If p(x) be a function defined on R such that p'(x) = p'(1 – x), ∀ x ϵ [0, 1], p(0) = 1 and p(1) = 41. Then, ∫01 p (x) dx = 1) √41 2) 21 3) 41 4) 42 Solution: (2) 21... View Article
If [x] denotes the greatest integer less than or equal to x, then the value of ∫02 [|x – 2| + [x]] dx is 1) 2 2) 3 3) 1 4) 4 5) 3/2 Solution: (2) 3... View Article
If [x] denotes the greatest integer function, the value of ∫01.5 x [x2] dx is 1) 5/4 2) 0 3) 3/2 4) 3/4 Solution: (4) ¾... View Article
The value of ∫01 {[8 log (1 + x)] / [1 + x2]} dx is 1) (π / 8) log 2 2) (π / 2) log 2 3) log 2 4) π log 2 Solution: (4) π log 2... View Article
If [x] denotes the greatest integer less than or equal to x, then the value of ∫-11 (|x| – 2 [x]) dx is 1) 3 2) 2 3) -2 4) -3 Solution: (1) 3... View Article
The value of ∫-22 (1 + 2 sin x) e|x| dx is 1) 0 2) e2 - 1 3) 2 (e2 - 1) 4) 1 Solution: (3) 2 (e2 - 1)... View Article
If [x] is the greatest integer function not greater than x, then ∫011 [x] dx = 1) 45 2) 66 3) 35 4) 55 Solution: (4) 55... View Article
If g (x) = ∫0x cos 4t dt, then g (x + π) = 1) g (x) / g (π) 2) g (x) ± g (π) 3) g (x) . g (π) 4) None of these Solution: (2) g (x) ± g (π)... View Article
∫-ππ sin x [f (cos x)] dx = 1) 2f (π) 2) 2f (2) 3) 2f (1) 4) None of these Solution: (4) None of these... View Article
∫0π/2 {[x sin x cos x] / [cos4 x + sin4 x]}dx = 1) π2 / 4 2) π2 / 8 3) π2 / 16 4) π2 / 32 Solution: (3) π2 / 16... View Article
05 July 2021: UPSC Exam Comprehensive News Analysis CNA 5th July 2021:- Download PDF Here TABLE OF CONTENTS A. GS 1 Related B. GS 2 Related C. GS 3 Related SECURITY 1. IB sounds alert on... View Article
In a bombing attack, there is 50% chance that a bomb will hit the target. In a bombing attack, there is 50% chance that a bomb will hit the target. At least two independent hits are required to destroy the target... View Article
If the lines x+y = a and x-y = b touch the curve y = x2-3x+2 at the points where the curve intersects the x-axis, then a/b is equal to Solution: y -0 = -1(x-1) x+y = 1 ⇒ a = 1 y-0 = x-2 x-y = 2 = b = 2 a/b = 1/2 Answer: 1/2... View Article
