ISS 2025 Statistics Paper 1 Solution Questions 26 to 30
- Gajender Raaz
- May 28
- 2 min read
ISS 2025 Statistics Paper 1 Solution Questions 26 to 30 complete solution with detailed explanation. Question 26 covers trapezoidal rule error, Question 27 explains Simpson’s one-third and trapezoidal rule concepts, Question 28 discusses Forward Euler method, Question 29 focuses on Picard method, while Question 30 is based on Euler’s numerical solution method.
Q. 26 Trapezoidal rule is used to find the absolute value of error in evaluating ∫ₐᵃ⁺ʰ f(x) dx.
If the absolute value of error is 2/3 · f''(ξ), a < ξ < b, then what is the value of h ?
(a) 2
(b) 3
(c) 4
(d) 8
Q. 27 Consider the following statements :
I. Trapezoidal rule for evaluating ∫ₐᵇ f(x) dx gives exact result for linear polynomial.
II. Trapezoidal rule for evaluating ∫ₐᵇ f(x) dx gives exact result for quadratic polynomial.
III. Simpson's one-third rule for evaluating ∫ₐᵇ f(x) dx gives exact result for cubic polynomial.
IV. Simpson's one-third rule for evaluating ∫ₐᵇ f(x) dx gives exact result for quadratic polynomial.
Which of the statements given above are correct ?
(a) I, III and IV
(b) I and IV only
(c) I and III only
(d) II, III and IV
Q. 28 Forward Euler method is used to find numerical solution y₁ at x = 0.2 with h = 0.2 of the initial value problem dy/dx = − 2xy², y(0) = 1. What is |y(0.2) − y₁| approximately equal to ?
(a) 0.0215
(b) 0.0385
(c) 0.9615
(d) 1
Q. 29 Picard method is used to find approximate solution y⁽¹⁾(x) (first iterate of Picard's approximation) of initial value problem dy/dx = − 2xy², y(0) = 1. What is the value of |y⁽¹⁾(x) − y(x)| at x = 0.2 ?
(a) 0.9915
(b) 0.9615
(c) 0.0015
(d) 0.0005
Q. 30 If y(x) is the solution of dy/dx = 1 + x + y, y(0) = 1 for step h = 0.1 by Euler's method, then y(0.3) is equal to :
(a) 0.963
(b) 1.125
(c) 1.693
(d) 1.963
Answer in Bilingual
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