GATE EC 2016 Set C Question no 4

GATE 2016 EC SET C QUESTION 4

The integral ∫01[dx/√(1−x)] is equal to _______

Solution

Required Integral,  ∫01[dx/√(1−x)]
= (1-x)[((-1/2)+1)]/[((-1/2)+1)]|01
= 2

Answer to Question No 4 of Set C of GATE 2016 Electronics and Communication Engineering Paper is 2.

GATE 2016 EC Set C Question 5

GATE 2016 EC Set C Question 5

Question

Consider the first order initial value problem y’ = y + 2x – x3 ,  y(0) = 1, (0 <= x < ∞) with exact solution  y( x)=x2 + ex . For x = 0.1, the percentage difference between the exact solution and the solution obtained using a single iteration of the second-order Runge-Kutta method with step size h=0.1 is ___________

Answer : 0.06 to 0.063