If x2 + y2 = t + 1/t and x4 + y4 = t2 + 1/t2, then dy/dx is equal to
1) y/x 2) – (y/x) 3) x/y 4) – 1/x3y Solution: Given x2 + y2 = t + 1/t x4... View Article
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If 8 f(x) + 6f(1/x) = x + 5 and y = x2 f(x), then dy/dx at x = – 1 is equal to
1) 0 2) 1/14 3) – (1/14) 4) 1 Solution: Given 8 f(x) + 6f(1/x) = x + 5 …(i)... View Article
If f(x) = 22x – 1 and ∅(x) = – 2x + 2x log 2 . If f ‘(x) > ∅’ (x), then
1) 0 < x < 1 2) 0 ≤ x < 1 3) x > 0 4) x ≥ 0... View Article
If y = sin-1√(1-x), then dy/dx is equal to
(1) 1/√(1-x) (2) -1/2√(1-x) (3) 1/√x (4) -1/2√x√(1-x) Solution: y = sin-1√(1-x) Differentiate w.r.t.x dy/dx = [1/√1-(1-x)] × (1/2√(1-x)) ×... View Article
If f : (–1, 1) → R be a differentiable function with f(0) = – 1 and f ‘(0) = 1. Let g(x) = [f{2f(x) + 2}]2. Then, g'(0) is equal to
1) 4 2) –4 3) 0 4) –2 Solution: Given f(0) = – 1 and f ‘(0) = 1 g(x)... View Article
If f(x) = sin2x/(1+ cot x) + cos2x/(1+tan x), then f’(π/4) is equal to
(1) √3 (2) 1/√3 (3) 0 (4) -√3 Solution: Given f(x) = sin2x/(1+ cot x) + cos2x/(1+tan x) = sin2x/(1+... View Article
If x ≠ 0 and y = loge |2x|, then dy/dx is equal to
1) 1/x 2) -1/x 3) ± 1/2x 4) None of these Solution: y = loge |2x| If x <0, y... View Article
If [latex]y = e^{log_{e}(1+x+x^{2}+…)}[/latex], then dy/dx is equal to
(1) 1/(1+x)2 (2) 1/(1-x)2 (3) -1/(1+x)2 (4) -1/(1-x)2 Solution: Given \(\begin{array}{l}y = e^{log_{e}(1+x+x^{2}+…)}\end{array} \) y = 1+x+x2+… (since elog x... View Article
If [latex]x=e^{y+e^{y+e^{y+…}}}[/latex], then dy/dx is equal to
(1) 1/x (2) (1-x)/x (3) x/(1+x) (4) none of these Solution: Given \(\begin{array}{l}x=e^{y+e^{y+e^{y+…}}}\end{array} \) x = ey+x Take log on... View Article
If y = tan-1 ( a cos x – b sin x )/(b cos x + a sin x),then dy/dx is equal to
(1) 2 (2) 0 (3) -1 (4) a/b Solution: y = tan-1 (( a cos x – b sin x... View Article
Curative Petition
A curative petition is a petition which requests the court to review its own decision even after a review petition... View Article
Raisina Dialogue 2024
The Raisina Dialogue is an annual Geo-political event organised by the Ministry of External Affairs in collaboration with the Observer... View Article
27 Jan 2021: The Hindu Analysis
UPSC Current Affairs Preparation: The Hindu Analysis Watch expert analysis of ‘The Hindu’ dated 27th January 2021. Important news and... View Article
27 Jan 2021: UPSC Exam Comprehensive News Analysis
CNA 27 Jan 2021:- Download PDF Here TABLE OF CONTENTS A. GS 1 Related B. GS 2 Related INTERNATIONAL RELATIONS... View Article
Express 140 as a product of its prime factor.
Answer: A prime number has exactly two factors and is a positive integer. If p is a prime number, then... View Article
One Volt is equal to (1) 1 Joule (2) 1 Newton/Coulomb (3) 1 Joule/Coulomb (4) 1 Coulomb/Newton
Answer: (3) 1 Joule/Coulomb One volt is characterized as the electrical potential difference between two points of a conducting wire... View Article
Using Euclid division algorithm find HCF of 867 and 255.
Answer: 51 According to Euclid’s Division Lemma if we have two positive integers a and b, then there exist unique... View Article
Write the difference between epihydrophily and hypohydrophily.
Answer: The difference between epihydrophily and hypohydrophily are tabulated below. Epihydrophily Hypohydrophily When the pollination occurs at the water surface,... View Article
The animals found in a particular region is called as (1) Flora (2) Fauna (3) Species (4) Both A and B
Answer: (2) Fauna The term fauna represents all the animal species found in a particular region at a particular time.... View Article
Give examples of combination reactions.
Answer: A chemical reaction is in which the bonds are broken within reactant molecules, and new bonds are formed within... View Article
