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
The value of ∫02π [dx / (esinx + 1)] is 1) π 2) 0 3) 2π 4) π/2 Solution: (1) π... 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
The value of ∫0π/2 [dx / (1 + tan3 x)] is 1) π 2) 0 3) 2π 4) π/4 Solution: (4) π/4... 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
Let the vectors [latex]vec{a}[/latex], [latex]vec{b}[/latex], [latex]vec{c}[/latex] such that [latex]left |vec{a} right | = 2[/latex], [latex]left |vec{b} right | = 4[/latex], and [latex]left |vec{c} right | = 4[/latex]. Let the vectors is : Solution: ⇒ ⇒ ⇒ ⇒ = √(a2+b2+c2 +2a.b-2b.c-2a.c) = √(4+16+16) = 6 Answer: 6... View Article
The coefficient of x4 in the expansion of (1+x+x2+x3)6 in powers of x, is Solution: (1+x+x2+x3)n = (1+x)n(1+x2)n (1+x+x2+x3)6= (1+x)6(1+x2)6 Coefficient of x4 ⇒ nC0 nC2+ nC2. nC1+ nC4. nC6 = 6C0 6C2+ 6C2. 6C1+... View Article
Let A = {a,b,c} and B = {1,2,3,4}. Then the number of elements in the set C = {f : A → B 2∈ f(A)and f is not one-one} is Solution: C = {f : A → B 2 ∈ f(A) and f is not one-one} Case-I : If f(x) = 2 ∀ x∈ A, then number of function = 1 Case-II... View Article
Which of the following points lies on the tangent to the curve 4x3ey+x4ey+2√(y+1) = 3 at the point (1,0)? 1) (2,6) 2) (2,2) 3) (-2,6) 4) (-2,4) Solution: 4x3ey+x4eyy’ +2y’/2√(y+1) = 0 At (1,0) 4+y’+(2y’/2) = 0... View Article
