Math Chapter Wise

EnglishUP PCS (Pre) 2006

Q341.x 4 cosx sinx lim x 4 π → − π − is equal to:

A–1 B−1/2 C2 D– 2

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EnglishUP PCS (Pre) 2006

Q342.The function f(x) defined by = + = 1/ x 1 f(x) 1 2 f(0) 1 is discontinuous at:

Ax=0 Bx=1 Cx=–1 Dx=2

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EnglishUP PCS (Pre) 2007

Q343.1 x x x x lim(3 4) is equal to –

A3e B4e C3 D4

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EnglishUP PCS (Pre) 2007

Q344.The value of 2 cot x x 0 lim(cosx) → is–

A1/e B1 2 e C1 Dnon-existent

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EnglishUP PCS (Pre) 2008

Q345.If the function ≤ 2 x + 3x + a: x 1 bx + 2: x > 1 f(x) = is differentiable for all real x, then the values of a and b are

A5 and 3 B3 and 5 C3 and 2 D2 and 3

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EnglishUP PCS (Pre) 2008

Q346.If f (3) = 4 and f'(3) = 1, then x 3 xf(3)- 3f(x) lim x - 3 →

A–1 B2 C3 D1

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EnglishUP PCS (Pre) 2008

Q347.If ≠ 2 1 f(x) = sin x, x 0 x f(0) = 0, x =0 then at x = 0 which of the following is true?

Af is continuous and differentiable. Bf is continuous but not differentiable. Cf is neither continuous nor differentiable. Df is differentiable but not continuous.

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EnglishUP PCS (Pre) 2009

Q348.The value of →∞ 1 n x n! lim is n

Ae B1/e Ce2 De–2

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EnglishUP PCS (Pre) 2009

Q349.→ π x 4 2cos x -1 lim equals cotx -1

A1/2 B1/2 2 C1/2 D1

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EnglishUP PCS (Pre) 2009

Q350.If ≤ x + 2,when x 1 f(x) = then 4x -1,when x > 1

Af is discontinuous at x = 1 Bx 1 lim f(x) = 3 → Cf is discontinuous at x = 0 DNone of the above

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EnglishUP PCS (Pre) 2009

Q351.The function e f(x) = log x is

ADiscontinuous at x = 1 BDifferentiable at x = 1 CNot differentiable at x = 1 DNone of the above

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EnglishUP PCS (Pre) 2009

Q352.If u = emx (y–z) y = m sin x, z = cos x then du dx is

Aemx (m3 +1) cos x Bemx/(m+1) cos x Cemx/(m+1) sin x Demx (m2 +1) sin x

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EnglishUP PCS (Pre) 2009

Q353.If sin x 2 f(x) sin x cos x 2 2 π = π + then 1 2 30 f f............f 31 31 31 + + is equal to

A100 B30 C15 D1

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EnglishUP PCS (Pre) 2009

Q354.Value of →∞ x 1 1 1 1 lim + + +....... 1+ n 2+ 2n 3+ 3n n+ nm is

A2 loge2 B2 loge3 Cloge3 Dloge2

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EnglishUP PCS (Pre) 2009

Q355.The value of → tan 2x x π/4 lim (tan x) is

Ae B1/e C1 1 e + D2 1 e

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EnglishUP PCS (Pre) 2009

Q356.A function f is defined as ≠ 3 2 tan x f (x) = for x 0 and f(0) 0 x =. Then

Af is continuous and derivable at x = 0 Bf is continuous but not derivable at x = 0 Cf is neither continuous nor derivable at x = 0 DNone of the above

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EnglishUP PCS (Pre) 2009

Q357.The differential coefficient of 1 2 2x tan 1 x − with respect to 1 2 2x sin 1 x − + is equal to

A() 2 2 1 x 1 x + − B() 2 2 1 x 1 x − + C0 D1

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EnglishGIC Lecturer Exam- 2015

Q358.n lim →∞ 2 2 2 2 1 2 3 n + + +....... 1-n 1-n 1-n 1-n is equal to

A–1/2 B0 C1/2 D1

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EnglishGIC Lecturer Exam- 2015

Q359.→∝ 1 n n n n lim(4 + 5) is equal to

A4 B5 Ce4 De5

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EnglishGIC Lecturer Exam- 2015

Q360.The derivative of sin–1 x with respect to -1 2 cos 1- x is equal to

A2 1 1 x − Btan x Ccot x D1

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