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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) Replace x by 1/x 8 f(1/x) + 6f(x) = 1/x + 5 …(ii)... View Article

If f(x) = 2^{2x – 1} and ∅(x) = – 2^x+ 2x log 2 . If f ‘(x) > ∅’ (x), then

1) 0 < x < 1 2) 0 ≤ x < 1 3) x > 0 4) x ≥ 0 Solution: Given f(x) = 22x – 1 f(x) = 22x/2 f’(x) = (½)22x 2 log 2 =... 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)] ×... 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) = [f{2f(x) + 2}]2 g’(x) = 2(f{2f(x) + 2}) f ‘{2f(x) + 2})... 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+ cos x/sin x) + cos2x/(1+sin... View Article

If x ≠ 0 and y = log_e |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 = log -2x If x> 0, y = log 2x If x <0,... 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 y = 1+x+x2+... (since elog x = x) = 1/(1-x) (infinite... 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 x = ey+x Take log on both sides log x = (y+x) log e... 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 )/(b cos x + a sin x)) = tan-1 b cos x (a/b - tan x)/ b cos 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 is dismissed. The issue of... 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 Research... View Article

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