Math Chapter Wise

EnglishJDD-75-PGT TIER II-X-15 28.06.2015

Q61.For the function f(z)= 2 z sinz, z − at the point z=0 is

Aa pole of order 2 Ban essential singularity Ca removable singularity Dnone of these

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EnglishJDD-75-PGT TIER II-X-15 28.06.2015

Q62.The value of c tanz dz ∫ ∫ where C is the circle z 2 = is–

A2 i/π B4 i/π C4 i/− π Dnone of these

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EnglishJDD-75-PGT TIER II-X-15 28.06.2015

Q63.The Laplace transform of (()) 3t e 2cos5t 3sin5t − − is–

A()2 s 9 s 3 5 − + + B()2 2s 9 s 3 25 − + + C()2 s 9 s 3 5 + + − D()2 2s 9 s 3 25 − − −

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EnglishJDD-75-PGT TIER II-X-15 28.06.2015

Q64.(((()))) L t is

A3/ 2 3 2 s Γ B1/ 2 1 2 s Γ C5/ 2 5 2 s Γ DNone of these

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EnglishJDD-75-PGT TIER II-X-15 28.06.2015

Q65.The Fourier transform of 2 x 2 e − is-

A2 s 4 e − B2 s 2 e 2 π C2 s 4 2 e 4 π D2 s 2 2 e − π

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EnglishUP PCS (Pre) 1995

Q66.1 y sin x a homogeneous function of x,y of degree-

A1 B2 C3 D0

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EnglishPGT 2003

Q67.An example of the function not analytic anywhere

A1/z B2/z C2/z Dlog Z

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EnglishPGT 2003

Q68.(())) (((()))) sin 3 sin 2 x iy z z + = − + = − + = − + = −

AIs a regular function BIs a not a regular function CIs a harmonic function DNone of these

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EnglishPGT 2003

Q69.The function () f z xy iy = + = + is

AContinuous everywhere and analytic any where BNot continuous but analytic CContinuous but not analytic DNone of these

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EnglishPGT 2003

Q70.The function f(z) = xy

Ais regular and Cauchy–Riemann (C–R) equation are satisfied Bis regular but C–R equations are not satisfied Cis not regular at z=0 and C–R equations are not satisfied Dis not regular at z=0 but C–R equations are satisfied

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EnglishPGT 2003

Q71.Find f(z) = u + iv where x u(x, y) = e (xcosy - ysiny)

A() z f z e c = + B() = z f z ze +z+c C1 () z f z ze c − = + DNone of these

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EnglishPGT 2000

Q72.The Cauchy -Riemann equations are:

AOnly sufficient condition for analyticity BOnly necessary condition for analyticity CBoth necessary and sufficient condition for analyticity DNone of these

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EnglishRajasthan TGT 2015

Q73.Which of the following statement is false?

A2 z, z i f(z) 0, z i ≠ = is continous at z i = B2 f(z) z = is continuous everywhere Cf(z)= n z, n∈z+ is differentiable everywhere. DThe derivative of 2 f(z) z = is exists only at origin.

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EnglishRajasthan TGT 2015

Q74.Which one of the following is true for the function f (z) = x y f (z) = x y f (z) = x y f (z) = x y?

AAnalytic everywhere BAnalytic at (0,0) only CCauchy–Riemann equations are satisfied at (0,0) DCauchy–Riemannm equations are not satisfied at (0,0)

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EnglishRajasthan TGT 2015

Q75.If the function x u(x,y) e cosy = is harmonic then its harmonic conjugate v(x,y) is

Ay e cos x C + Bx e sin y C + Cy e sin x C + Dx e cos y C − +

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EnglishRajasthan TGT 2013

Q76.The analytic function whose real part is ex cosy is-

Aze2z/+ ci Bzez/+ ci Ce2z/+ ci Dez/+ ci

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EnglishRajasthan TGT 2013

Q77.Cauchy-Riemann equations in polar form are-

Au 1 v 1 u v and r r r r ∂ ∂ ∂ ∂ =− ∂ ∂θ ∂θ ∂ Bu v u v r and r r r ∂ ∂ ∂ ∂ =− ∂ ∂θ ∂θ ∂ Cu 1 v 1 u v and r r r r ∂ ∂ ∂ ∂ = ∂ ∂θ ∂θ ∂ Du v u v r and r r r ∂ ∂ ∂ ∂ =− = ∂ ∂θ ∂θ ∂

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