Math Chapter Wise

EnglishOPSC PGT 2017

Q81.Frobenius method is used to find the power series solution of:

AIntegral equations BOrdinary differential equations with variable coefficients CPartial differential equations DIntegro-differential equations

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EnglishOPSC PGT 2017

Q82.The differential equation (1 – x2) 2 d y dy 2x m(m 1)y 0 dx is known as:

ABessel's equation BHermite's equation CKelvin's equation DLegendre's equation

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EnglishOPSC PGT 2017

Q83.For Jn(x) being Bessel's function of first kind n d x J (x) dx is equal to:

An n 1 x J (x) Bn 1/x J (x) Cn n 1 x J (x) Dn 1 n x J (x)

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EnglishOPSC PGT 2017

Q84.Heat conduction equation is classified as:

AHyperbolic equation BParabolic equation CElliptic equation DHarmonic equation

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EnglishOPSC PGT 2017

Q85.Laplace transform of sinht t is:

A1 s 1 log 2 s 1 B1 s 1 log 2 s 1 Cs 1 log s 1 − + D1 s 1 log 2 s 1

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EnglishOPSC PGT 2017

Q86.Inverse Laplace transform of 1 2s 5 is:

A1 3 exp t 2 2 B5 1 exp t 2 3 C2 3 exp t 5 2 D1 5 exp t 2 2

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EnglishOPSC PGT 2017

Q87.For a function, given by f(x) 1 for x a but f(x) 0 for x a, the Fourier transform is given by:

A1 cos(sa) s B2 sin(sa) s Ci cos(sa) a D2 sin(sa) a

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EnglishOPSC PGT 2017

Q88.If f (s) denotes the Fourier transform of F(x), then the Fourier transform of F(ax) is given by:

As af a B1 f sa a Caf sa D1 s f a a

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EnglishOPSC PGT 2017

Q89.The equation 2 u u 0, t x is known as:

ABurger's equation BTransport equation CSchrodinger's equation DMaxwell's equation

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EnglishUPPSC GDC 2021

Q90.What is the Laplace transform of the function sinx x?

A1 1 tan s − B1 1 sin s − C−1/tan s D−1/sin s

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EnglishUPPSC GDC 2021

Q91.The value of () () n d x J x dx is

A() n n 1 x J x − B() n 1 n x J x − C() n n 1 x J x + D() n 1 x J x −

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EnglishUP Higher Asst. Prof. 2021

Q92.The radius of curvature for the curve x = 3t, y = 3t2, z = 2t3 is

A() 2 3 1 2t 2 + B() 2 1 1 2t 2 + C() 2 1 1 3t 2 + D() 2 3 1 t 2 +

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EnglishUP Higher Asst. Prof. 2021

Q93.The principal radii at the origin of the surface 2z = 5x2 + 4xy + 2y2 is

A1 1, 6 B1 3, 2 C1 2, 6 D1 1, 2

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EnglishUP Higher Asst. Prof. 2021

Q94.The geodesic on a right circular cylinder is:

ACircle BHelix CLine DEllipse

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EnglishUP Higher Asst. Prof. 2021

Q95.The length of the curve given as the intersection of the surfaces 2 2 x y a b − = 1, x= a cosh z a from the point (a,0,0) to the point (x,y,z).

A2 2 y a b b + B2 2 x a b b + C2 2 y a b a + D2 2 x a b a +

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EnglishUP PGT 2021

Q96.If y = sin (log x), then which of the following is correct?

A2 d y xy 0 dx + = B2 d y y 0 dx + = C2 d y dy x x y 0 dx + + = D2 d y dy x – x y 0 dx + =

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EnglishUPPSC GDC 2021

Q97.The extermals of ∫ 2 '2 0 y dx x, satisfying y(0) = 0 and y(2) = 1, is

AA circle BA parabola CAn ellipse DA hyperbola

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EnglishUPPSC GDC 2021

Q98.If Ai is a covariant vector, then which of the following is correct?

Ai j A x ∂ is a covariant tensor Bi j A x ∂ is a contravariant tensor Ci j A x ∂ is not a tensor Di j A x ∂ is a mixed tensor

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EnglishUPPSC GDC 2021 UPPSC Polytechnic Lect. 2021 (II)

Q99.If L (F(t)) = f (s), then L (tn F(t)) is equal to

A() () () n d 1 f s ds − B() n d f s ds C() () () n n 1 n d 1 f s ds − D() () () n n 1 n d 1 f s ds + −

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EnglishUPPSC GDC 2021

Q100.Solution of the integral equation () () () ∫ x 0 y x = x + sin x – t y t dt is

A() 2 x y x x 3 = + B() 3 x y x x 6 = − C() 3 x y x x 6 = + D() 2 3 y x x x = +

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