Math Chapter Wise

EnglishDSSSB PGT 2021

Q21.If ω be a cube root of 1, then what is the value of (1–ω) (1–ω2) (1–ω4) (1–ω5)?

A9 B8 C7 D1

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EnglishDSE TGT 2019

Q22.What will be the argument of the complex number z = (i - 1)/(e(i π/3))?

Aπ/4 B5π/12 Cπ/3 D3π/8

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EnglishDSE TGT 2019

Q23.The product of the values of (cos π/6 + i sin π/6)3/2 is

Ai B1 C–i D–1

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EnglishKVS TGT 2017

Q24.sin icos 2 and c o s c o s c o s c o s θ - i s i n 2 θ - i s i n 2 θ - i s i n 2 θ - i s i n 2 θ are conjugate to each other for:

An B1 n 2 2 C0 Dno value of θ

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EnglishKVS TGT 2017

Q25.Let x, y ∈ R, then x + iy is a non-real complex number if–

Ax = 0 By = 0 Cx ≠ 0 Dy ≠ 0

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EnglishOPSC PGT 2017

Q26.For a complex number z, the value of sin2 z + cos2 z is:

Ai B1 C1 + i D1 – i

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EnglishOPSC PGT 2017

Q27.For z = x + iy, x > 0, the integral zt 0 e dt is equal to:

Az B1/z Clog z De–z

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EnglishUP TGT 2021

Q28.If 1 π x + = 2cos, x 5 then 5 5 1 x + x is equal to

A–2 B0 C1 D5

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EnglishUP PGT 2021

Q29.If complex numbers a1, a2, a3........ are in G.P. having common ratio r such that ≠ ∑ ∑ n n 2k-1 2k+2 k=1 k=1 a = a 0 then number of possible values of r is –

A1 B2 C3 D4

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EnglishUPPSC GIC 2021

Q30.The nth roots of unity can be arranged as-

Aan arithmetic progression Ba geometric procession Ca harmonic progression Dan arithmetico - geometric progression

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EnglishUP PGT 2021

Q31.If ω is cube root of unity, then 1 +ω + ω2 + ω3 +........+ ω52, ω ≠1 is equal to –

Aω B1–ω C–ω2 D1+ω2

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EnglishUP PGT 2021

Q32.If ω (≠ 1) is a cube root of unity and () ω 7 1+ = A +B then the value of A2 + B2 is–

A0 B1 C2 D4

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EnglishUP TGT 2021

Q33.For any complex number z, the minimum value of z +1 + z – 2 is

A–1 B1 C2 D3

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EnglishUP TGT 2021

Q34.If 1, ω, ω2 are the cube roots of unity, then the value of (1 + ω2)(1 + ω4) (1 + ω8)(1 + ω16) is

A–1 B0 C1 D2

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EnglishUP TGT 2021

Q35.If i = –1, then (1 + i)4 – (1 – i)4 is equal to

A–4i B4i C0 D2

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EnglishUP TGT 2021, 2004 Haryana PGT 2018 KVS PGT 2018 TGT - 1999

Q36.The smallest positive integer n for which n 1+ i = 1 1 – i, is

A8 B12 C4 D16

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EnglishUP TGT-2016 (08-03-2019)

Q37.If A+iB = tan (x+iy), then the value of tan 2x is as

A2 2 2A 1+ A + B B2 2 2A 1- A + B C2 2 2A 1- A - B DNone of these

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EnglishUP TGT-2016 (08-03-2019)

Q38.If sin2 (x + iy) = A + iB, then value of A is

A() 1 1 cos2xcosh2y 2 + B() 1 1 cos2xcosh2y 2 − C() 1 sin 2xsinh 2y 2 D() 1 sin2xsinh2y 2 −

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EnglishUP TGT-2016 (08-03-2019)

Q39.The polar form of ((()) 1 3 − − − − − − − − − − − − is

A2 2 2 cos isin 3 3 π − B2 cos isin 3 3 π + C2 2 2 cos isin 3 3 π + D2 cos isin 3 3 π −

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EnglishUP TGT-2016 (08-03-2019)

Q40.If ωis cube root of unity, then (3+ω+3ω2)6 is equal to

A32 B64 C128 D16

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