Math Chapter Wise

EnglishTGT 2005

Q401.If ((()) y a 1 cos, = + θ = + θ = + θ = + θ ((()) x a sin = θ + θ = θ + θ = θ + θ = θ + θ then 2 d y dx equals to if 2 π θ =

A-1/a B-1 C0 DNone of these

Show answer

EnglishTGT 2005

Q402.If 1 1 logsin x logcos x y e;0 x 1 e − − = + < < = + < < = + < < = + < < then

Ay1=0 By2=5 Cy1 does not exist Dy1=y2

Show answer

EnglishTGT 2005

Q403.The function ((()) 1 sin, x 0 f x x k, x 0 ≠ = make continuous at x = 0 for what value of k

A8 B1 C-1 DNone of these

Show answer

EnglishTGT 2005

Q404.Function ((()) 1: x 1 f x x: 1 x 1 1: x 1 − < − − < − − < − − < − = − − ≤ = − − ≤ = − − ≤ = − − ≤ > are continuous

AAt x =1 but not at x = –1 BAt x = –1 but not at x = 1 CBoth at x = 1 and x = –1 DNot at both x = 1 and x = –1

Show answer

EnglishTGT 2005

Q405.If [.] represent the Greatest Integer function and if ((())) 2 f x tan x = then

A() 0 lim → x f x does not exists Bf(x) is continuous at x = 0 Cf(x) is not differentiable at x = 0 Df(0) = 1

Show answer

EnglishTGT 2005

Q406.Function ((()) 3 x 1, 1 x f x x 1, x 1 − < < ∞ − < < ∞ − < < ∞ − < < ∞ = − −∞ < ≤ − −∞ < ≤ − −∞ < ≤ − −∞ < ≤ at x = 1 then

AContinuous and differentiable BContinuous and non-differentiable CDiscontinuous and differentiable DContinuous and differentiable both

Show answer

EnglishTGT 2005

Q407.If y log x,x 0 = ≠ = ≠ then the value of dy dx

A1/|x| B1/x C1/–x DDoes not exist

Show answer

EnglishTGT 2005

Q408.What will be the value of p when the function (()) (((()))) 3 x 2 4 1 f x x x sin log 1 p 3 − = + x≠0 = 12(log 4)3,x=0 is continuous at x = 0

A1 B2 C3 DNone of these

Show answer

EnglishTGT 2005

Q409.Differential coefficient of sec tan-1 x

A() 2 1+ x B2 1+ x x C2 1 − + x D2 1+ x

Show answer

EnglishTGT 2005

Q410.If y sinx sinx sinx.......... = + + + = + + + = + + + = + + + then the value of dy dx

A2 1 cos y x − Bcos 2 1 x y − C2 1 cos x y − Dcos 2 1 y x −

Show answer

EnglishTGT 2005

Q411.If x 1 y y 1 x 0 + + + = + + + = + + + = + + + = then dy dx equals to

A( )2/1/ 1+ x B( )2/-1/ 1+ x C( )/1/ 1+ x DNone of these

Show answer

EnglishTGT 2004

Q412.The least integral values of x which satisfy the equation x 3 2 x 1 4 is − + + = − + + = − + + = − + + =:

A–1 B–2 C1 D2

Show answer

EnglishTGT 2004

Q413.If f(x) be a quadratic expression which is positive for all x, and if g(x) = 2 df d f f(x) + dx dx + then for any real x

Ag (x) < 0 Bg (x) > 0 Cg (x) ≤ 0 Dg (x) ≥ 0

Show answer

EnglishTGT 2004

Q414.The value of the limit given by - x 2 2x lim cos x π → π is

A2 B4 C– 1 2 D–2

Show answer

EnglishTGT 2004

Q415.If 2a a 0 0 f(x)dx = 2 f(x)dx ∫ ∫ ∫ ∫, then

Af(x) is even Bf(x) is odd Cf(x) is periodic Df(2a–x) = f (x)

Show answer

EnglishTGT 2004

Q416.If xy = ex–y then dy dx is equal to

Ae 1 1 log + x B2 e 1 (1 log) + x Ce 2 e log (1 log) + x De log (1 log) + x

Show answer

EnglishTGT 2004

Q417.If x 0 x sin 3 lim k x → =, then the value of k is

A9 B3 C1/3 D1

Show answer

EnglishTGT 2004

Q418.Let f be a strictly increasing and differentiable function. Then 2 x 0 f(x)-f (x) lim f(x) - f(0) → equals–

A1 B2 C0 D–1

Show answer

EnglishTGT 2004

Q419.If n is a non-zero integer and (())) ((())) ((()) 2 x 0 sin nx a n nx tan x lim 0 x → − − = then a equal

A1/n B0 C(n 1) n + D1 n +

Show answer

EnglishTGT 2004

Q420.The integer n for which (()))(((()))) x n x 0 cosx 1 cosx e lim x → − − is a finite non-zero number is

A1 B2 C3 D4

Show answer