Math Chapter Wise

EnglishJSSC PGT 2018

Q21.Compute ∫ cos(z/2) dz, over (0, π + 2i).

Ae + 1/e Bsin (π/4) C2πi D0

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EnglishOPSC PGT 2017

Q22.Cauchy's residue theorem is used to solve:

AInitial value problems BBoundary value problems CIntegral in complex domain DIntegral equations

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EnglishOPSC PGT 2017

Q23.Necessary condition for an arc z = z(t) (a ≤ t ≤ b) to be smooth, is a:

AContinuous z′(t) BIntegrable z(t) CDifferentiable z(t) DHarmonic z(t)

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EnglishOPSC PGT 2017

Q24.Residue of complex valued function 1 zcos at z 0 is: z

A1/4 B1/3 C1/2 D1

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EnglishOPSC PGT 2017

Q25.The transformation az b w cz d with complex constants a, b, c, d makes a bilinear transformation when:

Aad – bc = 0 Bad – bc ≠ 0 Ca b/d c Da b/d c

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EnglishUPPSC GDC 2021

Q26.In the Laurent series expansion of the function f(z) = 1 1 –, z –1 z – 2 valid in the region |z| > 2, the coefficient of 2 1 z is

A0 B1 C– 1 D2

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EnglishUPPSC GDC 2021

Q27.For f (z) = z 4 e sinhz z, the residue at z = 0 is

A2/3 B1/3 C1/2 D1/6

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EnglishUPPSC Polytechnic Lecturer 2021 (I)

Q28.The value of the integral ∫ 3 z =1 1 1 z cos dz 2πi z is equal to

A0 B1 C1 – 6 D1/24

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EnglishUPPSC Polytechnic Lecturer 2021 (I)

Q29.The residue of the function f(z)= sinz zcosz at the pole z= π 2 is -

A0 B1 C2 – π D2/π

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EnglishUPPSC Polytechnic Lecturer 2021 (I)

Q30.Consider the function f(z)= 2 1. z sinz Which of the following is correct?

Af has pole of order 1 at z = 0 Bf has pole of order 2 at z = 0 CThe residue of f at z = 0 is 1 3 DThe residue of f at z = 0 is 1 6

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EnglishUPPSC Polytechnic Lecturer 2021 (I)

Q31.Consider the following statements- I. z 2 e f(z) = z is meromorphic in C II. f(z)=(z2 –4)–1 1 sin is z meromorphic in C then

AI and II both are true BI and II both are false CI is true but II is false DII is true but I is false

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EnglishUPPSC Polytechnic Lecturer 2021 (I)

Q32.The principal part of the Laurent series of 1 f(z) = z(z –1)(z – 2) in the annulus { } z:0 < z < 1 is -

A1 – z B1/z C1 – 2z D1/2z

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EnglishUPPSC Polytechnic Lecturer 2021 (I)

Q33.Let C be a circle 3 z = 2 that is oriented in the counter clockwise direction. The value of 'a' for which C ∫ 2 z +1 a + dz = 0 z – 3z + 2 z –1 is-

A1 B–1 C2 D–2

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EnglishUPPSC Polytechnic Lecturer 2021 (I)

Q34.If f(z) is analytic in circle C: z – a < r and if ≤ f(z) M on C, then-

An! r = B(n) n M f C(n) n M f DNone of the above

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EnglishUPPSC Polytechnic Lecturer 2021 (I)

Q35.The coefficient of 1 z –1 in the Laurent's series expansion of () z 2 e z –1 about z=1 is-

A1 Be C1/e D0

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EnglishUPPSC Polytechnic Lecturer 2021 (I)

Q36.If C is the unit circle z = 1, ()() C ∫ 2 z 2z +1 z + 2 dz is equal to-

A4 i/π B8 i/π Ci 6 π Di 12 π

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EnglishUPPSC Polytechnic Lecturer 2021 (I)

Q37.The value of the integral ∫ 2π 0 dθ 3 + 2cosθ is-

A2 5 π B5/π C2 5/π DNone of these

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EnglishUPPSC Polytechnic Lecturer 2021 (I)

Q38.The order of a canonical product P(z) is equal to-

AConvergence exponent of its zeros BConvergence exponent of its poles C1 always DNone of these

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EnglishUP Higher Asst. Prof. 2021

Q39.A function f(z) has no singularity in the finite part of the plane but has a pole of order m at infinity. then,

Af(z) is a polynomial of degree m. Bf(z) has zero of order m. Cf(z) has singularity. DNone of these

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EnglishUP Higher Asst. Prof. 2021

Q40.Value of integral ()() 2 c zdz 9 z z i − + ∫, where C is the circle z 2 = (Using Cauchy's integral formula) equals to,

Aπ/2 Bπ/3 Cπ/5 Dπ/7

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