The equation sin-1 x – cos-1 x = cos-1 (?3 / 2) has
1) no solution 2) unique solution 3) infinite number of solutions 4) None of the above Solution: (2) unique solution... View Article
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If tan-1 [1 – x] / [1 + x] = 1 / 2 tan-1 x, then the value of x is
1) 1/2 2) 1/√3 3) √3 4) 2 Solution: (2) 1 / √3 Put (1 / 2) tan-1 x =... View Article
If ? and ? are the roots of the equations 6x2 – 5x + 1 = 0, then the value of tan-1 ? + tan-1 ? is
1) 0 2) π/4 3) 1 4) π/2 Solution: (2) π/4 6x2 – 5x + 1 = 0 (α +... View Article
The value of cos [2 tan-1 (-7)] is
1) 49/50 2) – (49/50) 3) 24/25 4) – (24/25) 5) 48/49 Solution: (4) – (24/25) cos [2 tan-1 (-7)]... View Article
If a > b > 0, then the value of tan-1 (a / b) + tan-1 ((a + b) / (a – b))
1) both a and b 2) b but not a 3) a but not b 4) neither a nor b... View Article
The value of sin [sin-1 (1 / 3) + sec-1 (3)] + cos [tan-1 (1 / 2) + tan-1 (2)] is
1) 1 2) 2 3) 3 4) 4 Solution: (1) 1 y = sin [sin-1 (1 / 3) + sec-1... View Article
The number of real solutions of tan-1 ?x (x – 1) + sin-1 ?x2 + x + 1 = ? / 2, is
1) 0 2) 1 3) 2 4) ∞ Solution: (1) 0 The given function is tan-1 √x (x – 1)... View Article
d/dx tan-1 x/√(a2 – x2) =
(1) a/(a2 + x2) (2) 1/√(a2 – x2) (3) -1/(a2 + x2) (4) none of these Solution: Let y =... View Article
If [latex]y=\sin^{-1}\frac{2x}{1+x^{2}}+\sec^{-1}\frac{1+x^{2}}{1-x^{2}}[/latex], then dy/dx =
(1) 4/(1 – x2) (2) 4/(1 + x2) (3) 1/(1 + x2) (4) -4/(1 + x2) Solution: Given y =... View Article
[latex]\frac{d}{dx}\cos^{-1}\left ( \frac{x-x^{-1}}{x+x^{-1}} \right )=[/latex]
(1) -1/(1+x2) (2) 1/(1+x2) (3) -2/(1+x2) (4) 2/(1+x2) Solution: Let y = cos-1 ((x – x-1)/(x + x-1)) = cos-1... View Article
If y = cos-1 [(3 cos x – 4 sin x)/5], then dy/dx =
(1) 0 (2) 1 (3) -1 (4) 1/2 Solution: Given y = cos-1 [(3 cos x – 4 sin x)/5]... View Article
If y = sin (2 sin-1 x), then dy/dx =
(1) (2 – 4 x2)/√(1 – x2) (2) (2 + 4 x2)/√(1 – x2) (3) (2 – 4 x2)/√(1 +... View Article
If y = xsin x, then dy/dx =
(1) xsin x [x cos x log x + sin x]/x (2) xsin x [x cos x log x +... View Article
If xy = yx, then dy/dx =
(1) y (y + x log y)/x(x + y log x) (2) y (y – x log y)/x(x – y... View Article
If xpyq = (x+y)p+q, then dy/dx =
(1) y/x (2) -y/x (3) x/y (4) -x/y Solution: Given xpyq = (x+y)p+q Take log on both sides p log... View Article
If y = (tan x)cot x, then dy/dx =
(1) y cosec2 x (1 – log (tan x)) (2) y cosec2 x (1 + log (tan x)) (3) y... View Article
The derivative of tan-1 {(1 + x)/(1 – x)} with respect to x is
(1) 1 + x2 (2) 1/(1 + x2) (3) -1/(1 + x2) (4) none of these Solution: Let y =... View Article
If y = x2 + xlog x, then dy/dx =
(1) ( x2 + log x . xlog x)/x (2) 2( x2 + log x . xlog x)/x (3) (... View Article
If y = xx, then dy/dx is
(1) xx log ex (2) xx(1 + 1/x) (3) xx(1 + log x) (4) xx log x Solution: Given y... View Article
If x = sin t cos 2t and y = cos t sin 2t, then at t = ?/4, the value of dy/dx is equal to
(1) -1/2 (2) 1/2 (3) -2 (4) 2 Solution: Given x = sin t cos 2t y = cos t... View Article
