Archives

24 May 2021: The Hindu Analysis

UPSC Current Affairs Preparation: The Hindu Analysis Watch expert analysis of ‘The Hindu’ dated 24th May 2021. Important news and views to boost... View Article

WTO Agreement on Agriculture (AoA)

The Agreement on Agriculture (AoA) is a World Trade Organisation treaty that focuses on reducing the agricultural support and subsidies given to... View Article

24 May 2021: UPSC Exam Comprehensive News Analysis

CNA 24th May 2021:- Download PDF Here TABLE OF CONTENTS A. GS 1 Related GEOGRAPHY 1. Very severe cyclone Yaas to hit north Odisha coast B. GS 2... View Article

∫{(sin 2x) / (sin² x + 2 cos² x)} dx =

∫{(cos x) / [sin² x (sin x + cos x)]} dx =

[latex]\int \frac{x^{2}-1}{\left(x^{4}+3 x^{2}+1\right) \tan ^{-1}\left(x+\frac{1}{x}\right)} dx=[/latex]

1) tan-1 [x + (1 / x)] + c 2) cot-1 [x + (1 / x)] + c 3) log [x + (1 / x)] + c 4) log (tan-1 [x + (1 / x)]) + c Solution: (4) log (tan-1 [x +... View Article

∫[1 + x – (1 / x)] e^x+(1/x) dx =

1) (x - 1) ex+(1/x) + c 2) xex+(1/x) + c 3) (x + 1) ex+(1/x) + c 4) - xex+(1/x) + c Solution: (2) xex+(1/x) + c... View Article

∫√(1 + sin (x / 4)) dx =

1) 8 [sin (x / 8) + cos (x / 8)] + c 2) 8 [sin (x / 8) - cos (x / 8)] + c 3) 8 [sin (x / 8) - sin (x / 8)] + c 4) (1 / 8) [sin (x / 8) - cos... View Article

∫e^xloga e^x dx =

1) (ax / log ae) + c 2) [ex / (1 + loge a)] + c 3) (ae)x + c 4) [(ae)x / loge ae] + c 5) [axex / logx e] + c Solution: (4) [(ae)x / loge ae]... View Article

∫e^-logx dx =

1) e-logx + c 2) xe-logx + c 3) elogx + c 4) log |x| + c Solution: (4) log |x| + c ∫e-logx dx = ∫x-1 dx = log |x| + c... View Article

∫(1 – cos x) cosec² x dx =

1) tan (x / 2) + c 2) - cot (x / 2) + c 3) 2 tan (x / 2) + c 4) - 2 cot (x / 2) + c Solution: (1) tan (x / 2) + c ∫(1 - cos x) cosec2 x dx =... View Article

∫{1 / (x + x⁵)} dx = f (x) + c, then the value of ∫(x⁴) / (x + x⁵) dx is

1) log x - f (x) + C 2) f (x) + log x + C 3) f (x) - log x + C 4) None of these Solution: (1) log x - f (x) + C... View Article

∫{(cos 4x + 1) / (cot x – tan x)} dx = k cos 4x + c, then

1) k = - 1 / 2 2) k = - 1 / 8 3) k = - 1 / 4 4) None of these Solution: (2) k = - 1 / 8... View Article

If ∫cosec x dx = f (x) + constant, then f (x) =

If f (x) = sin² πx / (1 + π^x), then ∫[f (x) + f (- x)] dx =

1) 0 2) x + C 3) (x / 2) - (cos πx / 2π) + c 4) [1 / (1 + π)] [(cos2 πx / 2π)] + c 5) (x / 2) - (sin 2πx / 4π) + c Solution: (5) (x / 2) -... View Article

Let f be a function such that f (1) = 4 and f ‘ (x) ≥ 2 for 1 ≤ x ≤ 4. How small can f (4) possible be?

1) 8 2) 12 3) 16 4) 2 5) 10 Solution: (5) 10 f’ (x) ≥ 2 f (x) ≥ 2x + c f (1) ≥ 2 * 1 + c 4 ≥ 2 + c f (x) ≥ 2x + 2 f (4) ≥ 2 * 4 + 2 f (4) ≥ 10... View Article

If f ‘ (x) = x + (1 / x), then the value of f(x) is

1) x2 + log x + c 2) x2 / 2 + log x + c 3) x / 2 - log x + c 4) None of these Solution: (2) x2 / 2 + log x + c f ' (x) = x + (1 / x)... View Article

∫√[(x – 1) / (x + 1)] dx =

1) 2 √(x2 + 1) + sin-1 x + c 2) √(x2 - 1) + sin-1 x + c 3) 2 √(x2 - 1) + sin-1 x + c 4) √(x2 - 1) - log |x + √(x2 - 1)| + c Solution: (4)... View Article

∫{(log x – 1) / (1 + (log x)²} dx =

1) x / [(log x)2 + 1] + c 2) [xex / (1 + x2)] + c 3) [x / (x2 + 1)] + c 4) {(log x) / [(log x)2 + 1]} + c Solution: (1) x / [(log x)2 + 1] + c... View Article

∫1 / (1 + cos ax) dx =

1) cot (ax / 2) + c 2) (1 / a) tan (ax / 2) + c 3) (1 / a) (cosec ax - cot ax) + c 4) (1 / a) (cosec ax + cot ax) + c Solution: (2) (1 / a)... View Article

M	T	W	T	F	S	S
					1	2
3	4	5	6	7	8	9
10	11	12	13	14	15	16
17	18	19	20	21	22	23
24	25	26	27	28	29	30
31