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If F X A X B X A B 2x Then F 0

1) 2) 3) 4) None of these Solution: (2)... View Article

Let F X X 2 Xg 1 G 2 And G X X 2 X F 2 F 3 Then

1) f’ (1) = 4 + f’ (2) 2) g’ (2) = g’ (1) + 4 3) g’’ (2) + f’ (3) = 8 4) None of these Solution: f (x) = x2 + xg'(1) + g''(2)... View Article

If F X Y F X F Y And F X Y Are In Ap For All X Y And F 0 0 Then

1) f(3) = f(−3) 2) f(3) + f(−3) = 0 3) f’(2) + f’(−2) = 0 4) f'(2) = f'(2) Solution: (3) f’(2) + f’(−2) = 0 f (x − y), f (x), f... View Article

The Values Of X Satisfying D Cosx A Dx Sin 2x Are

1) (3nπ / 2) 2) (3nπ / 4) 3) (2nπ / 3) 4) None of these Solution: (3) (2nπ / 3) d [cosx + a] / dx = sin 2x - sinx = sin2x sin x... View Article

Let F X Be A Polynomial Of The Second Degree

1) A.P 2) G.P 3) H.P 4) None of these Solution: (1) A.P Let f (x) = ax2 + bx + c f (1) = a + b + c f (-1) = a - b + c f (1) = f... View Article

If Xy Xe X Y 6 Then Dy Dx

1) [x - y] / [x (1 + loge x)] 2) [1 + x - y] / [x (1 + loge x)] 3) y / [x (1 + loge x)] 4) None of these Solution: (2) [1 + x - y] /... View Article

If X Y Y X 1 Then Dy Dx Is

1) - [y (y + x log y) / x (y log x + x)] 2) [y (x + y log x) / x (y + x log y)] 3) [y (y + x log y) / x (y log x + x)] 4) None of these... View Article

If Y Log X X 2 1 X X 2 1 Then

1) 2 [(1 / 3√3) - (1 / 5√5)] 2) 2 [(1 / 3√3) + (1 / 5√5)] 3) [(1 / 3√3) - (1 / 5√5)] 4) None of these Solution: (1) 2 [(1 / 3√3) - (1... View Article

If Y Sin 1 Sin Alpha Sin X 1 Cos Alpha Sin X Then Y 0 Is

1) 1 2) 2 sin α 3) tan α 4) sin α / [1 - cos α] Solution: (4) sin α / [1 - cos α]... View Article

If F X X Then

, then 1) f(x) is continuous on R 2) f(x) is continuous on R but is not differentiable on R 3) f(x) is discontinuous at every integer 4) None... View Article

If X 1 T T 3 Y 3 2t 2 2 T Satisfying

1) x2 / [1 + x2] 2) [x2 + 1] / x2 3) x + (1 / x) 4) x Solution: (4) x x = [1 + t] / t3 dx / dt = [t3 - 4 (t) 3t2] / t6 = -... View Article

If Y X N Nx 1 Log X N Then Value Of Y N Is Given By

1) 1 / n 2) (1 / n)n 3) [n2 + 1] / n 4) (1 / n)n ([n2 + 1] / n) Solution: (3) [n2 + 1] / n y = (x / n)nx (1 + log (x / n)) log y... View Article

Let F X X 1 X 24 10 X 1 A X 26

1) 0 2) 1 / √(x - 1) 3) 2√(x - 1) - 5 4) None of these Solution: (1) 0 f (x) = √(x – 1) + √{x + 24 – 10√(x – 1)} = √(x – 1) +... View Article

If F X X 1 X Then F E Is

1) - e (1/e-3) 2) e1/e 3) e1/-2 4) None of these Solution: (1) - e (1/e-3) f (x) = x1/x log f (x) = (1 / x) log x (1 / f (x))... View Article

D Sin 2 Cot 1 1 X 1 X Dx

1) 0 2) -1 / 2 3) 1 / 2 4) –1 Solution: (2) -1 / 2 y = [sin2 cot-1 √(1 + x) / (1 - x)] Let cot θ = √(1 + x) / (1 - x) cot2 θ = (1 + x) /... View Article

If F X Log Cos Tanx Log Tanx Cotx 1 Tan 1 X Root 4 X 2 Then F 1 Is

1) 0 2) – 2 3) 1 / √3 4) √3 Solution: (3) 1 / √3... View Article

If F 3 2 Then Lim H 0 F 3 H 2 F 3 H 2 2h 2 Is

1) 5 2) 1/5 3) 2 4) None of these Solution: limh→0 [f (3 + h2) - f (3 - h2)] / 2h2 = limh→0 [f’ (3 + h2) * 2h + 2h f (3 - h2)]... View Article

If Y 1 X 1 X 2 1 X 2n Then Dy Dx At X 0 Is

1) 1 2) –1 3) 0 4) None of these Solution: (1) 1 y = (1 + x) (1 + x2) …… (1 + x2n) Taking log on both sides, ln y = ln (1 + x) +... View Article

If G X Is A Polynomial Such That G X G Y G X G Y G Xy 2

1) 2 2) 3 3) 4 4) None of these Solution: (3) 4 g (x) g (y) = g (x) + g (y) + g (xy) - 2 g (2) + 1 + g (2) - 2 5 g (1) = 8 + g... View Article

If F X 1 X N Then The Value Of F 0 F 0 F 0 2 F 0 N Is

1) n 2) 2n 3) 2n – 1 4) None of these Solution: (2) 2n f (x) = (1 + x)n f’ (x) = n (1 + x)n-1 f’’ (x) = n (n - 1) (1 + x)n-2... View Article

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