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If tan^-1 (1 / 3) + tan^-1 (3/4) – tan^-1 (x / 3) = 0, then x is equal

1) 7/3 2) 3 3) 11/3 4) 13/3 Solution: (4) 13 / 3 tan-1 (1 / 3) + tan-1 (3/4) - tan-1 (x / 3) = 0 tan-1 (1 / 3) + tan-1 (3 / 4) =... View Article

The solution of tan^-1 x + 2 cot^-1 x = 2? / 3 is

1) - (1/√3) 2) 1/√3 3) -√3 4) √3 Solution: (4) √3 tan-1 x + 2 cot-1 x = 2π / 3 tan-1 x + 2 [(π / 2) - tan-1 x] = 2π / 3 - tan-1... View Article

If ? = sin^-1 (?3 / 2) + sin^-1 (1 / 3) and ? = cos^-1 (?3 / 2) + cos^-1 (1 / 3), then

1) α > β 2) α = β 3) α < β 4) α + β = 2π Solution: (3) α < β α = sin-1 (√3 / 2) + sin-1 (1 / 3) and β = cos-1 (√3 / 2) + cos-1 (1 /... View Article

The simplified expression of sin (tan^-1 x), for any real number x is given by

1) 1 / √1 + x2 2) x / √1 + x2 3) - 1 / √1 + x2 4) - x / √1 + x2 Solution: (2) x / √1 + x2 Let tan-1 x = θ x = tan θ = sin θ / cos... View Article

If sin^-1 (3 / x) + sin^-1 (4 / x) = ? / 2, then x =

1) 3 2) 5 3) 7 4) 11 Solution: (2) 5 sin-1 (3 / x) + sin-1 (4 / x) = π / 2 sin-1 (3x) = cos-1 (4x) sin-1 (3x) = sin-1 (√x2 - 16 / x) 3 / x =... View Article

The value of cot (cosec^-1 (5 / 3) + tan^-1 (2 / 3)) is

1) 5/17 2) 6/17 3) 3/17 4) 4/17 Solution: (2) 6 / 17 Let (cosec-1 (5 / 3) = θ, tan-1 (2 / 3) = ɸ cosec θ = 5 / 3 and tan ɸ = 2 /... View Article

If 0 < x < 1, then ?1 + x² [{x cos (cot^-1 x)} + sin (cot^-1 x)}² – 1]^½ =

1) x / √1 + x2 2) x 3) x √1 + x2 4) √1 + x2 Solution: (3) x √1 + x2 0 < x < 1 (cot-1 x) = θ cot θ = x sin θ = 1 / √1 + x2... View Article

The derivative of F[f{?(x)}] is

(1) F’[f{φ(x)}] (2) F’[f{φ(x)}] f’{φ(x)} (3) F’[f{φ(x)}] f’{φ(x)} φ’(x) (4) none of these Solution: Let y = F[f{φ(x)}]... View Article

The differential coefficient of f(log x) when f(x) = log x is

(1) x log x (2) x/log x (3) 1/x log x (4) log x/x Solution: Given f(x) = log x f(log x ) = log log x Differentiate w.r.t.x... View Article

Let f and g be differentiable function satisfying g’(a) = 2, g(a) = b and fog = I(Identity function). Then f’(b) is equal to

(1) 1/2 (2) 2/3 (3) 2 (4) none of these Solution: Given fog = I(identity function) So f(g(x)) = x Differentiate w.r.t.x... View Article

Let g(x) be the inverse of a function f(x) and f’(x) = 1/(1+x³), then g’(x) is equal to

1) 1/(1 + {f(x)}3) 2) (1 + {f(x)}3) 3) 1/(1 + {g(x)}3) 4) 1 + {g(x)}3 Solution: Given g(x) is the inverse of a function f(x). So... View Article

Let g(x) be the inverse of an invertible function f(x) which is differentiable at x = c, then g’(f(c)) equals

(1) f’(c) (2) 1/f’(c) (3) f(c) (4) None of these Solution: gof(x)) = I(x) (I(x) is the identity function since g(x) is the inverse... View Article

If x³ + 8xy + y³ = 64, then dy/dx =

(1) -(3x2 + 8y)/(8x + 3y2) (2) (3x2 + 8y)/(8x + 3y2) (3) (3x + 8y)/(8x2 + 3y) (4) none of these Solution: Given x3 + 8xy + y3 = 64... View Article

If sin² x + 2 cos y + xy = 0, then dy/dx =

(1) (y + 2 sin x)/(2 sin y + x) (2) (y + sin 2x)/(2 sin y - x) (3) (y + sin 2x)/( sin y + x) (4) none of these Solution: Given... View Article

If sin (xy) + x/y = x² -y, then dy/dx =

(1) y(2xy -x2 cos xy -1)/(xy2 cos xy - x + y2) (2) (2xy -y2 cos xy -1)/(xy2 cos xy - x + y2) (3) y(2xy -y2 cos xy -1)/(xy2 cos xy - x + y2)... View Article

If y sec x + tan x+ x²y = 0, then dy/dx =

(1) (2xy + sec2x + y sec x tan x )/(x2 + sec x) (2) (2xy + sec2x sec x tan x )/(x2 + sec x) (3) -(2xy + sec2x + y sec x tan x )/(x2 + sec... View Article

If tan (x+y) + tan (x-y) = 1, then dy/dx =

(1) [sec2(x+y) + sec2(x-y)]/(sec2 (x+y) - sec2(x-y)) (2) [sec2(x+y) + sec2(x-y)]/(sec2 (x-y) - sec2(x+y)) (3) [sec2(x+y) -... View Article

If x = 2 cos t – cos 2t, y = 2 sin t – sin 2t, then at t = ?/4, dy/dx

(1) (√2+1) (2) √(2-1) (3) √(2+1)/2 (4) none of these Solution: Given x = 2 cos t - cos 2t Differentiate w.r.t.t dx/dt = -2 sin t... View Article

x?(1+y) + y?(1+x) = 0, then dy/dx =

(1) 1+x (2) (1+x)-2 (3) -(1+x)-1 (4) -(1+x)-2 Solution: Given x√(1+y) + y√(1+x) = 0 x√(1+y) = -y√(1+x) Squaring both sides... View Article

If y = (¼) u⁴, u = (?)x³ + 5, then dy/dx

(1) (x2/27)(2x3 + 15)3 (2) (2x/27)(2x3 + 5)3 (3) (2x2/27)(2x3 + 15)3 (4) none of these Solution: Given y = (¼) u4 u = (⅔)x3 + 5... View Article

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