Math Chapter Wise

EnglishUP Higher Asst. Prof. 2021

Q41.Contour integration () 2 0 log 1 x dx 1 x ∞ + + ∫ gives value equals to,

Aπlog2 B–πlog2 Clog2 2 π Dlog2 2 π −

Show answer

EnglishUP Higher Asst. Prof. 2021

Q42.Value of integration () 2 cos 0 e.cos sin n d π θ − θ = ∫

A2πi/n B2 / n/π C2π /n D2πni

Show answer

EnglishUP Higher Asst. Prof. 2021 UPPSC Polytechnic Lecturer 2021 (I)

Q43.If an entire function is bounded then it is

A() f z M ≥ BConstant CAnalytic DNone of these

Show answer

EnglishDSSSB TGT 04-09-2021 Shift-I (Male)

Q44.Let G be a connected open set and let f: G → → → C be analytic. Then which of the following is not an equivalent statements:

A= 0 for each n ≥ 0; Bthere is a point a in G such that fn Cf ≡ 0 DR > 0 is arbitrary, radius of convergence is infinite

Show answer

EnglishDSSSB TGT 04-09-2021 Shift-I (Male)

Q45.Find the residues of a function: f (z) = [ 1 ÷ ÷ ÷ {(z– 2)(z+1)3 }]

A(1÷27)&(–1÷125) B(1÷27)&(–1÷27) C(1÷27)&(1÷125) D(1÷125)&(–1÷125)

Show answer

EnglishDSSSB TGT 04-09-2021 Shift-I (Male)

Q46.What is the analytic region of f (z) = (x- y)2 +2i(x+y)?

Ax + y = 2 Bx + y = – 2 Cx – y = – 1 Dx – y = 1

Show answer

EnglishUK SSSC LT 2020

Q47.Polar form of Cauchy Riemann condition is:

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

Show answer

EnglishKVS PGT 23-12-2018

Q48.Singularity of 1 f(z) sin 1 z = − at z 1 = is:

Aisolated singularity Bessential singularity Cisolated essential singularity Dnon-isolated essential singularity

Show answer

EnglishUP PGT-2016 (02-02-2019)

Q49.If (((()))) 1 1 2 2 5 z sin x y, − = + = + then z z x y ∂ ∂ + ∂ ∂ is equal to

A1 sinz 5 B2 tan z 5 C2 sinz 5 Dtan z

Show answer

EnglishUP PGT-2016 (02-02-2019)

Q50.If z=f(x–y, y–t, t–x), then z z z x y t ∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂ + + ∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂ is equal to

Ax+y+t Bx+y+y+1 C1 D0

Show answer

EnglishUP PGT-2016 (02-02-2019)

Q51.Which one of the following is not correct?

Atan i θ=i tan h θ Bcos i θ = cos h θ Ccot i θ= i cos h θ Dsin i θ= i sin h θ

Show answer

EnglishUP PGT-2016 (02-02-2019)

Q52.If ((()) sin x iy e A iB, + = + = + where A and B are real, then 2 2 A B + + is equal to

Asin xcosh y/e Bsinh xcosy/e Csinh xcosh y/e Dsin xcosy/e

Show answer

EnglishUP PGT-2016 (02-02-2019)

Q53.(())) ((()) 2sinh x y cosh x y + − + − is equal to

Asin2x sin2y/+ Bsin2x sinh2y/+ Csinh 2x sinh2y/+ Dsinh 2x sin2y/+

Show answer

EnglishLT 2018

Q54.If 3 3 x y u log, x y + = + then the value of u u x y ∂ ∂ + ∂ ∂ is

Au B2 C0 Du+1

Show answer

EnglishLT 2018

Q55.If f(z)=(x2 +ay2)+ibxy is a complex analytic function of z=x+iy, then the value of a+b is

A0 B1 C–1 D2

Show answer

EnglishLT 2018

Q56.Which one of the following is false?

A() f z z = is no where analytic. B() 2 f z z = is analytic everywhere. C() 2 f z z = is analytic at z=0 D() z f z e = is analytic everywhere.

Show answer

EnglishSECTION B PGT TIER-I 31.11.2014

Q57.If f(z) = u (x,y) + iv (x,y), then Cauchy- Riemann equations are

Au u v v and x y x y Bu v u v and x y y x ∂ ∂ ∂ −∂ = ∂ ∂ ∂ ∂ Cu v u v and x x y y DNone of these

Show answer

EnglishSECTION B PGT TIER-I 31.11.2014

Q58.2t f(t) e cos3t Laplace transform of the function is–

A2 1 3 S 2 S 9 B2 1 S S 2 S 9 C2 1 3 S 2 S 3 DNone of these

Show answer

EnglishSECTION B PGT TIER-I 31.11.2014

Q59.A real valued bounded function f(x) is Riemann integrable on [a,b], then–

Ab -b a a f(x)dx and f(x)dx exist Bb -b a a f(x)dx f (x)dx Cb -b a a f(x)dx f(x)dx DNone of these

Show answer

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

Q60.The value of 2 c z z 1 dz, z 1 where C is the circle z 1 = is–

A0 B2 i C2 i DNone of these

Show answer