Math Chapter Wise

EnglishJharkhand TGT 2017

Q281.For a>0, b>0, b≠1, (((()))) (((()))) x x 0 a 1 lim b 1 → − = −

Aa/b Blogea Cloge ab De log a log b

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EnglishJharkhand TGT 2017

Q282.If ((()) y z f x y x = + then ((())) ((()) y x y f ' x y x + + = + + = + + = + + =

Ayzx+xzy Bxyz(xy) Cxzx+yzy Dzx + zy

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EnglishJharkhand TGT 2017

Q283.If f(–x)= –f(x) for all x ∈R then the function f is called

Aan even function Ban odd function Cinverse function Didentity function

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EnglishKVS TGT DEC 2017

Q284.If 1 3 x sin (3t 4t) and 1 2 y cos 1 t then dy dx is equal to–

A1/2 B2/5 C3/2 D1/3

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EnglishKVS TGT DEC 2017

Q285.2 x x 1 lim 2x 1 is equal to–

A1 B0 C–1 D1/2

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EnglishKVS TGT DEC 2017

Q286.Derivative of 2 1 1 x 1 tan x w.r.t. 1 tan x is–

A1 B2 C1/2 D1/4

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EnglishKVS TGT DEC 2017

Q287.1 2 d 1 (cos x) dx 1 x Where–

A1 x 1 B1 x 1 C1 x 1 D1 x 1

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EnglishTGT 2011

Q288.Solution of differential equation 2 2 dy x y x y dx = + + = + + = + + = + +

A2 2 2 y x y cx − + = B2 2 2 y x y cx + + = C2 2 2 x x y cy + + = D2 2 2 x x y cy − + =

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EnglishTGT 2011

Q289.The value of n r /n n r 1 1 lim e n →∞ = ∑

Ae Be–1 C1–e De+1

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EnglishTGT 2011

Q290.If f(a) = 2, f'

A–5 B1/5 C5 D0

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EnglishTGT 2011

Q291.If y = x + x + x +........∞ ∞ ∞ then dy = dx

A1 B1/xy C−1/2y x D−1/2y 1

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EnglishTGT 2011

Q292.If () 3 2 3 x sinx cosx f x = 6 -1 0, p p p where P is a constant then the value of () { } 3 d f x dx at x = 0

AP Bp+p2 Cp+p3 DFree from p

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EnglishUP PCS (Pre) 1998

Q293.The value of n 1 1 1 lim 1...... n 1 n 2 2n →∞ + + + + + + + + + + + + + + + + + + is:

A1 Blog 2e Clog e D∞

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EnglishUP PCS (Pre) 1998

Q294.The value of (((()))) (((()))) (((()))) 2 2 2 3/ 2 3/ 2 3/ 2 n 2 2 2 2 n n n lim...... n 1 n 2 2n →∞ + + + + + + + + + + + + + +

A1 B1/2 C3 D1/3

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EnglishUP PCS (Pre) 1998

Q295.If f: R → → → R is defined by ((()) | x |; x 0 f x x k; x 0 ≠ =

Af is not continuous at any point Bfor k = 0, f is continuous everywhere Cfor k = 1, f is continuous everywhere Df is continuous at all points except at x = 0

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EnglishUP PCS (Pre) 1998

Q296.A function with a removable discontinuity at x = a is:

A2 2 x a,x a x a − ≠ − B1 sin,x a | x a | ≠ − C2 2 x a,x a x a − ≠ − Dx a,x a x a + ≠ −

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EnglishUP PCS (Pre) 1998

Q297.If 2 x 0 x 0 1 t dt lim 1 x sinx a t → = − − + + ∫ ∫ then the value of a is:

A2 B3 C4 D5

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EnglishUP PCS (Pre) 1998

Q298.If a function f is continuous for x 0 ≥ and satisfices ((()) x 2 0 1 1 f t dt x xsin 2x cos2x 2 2 = − + + + = − + + + = − + + + = − + + + ∫ then the value of ' f 4 π is:

Aπ – 2 Bπ + 2 C0 D2 – π

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EnglishUP PCS (Pre) 1998

Q299.If f (x) is the integral of 3 2sin x sin 2x,x 0 x − ≠ then ((()) x 0 lim f x → equals:

A1 B0 C–1 D–2

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EnglishUP PCS (Pre) 1998

Q300.The function ((()) sin x, x 0 | x | f x 0, x 0 ≠ =, at x = 0 is:

Adiscontinuous Bcontinuous but not differentiable Ccontinuous and differentiable Ddifferentiable but not continuous

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