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If sec^-1 (?1 + x²) + cosec^-1 (?1 + y²) / y + cot^-1 (1 / z) = 3?, then x + y + z =

1) xyz 2) 2xyz 3) xyz2 4) x2yz Solution: (1) xyz sec-1 (√1 + x2) + cosec-1 (√1 + y2)... View Article

The cos^-1 x = ?, (0 < x < 1) and sin^-1 (2x ?1 – x²) + sec^-1 1 / (2x² – 1) = 2? / 3, then tan^-1 (2x) =

1) π/6 2) π/4 3) π/3 4) π/2 Solution: (3) π / 3 cos-1 x = ɑ, (0 < x... View Article

The value of cot (?_n=1²³ cot^-1 (1 + ?_k=1ⁿ 2k)) is

1) 23 / 25 2) 25 / 23 3) 23 / 24 4) 24 / 23 Solution: (2) 25 /... View Article

The principal value of sin^-1 {tan (- 5? / 4)} is

1) π / 4 2) – (π / 4) 3) π / 2 4) – (π / 2) Solution: (4)... View Article

If (tan^-1 x)² + (cot^-1 x)² = 5?² / 8, then x is equal to

1) 0 2) 2 3) 1 4) – 1 5) 2√2 Solution: (4) – 1 (tan-1 x)2 + (cot-1 x)2... View Article

If 5 cos^-1 [1 – x²] / [1 + x²] + 7 sin^-1 2x / [1 + x²] – 4 tan^-1 2x / [1 – x²] – tan^-1 x = 5?, then x =

1) 3 2) -√3 3) √2 4) 2 5) √3 Solution: (5) √3 5 cos-1 [1 – x2] / [1... View Article

sin (2 sin^-1 ?63 / 65) =

1) 2√126 / 65 2) 4√65 / 65 3) 8√63 / 65 4) √63 / 65 Solution: (1) 2√126 /... View Article

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)... 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... 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)... 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)... 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)... 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,... 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... 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)}] Differentiate w.r.t.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... 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... 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... 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... 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... View Article

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