Latest Posts

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 \(\begin{array}{l}p^{\prime}(x)=p^{\prime}(1-x) \quad \forall x \in[0,1]\\ \text { Integrate both... View Article

The value of ∫₀^π sin⁵⁰ x . cos⁴⁹ x dx is

1) 0 2) π/4 3) π/2 4) 1 Solution: (1) 0 \(\begin{array}{l}I= \int_{0}^{\pi} \sin ^{50} x \cos ^{49} x d... View Article

∫_π^16π |sin x| dx =

1) 0 2) 32 3) 30 4) 28 Solution: (3) 30 \(\begin{array}{l}I =\int_{\pi}^{16 \pi}|\sin x| d x \\ =15 \int_{0}^{\pi}|\sin... 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 \(\begin{array}{l}\int_{0}^{1}(|x-z|+[x]) d x+\int_{1}^{x}(|x-z|+[x]) d x \\ =\int_{0}^{1}(2-x+0)... View Article

The value of ∫₀⁴ |x – 1| dx is

1) 5/2 2) 5 3) 4 4) 1 Solution: (2) 5 \(\begin{array}{l}\begin{array}{l} \int_{0}^{4}|x-1| d x \\ \int_{0}^{1}(1-x) d x+\int_{1}^{4}(x-1) d... View Article

If [x] denotes the greatest integer function, the value of ∫₀^1.5 x [x²] dx is

1) 5/4 2) 0 3) 3/2 4) 3/4 Solution: (4) ¾ \(\begin{array}{l}\int_{0}^{1.5} x\left[x^{2}\right] d x \\ =\int_{0}^{1} x\left[x^{2}\right] d x+\int_{1}^{\sqrt{2}}... 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:... 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 \(\begin{array}{l}I =\int_{-1}^{1}(|x|-2[x]) d x \\ =\int_{-1}^{0}(|x|-2[x]) d x+\int_{0}^{1}(|x|-2[x]) d... 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) \(\begin{array}{l}I... 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 \(\begin{array}{l}\begin{array}{l} =\int_{0}^{11}[x] d x \\ =\int_{0}^{1}[x] d x+\int_{1}^{2}[x] d... View Article

∫₀^2π |sin x| dx =

1) 2 2) √3 3) 4 4) 0 Solution: (3) 4 \(\begin{array}{l}I =\int_{0}^{2 \pi}|\sin x| d x \\ =\int_{0}^{\pi} \sin... View Article

The value of ∫₀^2π [dx / (e^sinx + 1)] is

1) π 2) 0 3) 2π 4) π/2 Solution: (1) π \(\begin{array}{l}I =\int_{0}^{2 \pi} \frac{d x}{e^{\sin x}+1} \\ I =\int_{0}^{2... View Article

If g (x) = ∫₀^x cos 4t dt, then g (x + π) =

1) g (x) / g (π) 2) g (x) ± g (π) 3) g (x) . g (π) 4) None... View Article

∫_-π^π sin x [f (cos x)] dx =

1) 2f (π) 2) 2f (2) 3) 2f (1) 4) None of these Solution: (4) None of these \(\begin{array}{l}I =\int_{-\pi}^{\pi}... View Article

∫₀^π/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 /... View Article

The value of ∫₀^π/2 [dx / (1 + tan³ x)] is

1) π 2) 0 3) 2π 4) π/4 Solution: (4) π/4 \(\begin{array}{l}I =\int_{0}^{\frac{\pi}{2}} \frac{d x}{1+\tan ^{3} x} d x \\... View Article

∫₀^π √[(1 + cos 2x) / 2] dx =

1) 0 2) 2 3) 4 4) -2 Solution: (2) 2 \(\begin{array}{l}I =\int_{0}^{\pi} \sqrt{\frac{1+\cos 2 x}{2}}=\int_{0}^{\pi}|\cos x| d x \\... 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... 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... 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... View Article

«
1
…
2,394
2,395
2,396
2,397
2,398
…
5,472
»