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Operation Pawan

Operation Pawan was a military operation undertaken in 1987 by the Indian Peace Keeping Force (IPKF) to take control of the Jaffna Peninsula from... View Article

Election Laws in India

Election law is a discipline falling at the juncture of constitutional law and political science. It researches "the politics of law and the law... View Article

TRIPS Waiver for COVID-19 Vaccine: RSTV- Big Picture

TRIPS Waiver for COVID-19 Vaccine:- Download PDF Here Anchor: Vishal Dahiya Participants: Leena Menghaney, Regional Head, South Asia Access... View Article

26 May 2021: UPSC Exam Comprehensive News Analysis

CNA 26th May 2021:- Download PDF Here TABLE OF CONTENTS A. GS 1 Related GEOGRAPHY 1. Bay of Bengal, fomenting Yaas, hotter than normal for season... View Article

∫[(√tan x) / (sin x cos x)] dx = ….. + c; x ≠ kπ / 2 and tan x > 0

1) (1 / 2 √tan x) 2) √(2 tan x) 3) 2 √(tan x) 4) √tan x Solution: (3) 2 √(tan x)... View Article

∫[f’ (x) / √f (x)] dx = ….. + c; f (x) ≠ 0

1) (1 / 2) √f (x) 2) 2 √f (x) 3) (1 / 2) f (x) 4) 2 f (x) Solution: (2) 2 √f (x)... View Article

∫tan^-1 x dx = …… + c

1) 1 / (1 + x2) 2) x tan-1 x + (1 / 2) log |1 + x2| 3) x tan-1 x + (1 / 2) (tan-1 x / (1 + x2)) 4) x tan-1 x - (1 / 2) log |1 + x2| Solution:... View Article

∫dx / [(x + 1) (√4x + 3)] =

1) tan-1 √4x + 3 + c 2) 3 tan-1 √4x + 3 + c 3) 2 tan-1 √4x + 3 + c 4) 4 tan-1 √4x + 3 + c Solution: (3) 2 tan-1 √4x + 3 + c... View Article

∫(log x)² dx = x [f (x)]² + Ax [f (x) – 1] + c, then

1) f (x) = log x, A = 2 2) f (x) = log x, A = - 2 3) f (x) = - log x, A = 2 4) f (x) = - log x, A = - 2 Solution: (2) f (x) = log x, A = - 2... View Article

∫{(x + 1) / [x (1 + xe^x)²]} dx =

If ∫(x² / √1 – x) dx = p √(1 – x) [3x² + 4x + 8], then the value of p is

1) - 2 / 15 2) 2 / 15 3) 4 / 15 4) None of these Solution: (1) - 2 / 15... View Article

∫{dx / [x (x + 1)]} =

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

∫[(sin^-1 x) / (√1 – x²)] dx =

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

∫(1 / x) log x dx =

1) loge (1 - loge x) + c 2) loge (loge ex - 1) + c 3) log (log x - 1) + c 4) loge (loge x + x) + c 5) log (log x) + c Solution: (5) log (log... View Article

∫{[cos x – sin x] / [1 + 2 sin x cos x]} dx =

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

[latex]\int(\sqrt[3]{x})\left(\sqrt[5]{1+\sqrt[3]{x^{4}}}\right) d x=[/latex]

1) 2) 3) 4) 5) Solution: (3)... View Article

[latex]\int\left(1+x-x^{-1}\right) e^{x+x^{-1}} dx =[/latex]

1) 2) 3) 4) Solution: (4)... View Article

∫sin³ x . cos² x dx =

1) (sin5 x / 5) - (sin3 x / 3) + c 2) (sin5 x / 5) + (sin3 x / 3) + c 3) (cos5 x / 5) - (cos3 x / 3) + c 4) (cos5 x / 5) + (cos3 x / 3) + c... View Article

∫{1 / [1 + cos x + sin x]} dx =

∫x log x dx =

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

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