Math Chapter Wise

EnglishGIC Lecturer Exam- 2015

Q361.Which one of the following is the differential equation of the system of circles touching the y- axis

A2 2 dy x + y - 2xy = 0 dx B2 2 dy x - y + 2xy = 0 dx C2 2 dy x + y + 2xy = 0 dx D2 2 dy x - y - 2xy = 0 dx

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EnglishGIC Lecturer Exam- 2015

Q362.If ey =xy, then value of dy dx is equal to

Axey Bxy/y -1 Cy/x(y +1) Dy/x(y -1)

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EnglishGIC Lecturer Exam- 2015

Q363.If 3 y x,x R, = ∈∈∈∈ then dy dx at x = 0 is equal to

A0 B1 C3 DNone of these

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EnglishGIC Lecturer Exam- 2015

Q364.3x x 2x 2 x 0 8 - 2 -4 +1 lim sin x → is equal to

Aloge4 Bloge2 C2(loge2)2 Dlogeg

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EnglishGIC Lecturer Exam- 2015

Q365.If 2 1-sin x π f(x) =, x 2 (π - 2x) ≠ is continuous at, π x 2 = then π f 2 is equal to

A–1 B1 C2/3 D1/8

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EnglishGIC Lecturer Exam- 2015

Q366.What is the value of f(0) for which the function 2 x 4 f(x) sin2x is a continuous at x = 0?

A1/2 B1/4 C1/8 D1

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EnglishGIC Lecturer Exam- 2015

Q367.x 1 x lim(1 x)tan 2 has the value–

A2/π Bπ/2 Cπ D0

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EnglishGIC Lecturer Exam- 2015

Q368.Let n 1 1 1 1 S...... 1.4 4.7 7.10 (3n 2)(3n 1) n 1, then n n lim S is equal to–

A0 B1/3 C1 D3

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EnglishGIC Lecturer Exam- 2015

Q369.If y = log2(logex), then dy dx is equal to –

A2 x 1 log elog e x B2 1 log x x C2 1 log e x De 1 log 2 x

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EnglishGIC Lecturer Exam- 2015

Q370.n 2 n 1 1 (1) lim 1 n is equal to–

A1 Bi C2 D1 i 2

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EnglishTGT 2013

Q371.Let y=|x|+|x–2| then the value of dy dx at x = 2

A2 B0 CDoes not exist D1

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EnglishTGT 2013

Q372.The value of 2 x 0 xcosx log(1 x) lim x → − +

A1 B1/2 C3 D0

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EnglishTGT 2013

Q373.The function f(x) is define as follow () x, x 0 f x x, 0 x 1 2 x, x 1 − ≤ = < < − ≥ In this case function f(x) will be

AContinuous at x = 0, x = 1 BContinuous at x = 0 and discontinuous at x = 1 CDiscontinuous at x = 0 and continuous at x = 1 DDiscontinuous at both x = 0 and x = 1

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EnglishTGT 2013

Q374.The value of 4n n r 1 1 lim n r →∞ = + ∑

Aloge5 Bloge3 C0 D1

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EnglishUP PCS (Pre) 1997

Q375.The value of: (())) ((()) { { } } 1/ 2 1/ 2 1/ 2 3/ 2 3/ 2 3/ 2 n n n n lim..... n n 3 n 3 n 1 →∞ + + + + + − + −

A() 1 3/ 2 0 dx 1 3x + ∫ B() 3/ 2 0 dx 1 3x ∞ + ∫ C() 1 1/ 2 0 dx 1 3x + ∫ DNone of these

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EnglishUP PCS (Pre) 1997

Q376.(()) x 1 2 x 1 e x lim x 1 − → − is:

A–1/2 B0 C1/2 D1

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EnglishUP PCS (Pre) 1997

Q377.The function ((()) 2 x,x 0 f x 2 x,x 0 + ≥ = − < is:

Adiscontinuous at x=0 Bcontinuous and differentiable at x=0 Ccontinuous but not differentiable at x= Dcontinuously differentiable at x=0

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EnglishUP PCS (Pre) 1997

Q378.The value of x 0 1 cotx x lim x → − is:

A1 B1/2 C1/3 D−1/3

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EnglishUP PCS (Pre) 1997

Q379.The limit of xx as x→ → →0 is:

A1 B0 C∞ DNone of these

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EnglishUP PCS (Pre) 1997

Q380.The function f(x) differentiable at the origin is

Af(x) = |x| B1 xsin,x 0 f(x) x 0,x 0 ≠ = Cf(x)= x2/3 D2 1/ x f(x) e− =

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