0

Question 6.
If m and n are positive integers then ∆mn f(x) = _______
(a) ∆m+n f(x)
(b) ∆m f(x)
(c) ∆n f(x)
(d) ∆m-n f(x)
Answer:
(a) ∆m+n f(x)

Samacheer Kalvi 12th Business Maths Solutions Chapter 5 Numerical Methods Ex 5.3

Question 7.
If ‘n’ is a positive integer ∆n [∆-n f(x)] _______
(a) f(2x)
(b) f(x + h)
(c) f(x)
(d) ∆ f(2x)
Answer:
(c) f(x)

Question 8.
E f(x) = _______
(a) f(x – h)
(b) f(x)
(c) f(x + h)
(d) f(x + 2h)
Answer:
(c) f(x + h)

Samacheer Kalvi 12th Business Maths Solutions Chapter 5 Numerical Methods Ex 5.3

Question 9.
∇ = _______
(a) 1 + E
(b) 1 – E
(c) 1 – E-1
(d) 1 + E-1
Answer:
(c) 1 – E-1

Question 10.
∇ f(a) = ______
(a) f(a) + f(a – h)
(b) f(a) – f(a + h)
(c) f(a) – f(a – h)
(d) f(a)
Answer:
(c) f(a) – f(a – h)

Samacheer Kalvi 12th Business Maths Solutions Chapter 5 Numerical Methods Ex 5.3

Question 11.
For the given points (x0 , y0) and (x1, y1) the Lagrange’s formula is ______
Samacheer Kalvi 12th Business Maths Solutions Chapter 5 Numerical Methods Ex 5.3 Q11
Answer:
Samacheer Kalvi 12th Business Maths Solutions Chapter 5 Numerical Methods Ex 5.3 Q11.1

Question 12.
Lagrange’s interpolation formula can be used for ________
(a) equal intervals only
(b) unequal intervals only
(c) both equal and unequal intervals
(d) none of these
Answer:
(c) both equal and unequal intervals

Samacheer Kalvi 12th Business Maths Solutions Chapter 5 Numerical Methods Ex 5.3

Question 13.
If f(x) = x2 + 2x + 2 and the interval of differencing is unity then ∆ f(x) _______
(a) 2x – 3
(b) 2x + 3
(c) x + 3
(d) x – 3
Answer:
(b) 2x + 3
Hint:
f(x) = 2x2 + 2x + 2
h = 1
∆f(x) = (x + 1)2 + 2(x + 1) + 2 – x2 – 2x – 2
= x2 + 2x + 1 +2x + 2 + 2 – x2 – 2x – 2
= 2x + 3

Question 14.
For the given data find the value of ∆3 y0 is _________
Samacheer Kalvi 12th Business Maths Solutions Chapter 5 Numerical Methods Ex 5.3 Q14
(a) 1
(b) 0
(c) 2
(d) -1
Answer:
(b) 0
Hint:
Samacheer Kalvi 12th Business Maths Solutions Chapter 5 Numerical Methods Ex 5.3 Q14.1

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