Math Chapter Wise

EnglishTGT 2010

Q381.The function 1 x f(x) 2 = is not continuous when x is

A0 B1 C–1 DNone of these

Show answer

EnglishTGT 2010

Q382.Let 1 sinx,x 2x 2 f(x), x 2 − π ≠ π − = π λ = is continuous at x 2 π = then the value of λ

A–1 B1 C0 D2

Show answer

EnglishTGT 2010

Q383.If f(x) is a differentiable function then x a af(x) xf(a) lim x a → −

Aa f'(a) – f(a) Ba f(a) – f'(a) Ca f'(a) + f(a) Da f(a) + f'(a)

Show answer

EnglishTGT 2010

Q384.The function 4 x 3,x 1 f(x) x 3 13 x,x 1 4 2 4 − ≥ = − + < − + < − + < − + < at x =1

Acontinuous and differentiable Bcontinuous and not differentiable Cdiscontinuous and differentiable Ddiscountinuous and not differentiable

Show answer

EnglishTGT 2010

Q385.The function x a 2 sinx 0 x 4 f(x) 2xcotx b, x 4 2 acos2x bsinx, x 2 π + ≤ < + ≤ < + ≤ < + ≤ < π = + ≤ = + ≤ = + ≤ = + ≤ π − < ≤ π − < ≤ π − < ≤ π − < ≤ π is continuous for 0 ≤ x ≤ π then, a, b are

A, 6 12 π B, 6 12 π − C, 3 6 π DNone of these

Show answer

EnglishTGT 2010

Q386.The value of k for which the function 3 2 2 x x 16x 20,x 2 f(x) (x 2) k, x 2 + − + + − + + − + + − + ≠ = − − = may be continuous at x = 2 is

A5 B6 C7 D8

Show answer

EnglishTGT 2009

Q387.Function f:R|{0} → → → R, and 2x 1 2 f(x),x 0 x e 1 = − = − = − = − = − is continuous at x = 0 then defined the value of f(0)

A2 B–1 C0 D1

Show answer

EnglishTGT 2009

Q388.If f(x) = (()) 1 x 1 sin,if x 1, x 1 0, if x 0, − ≠ − = then which one is correct in following options

Af is not differentiable at both x = 0 and x = 1 Bf is differentiable at both x = 0 and x = 1 Cf is differentiable at x = 0, not differentiable at x = 1 Df is differentiable at x = 1, not differentiable at x = 0

Show answer

EnglishTGT 2009

Q389.If y = ((())) ((()))((()) sinx...... sinx ∞ then dy dx =

A() ycot x 1 ylogsin x − B() 2 y cot x 1 ylogsin x − C3 y cot x 1 ylogsin x − DNone of these

Show answer

EnglishTGT 2009

Q390.The value of differentiation of 1 1 cos asin x − with respect to x

A() 1 2 acos acos x x x 1 − B() 1 2 asin a cosec x x x 1 − C() 1 2 acos acosec x x x 1 − DNone of these

Show answer

EnglishTGT 2009

Q391.The value of x 3 Lim 1 x →∞ +

A3 Be Ce3 D3e

Show answer

EnglishTGT 2009

Q392.The value of 0 sin5 lim θ→ θ

A0 B4 C5 D∞

Show answer

EnglishTGT 2005

Q393.Let f be real-valued function such that f (2) = 2 and f' (2) = 1 then 3 f (x) 2 x 2 4t lim x 2 → → − − ∫ ∫ dt is equal to:

A6 B12 C32 DNone of these

Show answer

EnglishTGT 2005

Q394.2 (1) lim 2 1 →∞ − + x is equal to:

A1 B0 C–1 D1/2

Show answer

EnglishTGT 2005

Q395./ x x 0 lim tan x 4 1 → π + is equal to:

A1 B–1 Ce2 De

Show answer

EnglishTGT 2005

Q396.x 2 lim 1 x →∞ + is equal:

Ae B∞ Ce2 D1/e

Show answer

EnglishTGT 2005

Q397.If tan 2 1 2 1 x y 1 x − = + then dy dx is equal to:

A4 1 (1) x + B4 2 (1) x − + C4 –1 (1) x + DNone of these

Show answer

EnglishTGT 2005

Q398.If sin cos tan cos sin 1 x x y x x − − + + = − then the value of dy dx is:

A0 B1/2 C1 DNone of these

Show answer

EnglishTGT 2005

Q399.If ((()) 2 x y x = then the value of dy dx

A() 2 2ln 1 + x x x B() () 2 1 2ln 1 + x x x C()() 2 1 1 2ln 1 − = + x y x x DNone of these

Show answer

EnglishTGT 2005

Q400.If ((()) 2 2x 2 y ae cosx 2sinx 5 − = + − = + − = + − = + − then 2 d y sinx dx equal to

A-1 B1 C0 DNone of these

Show answer