If X A 1 Cos 3 Theta Y A Sin 3 Theta And D 2 Y Dx 2 Pi 6 A A Then A 1) 27 / 32 2) 32 / 27a 3) 32 / 27 4) 27 / 32 Solution: (2) 32 / 27a dy / dx = (dy / dθ) / (dx / dθ) = [3a sin2 θ cos θ] / [-a3... View Article
D 3 Log 10 Cosec 1 X 4) None of these Solution: (2) (d / dx) (3(log)10 (cosec)–1x) = 3x(log)10 (cosec)–1x ∙ log103 ∙ (d / dx) log10 (cosec–1x) =... View Article
F And G Are Two Differentiable Function And Fog I Identity Function And G A 2 G A B Then F X 1) 2 2) 1 / 2 3) - 2 4) - 1 / 2 Solution: (2) 1 / 2 y = x f (x) = x g (a) = b g’ (a) = 2 f (g (x)) = x [f’ g (x)] = g’ (x) =... View Article
If Two Variables X And Y And X 0 Xy 1 Then Minimum Value Of X Y Is 1) 1 2) 2 3) 2 (1 / 2) 4) 3 (1 / 3) Solution: (2) 2 xy = 1 y = 1 / x x + y = x + (1 / x) ds / dx = [1 - (1 / x2)] = [x2 - 1] /... View Article
If F X F X And F X G X M X F X 2 G X 2 Then 1) 22 2) 11 3) 0 4) 5 Solution: (1) 22 f’’ (x) = f (x) and f’ (x) = g (x) m (x) = [f (x)]2 + [g (x)]2 m’ (x) = 2 f (x) . f’... View Article
If F Dash X 0 And G X 0 X Belongs To R Then 1) f (g (x)) > f (g (x + 1)) 2) f (g (x) < f (g (x + 1)) 3) g (f (x)) ≯ g (f (x + 1)) 4) g (f (x)) > g (f (x - 1)) Solution:... View Article
Approximate Value Of 1 0002 3000 Is 1) 1.2 2) 1.4 3) 1.6 4) 1.8 Solution: (3) 1.6 Let y = f (x) = x3000 x = 1 and δ(x) = 0.0002 x + δx = 1.0002 (dy / dx) = 3000... View Article
The Derivative Of Function F X X 2 1 Sin 2 X Is 1) Even function 2) Odd function 3) Not define 4) Increasing Function Solution: (2) Odd function It is an odd function.... View Article
Derivative Of Sin 1 3x 4x 3 With Respect To Sin 1 X Is 1) 3, |x| < 1 2) 3, |x| ≤ 1 / 2 and -3, 1 / 2 < |x| < 1 3) -3, |x| < 1 4) 3, |x| ≤ 1 / 2 and 3, 1 / 2 < |x| < 1... View Article
If Y F F F X And F 0 0 F 0 1 Then Dy Dx At X 0 1) 0 2) 1 3) –1 4) 2 Solution: (2) 1 (dy / dx)x=0 = f (f (f (x))), dy / dx x sec2 (x / 2) (1 / 2) tan (x / 2) = f’ (f (f (x)). F’... View Article
If F X F X And G X F X And F X F X 2 2 1) 5 2) 10 3) 0 4) 15 Solution: g (x) = f ‘ (x) --- (i) g’ (x) = f’’ (x) = - f (x) ---- (ii) F (x) = [f (x / 2)]2 + [g (x /... View Article
If F X X N Then The Value Of F X Is F 1 F 1 1 Factorial 1) 2n 2) 2n-1 3) 0 4) 1 Solution: (3) 0 f (x) = xn f’ (x) = nxn-1 f’’ (x) = n (n - 1)x2 fn (x) = n (n - 1) (n - 2) ….. 2... View Article
If X X 2 And G X F F X X 20 Then G Dash X 1) 1 2) 0 3) 9 4) 18 Solution: (1) 1 g (x) = f (f (x)) = |f (x) - 2| = ||(x - 2) - 2| = ||x - 2| - 2| = |x - 2 - 2| = |x - 4|... View Article
If X 2e Y 2xye X 23 0 Then Dy Dx 1) 2xey-x + 2y (x + 1) 2) 2xex-y - 3y (x + 1) 3) [2xey-x - 2y (x + 1)] / [x (xey-x + 2)] 4) [2xey-x - y (x + 1)] Solution: (3)... View Article
If F X Ax B And F 0 F X 2 Then F 1 1) 4 2) 2 3) 1 4) –4 Solution: (1) 4 f (x) = Ax + B f' (x) = A as f'(x) = 2 A = 2 and f (0) = B f (0) = 2 B = 2 f (x) = 2x +... View Article
If Y Cos N X Sinnx And Dy Dx N Cos N 1 X Cos B Then B 1) (n - 1) x 2) (n + 1) x 3) nx 4) (1 - n) x Solution: (2) (n + 1) x y = cosn x . sinnx (dy / dx) = n ∙cosn–1 x ∙ (– sinx) ∙ sin... View Article
If A B C D Are Any Four Consecutive Coefficients Of Any Expanded Binomial Then (1) AP (2) GP (3) HP (4) None of these Solution: We know (x+y)n = nC0xn + nC1xn-1y + nC2xn-2y2 + …..nCnyn where a = nC0 , b =... View Article
Let A Be A Positive Number Such That The Arithmetic Mean Of A And 2 Exceeds Their Geometric Mean Be 1 Then The Value Of A Is (1) 3 (2) 5 (3) 9 (4) 8 Solution: AM of a and 2 = (a+2)/2 GM of a and 2 = √(2a) Given AM exceeds GM by 1 So (a+2)/2 - √(2a) = 1... View Article
If The Product Of Three Terms Of Gp If 512 If 8 Added To First And 6 Added To Second Term So That Number May Be In Ap Then The Numbers Are (1) 2,4,8 (2) 4,8,16 (3) 3,6,12 (4) None of these Solution: Let a/r, a, ar be the terms in GP. Then product = (a/r)a(ar) = 512... View Article
If A B C Are In Hp Then For All N N The True Statement Is (1) an + cn < 2bn (2) an + cn > 2bn (3) an + cn = 2bn (4) None of these Solution: Given a,b,c are in HP. Then HM, b =... View Article
