If f (x) = cos-1 x + cos-1 {(x / 2) + (1 / 2) (?3 – 3x2)} then
1) f (2 / 3) = π / 3 2) f (2 / 3) = 2 cos-1 (2 / 3)... View Article
1) f (2 / 3) = π / 3 2) f (2 / 3) = 2 cos-1 (2 / 3)... View Article
1) f (8π / 9) = e13π/18 2) f (8π / 9) = e5π/18 3) f (- 7π / 4)... View Article
1) √5 / 3 2) 3 / √5 3) 2 / √5 4) √5 / 2 Solution: (2) 3 /... View Article
1) nπ – (π / 4), n ∈ I 2) nπ + (π / 4), n ∈ I 3) 2nπ... View Article
1) π / 3 2) π / 4 3) π / 2 4) π / 6 Solution: (3) π / 2 LHS... View Article
1) 7π / 12 2) 17π / 12 3) 5π / 12 4) π / 12 Solution: (2) 17π / 12 sin-1... View Article
1) 1 2) 0 3) -1 4) 2 Solution: (2) 0 √(2 – √3) / 4 = √4 – 2√3)... View Article
1) 0 2) 1 3) 2 4) 3 Solution: (3) 2 tan-1 (x – 1) + tan-1 x + tan-1... View Article
1) x = 2 – √9 – 2π 2) x = 2 + √9 – 2π 3) x ∈ (2... View Article
1) one solution 2) two solutions 3) three solutions 4) no solution Solution: (2) two solutions tan-1 1 / (2x... View Article
1) one solution 2) two solutions 3) three solutions 4) no solution Solution: (4) no solution Put (1 / 2)... View Article
1) 1 2) 2 3) 3 4) 4 Solution: (2) 2 tan-1 [x + (2 / x)] – tan-1 (4... View Article
(1) anx (log a)n (2) nax log a (3) (ax)n log a (4) ax (log a)n Solution: Given y =... View Article
(1) (e2x + (-1)n e-2x) (2) 2n (e2x + e-2x) (3) 2n (e2x + (-1)n e-2x) (4) none of these... View Article
(1) d2y/dx2 – 2p = 0 (2) d2y/dx2 + y = 0 (3) d2y/dx2 + dy/dx = 0 (4) d2y/dx2... View Article
(1) n2y (2) -y (3) -n2y (4) none of these Solution: Given y =A cos nx + B sin nx... View Article
(1) 4√2/3a (2) 2 (3) 1/12a (4) none of these Solution: Let u = a sin3 t du/dt = 3a... View Article
(1) \(\begin{array}{l}e^{x^{3}}3x^{3}\end{array} \) (2) \(\begin{array}{l}3x^{2}e^{x^{3}}\end{array} \) (3) \(\begin{array}{l}e^{x^{3}}\end{array} \) (4) \(\begin{array}{l}3x^{2}e^{x^{3}}+3x^{2}\end{array} \) Solution: Let \(\begin{array}{l}u= e^{x^{3}}\end{array} \) \(\begin{array}{l}\frac{du}{dx}= e^{x^{3}}3x^{2}\end{array} \)... View Article
(1) 1 (2) 3/2 (3) 2/3 (4) 1/2 Solution: Let u = cos-1 (1-x2)/(1+x2) Put x = tan θ So... View Article
(1) tan x (2) tan2 x (3) -tan x (4) none of these Solution: Let u = sin2x Differentiate w.r.t.x... View Article