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If U F X 3 V G X 2 F X Cosx G X Sinx

1) tanx 2) (3 / 2) x cos (x3) cosec (x2) 3) (2 / 3) sin x3 sin x2 4) None of these Solution: (2) (3 / 2) x cos (x3) cosec (x2) u... View Article

1) y’ (1) = 2 / 3 2) y’ (1) = 4 / 3 3) y’’ (1) = - 8 (22 / 7) 4) y’ (1) = - 4 / 3 Solution: (3) y’ (1) = - 8 (22 / 7) x3 - 2x2y2 +... View Article

1) (-∞,∞) 2) (-∞,∞) - {2} 3) (-∞,∞) - {3} 4) (-∞,∞) - {2,3} Solution: (4) (-∞, ∞) - {2, 3} f (x) = sin [|x2 - 5x + 6| / [x2 - 5x... View Article

1) 1 2) e-2x 3) - 2e-2x 4) y = e2x Solution: (3) - 2e-2x y = e2x dy / dx = 2e2x d2y / dx2 = 4e2x dx / dy = 1 / 2e2x = 1 /... View Article

1) y’’ = z 2) y’’ = 2z 3) y’’ + z’’ = 2 (z - y) 4) z’’ = - y Solution: (2) y’’ = 2z y = ex sinx y’ = ex cosx + ex sinx y’ = z + y... View Article

1) (a / e)e-π/2 2) aeπ/2 3) [- 2e-π/2 / a] 4) (a / e)eπ/2 Solution: (3) [- 2e-π/2 / a] √x2 + y2 = aetan^(-1)(y/x) Taking log on... View Article

1) 8 2) 16 3) 32 4) 64 Solution: (1) 8 h (x) = [f (x)2 + g (x)2] h’ (x) = 2 f (x) f’ (x) + 2 g (x) g’ (x) = 2 f (x) g (x) + 2 g... View Article

1) (−∞, ∞) 2) (1, ∞) 3) Z - {0} 4) R − {0} Solution: (4) R − {0} f (x) = x |x| = {x2, when x ≥ 0 and - x2, when x < 0 f’ (x)... View Article

1) ex 2) ex + e^x 3) logx 4) x Solution: (2) ex + e^x ef(x) = logx f-1 (x) = g (x) x = ee^f(x) g (x) = f-1 (x) = ee^x g’... View Article

1) 1 2) 2 3) 3 4) None of these Solution: (3) 3 f (x2) = x3 d [f (x2)] / dx = d [x3] / dx f’ (x2) d [(x2)] / dx = 3x2 f’... View Article

1) - 4 2) 30 3) - 2 4) 8 Solution: (3) - 2 f (x) = x3 + x2 f’ (1) + xf’’ (2) + f’’’ (3) f’ (x) = 3x2 + 2x f’ (1) + f’’ (2) f’’... View Article

1) x2 2) 3x2 3) 2x2 4) None of these Solution: (4) None of these limx→0 (1 + x + [f (x) / x])1/x = e3 = limx→0 (1 + x)3/x =... View Article

1) P(E’)+P(F’) 2) P(E’)-P(F’) 3) P(E’) -P(F) 4) P(E) - P(F’) Solution: Option (3) P(E’) -P(F) P(E’∩F’|G) = P(E’∩F’∩G)/P(G) = [P(G)... View Article

1) 0.8750 2) 0.0875 3) 0.0625 4) 0.0250 Solution: Option (2) 0.0875 Total number of matches played by India = 4 Maximum point in... View Article

1) 16/81 2) 1/81 3) 80/81 4) 65/81 Solution: Option (1) 16/81 The probability that the minimum face value is not less than 2 and the... View Article

1) 4/7 2) 3/4 3) 37/56 4) None of these Solution: Option (3) 37/56 The probability of getting copper coin = (½) (4/7) + (½) (6/8) =... View Article

I. P(A’/B’)= ¾ II. The events A and B are mutually exclusive III. P(A/B) + P(A/B’) = 1 1) I only 2) I and II 3) I and III 4) II and... View Article

1) 0.18 2) 0.35 3) 0.10 4) 0.63 Solution: Option (4) 0.63 Let X be the event of introducing a new product. Given that, P(A) = 0.5,... View Article

1) 8/17 2) 40/153 3) 5/9 4) 4/9 Solution: Option (4) 4/9 The probability of selecting white ball from first bag = 5/9 The... View Article

1) P(AUB) ≥ 2/3 2) ⅙ ≤P(A∩B)≤ 1/2 3) ⅙ ≤ P(A’∩B) ≤1/2 4) All of these Solution: Option (4) All of these (1) P(AUB)≥ max {P(A), P(B)... View Article