ISS 2025 Statistics Paper 1 Solution Questions 21to 25

Answer

ISS 2025 Statistics Paper 1 Solution Questions 21to 25 complete solution with detailed explanation. Question 21 covers finite difference operators, Question 22 explains difference calculus, Question 23 discusses divided differences, Question 24 focuses on Simpson’s and trapezoidal rule, while Question 25 is based on numerical integration using Simpson’s one-third rule.

ISS 2025 Statistics Paper 1 Solution Questions 21to 25

Q. 21 What is 1/(1 − E²) · (abˣ) equal to, where 0 < b < 1 ?

(take the interval of differencing to be unity)

(a) abˣ / (1 − b²)

(b) abˣ / (1 − a²)

(c) abˣ / (1 − a⁴)

(d) abˣ / (1 − b⁴)

Q. 22 What is the value of Δ⁵(1/x) at x = 2 ?

(take the interval of differencing to be unity)

(a) 1

(b) − 1

(c) − 1/21

(d) − 1/42

Q. 23 If the 9th divided difference of f(x) = 1/x based on points xᵢ = ih, 1 ≤ i ≤ 10 is α, then what is the 10th divided difference of f(x) based on points xᵢ = ih, 1 ≤ i ≤ 11 ?

(a) − α / 11h

(b) − α / 10h

(c) α / 11h

(d) α / 10h

Q. 24 The Simpson's one-third rule applied to ∫₀² f(x) dx gives the value 2, where f(1) = 0.5.

If trapezoidal rule is applied, then what is the value of ∫₀² f(x) dx ?

(a) 8

(b) 4

(c) 2

(d) 1

Q. 25 Consider the following table :

x	0	1/4	1/2	3/4	1
f(x)	1	4/5	2/3	4/7	1/2

Simpson's one-third rule with 4 equal intervals is used to approximate the area bounded by the curve f(x) and x-axis from x = 0 to x = 1. What is the approximate value of the area ?

(a) 0.6951

(b) 0.6944

(c) 0.6932

(d) 0.70

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