Math Chapter Wise

EnglishPGT 2010

Q101.If 100 z (2 2 3 i) = + = + then (()) Re(z) Im z will be equal to

A() 100 3 B1/3 C100 1 3 D3

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EnglishPGT 2010

Q102.If tan (θ + iφ)= cos α+i sin α then

A2 2 4 nπ θ = + + α B2 4 nπ θ = + C4 2 nπ θ = + + α D2 4 2 nπ θ = + + α

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EnglishPGT 2009

Q103.The value of 8 8 1 1 2 2 + − + i i is

A1 B2 C–1 D–2

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EnglishPGT 2009

Q104.If 1 2 + = x cosθ, then the value of 6 6 1 + x is

A2 cos 6θ B2 cos 4θ C2 cos 3θ D2 cos 2θ

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EnglishPGT 2009

Q105.If tan [log (x + iy)] = a + ib, where a, b, x and y are real and a2 + b2 ≠ 1, then the value of tan [log(x2 + y2)] is

A2 2 2 1+ + a a b B2 2 2 1− + a a b C2 2 2 1− − a a b D2 2 2 2 1+ − a a b

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EnglishPGT 2009

Q106.If cos, sin 2 2 = + r r r x π, then value of 1 2 3.........∞ ∞ x x x is

A0 B–1 C1 D∞

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EnglishPGT 2005

Q107.Let Z1, Z2, Z3 are the vertices of the triangle having its circum centre at origin. If Z is the coordinate of its orthocenter, then

AZ1 + Z2 + Z3 – Z = 0 BZ1 + Z2 – Z3+ Z = 0 CZ1 – Z2 + Z3 + Z = 0 D–Z1 + Z2 + Z3 + Z = 0

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English–2048 PGT 2005

Q108.The value of (((()))) (((()))) 10 10 1 3 1 3 i i + + − + + − + + − + + − is:

A2048 B1024 C–1024 DImage/formula option D (see source)

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EnglishPGT 2004

Q109.If α and β are roots of the equation x2 – x + 1 = 0 then the value of α1030 + β1030 will be-

A1 B0 C–1 DNone of the above

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EnglishPGT 2004

Q110.If m, n, p and q are consecutive integers then the value of im + in + ip + iq will be

A1 B4 C0 DNone of the above

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EnglishPGT 2004

Q111.If xn = cos (π/3n + i sin (π/3n), then the value of x1. x2. x3…..xn…..∞ ∞ ∞ is?

A1 Bi C-1 D- i

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EnglishPGT 2004

Q112.The least positive integer n for which n 1 i + − is real, is?

A2 B4 C8 DNone of the above

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EnglishPGT 2004

Q113.The triangle formed by the points 1,, 2 ω as vertices in the Argand diagram is

AScalene Bequilateral Cisosceles Dright-handed

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EnglishPGT 2004

Q114.If |z–2–2i|=1, then the minimum value of |z| is?

A2 2 1 B2 2 C2 2 1/+ D2 2 2

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EnglishPGT 2004

Q115.For all complex numbers z1, z2 satisfying |z1| = 12 and 2 | z 3- 4i |= 5 -, the minimum value of |z1 - z2| is

A0 B2 C7 D17

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EnglishPGT 2003

Q116.The value of x iy e + is

Ax/e Bx/e C2 2 + x y e D+ x y e

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EnglishPGT 2003

Q117.The argument of –1–i is

A4/π B3 4 π C3 4 π − D5 4 π

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EnglishPGT 2003

Q118.If 3, x iy a ib + = + + = + + = + + = + then

A2 2 () − = + x y a b B2 2 () − = − x y a b C2 2 () + = − x y a b DNone of these

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EnglishPGT 2002

Q119.The value of the sum (((()))) 13 n n 1 n 1 i i, + = + ∑ ∑ where (()) i 1 = − = − equals:

Ai Bi–1 C–i D0

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EnglishPGT 2002

Q120.The z1 and z2 are two non zero complex numbers such that |z1+z2|=|z1|+|z2|, then Arg z1–Arg z2

A–π B−2/π C0 D2/π

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