Math Chapter Wise

EnglishTGT 1999

Q81.If the imaginary part of 2z 1 iz 1 + is –2, then what will be the point path formed by z represent?

Aa circle Ba straight line Ca parabola DNone of these

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EnglishTGT 1999

Q82.If 1, ω, ω2 is the unit cube root then (1–ω + ω2)5 + (1+ω–ω2)5 =

A–8 B8 C32 D–32

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EnglishPGT 2011

Q83.If z=x+iy, z = x–iy then real part of z is:

A−z z/2i Bz z 2i + Cz z 2 + Dz.z

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EnglishPGT 2011

Q84.The value of 2 1 i − = +

A1 B−1/2 C1/2 D–1

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EnglishPGT 2011

Q85.If ω is an imaginary cube root of unity then (1+ω–ω2)7 is equal to:

A128ω B–128ω C128ω2 D–128ω2

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EnglishPGT 2011

Q86.If ω is an imaginary cube root of unity then (1–ω+ω2)6 +(1–ω2 +ω)6 = (1–ω+ω2)6 +(1–ω2 +ω)6 =

A0 B6 C64 D128

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EnglishPGT 2011

Q87.If 1 x 2cos x + = θ + = θ + = θ + = θ then n n 1 x + + is equal to:

A2cos nθ B2sin nθ Ccos nθ Dsin nθ

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EnglishPGT 2011

Q88.If 1 ix a ib, 1 ix − = + + then 2 2 a b + =

A1 B–1 C0 DNone of these

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EnglishPGT 2011

Q89.If x+iy= (cosθ–isinθ)2 then value of x2 +y2 =

A1 B–1 C0 DNone of these

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EnglishPGT 2011

Q90.If x+iy=(1+i)(1+2i)(1+3i) then x2 +y2 =

A0 B1 C100 DNone of these

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EnglishPGT 2013

Q91.If { { { } } 1, ∈ − n N then the value of sin n 1 cos. 1 cos − + + + − + + + − + + + − + + + − n n i sin i n n n π will be?

A–2 B–1 C2 D1

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EnglishPGT 2013

Q92.If (((()))) ((()) 100 98 3 2 + = + + = + + = + + = + i a ib then 2 2 + a b is equal to?

A1 B4 C8 D16

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EnglishPGT 2013

Q93.If 1, Z1,Z2,..........Zn–1 be the nth root, then (()))((())) ((()) 1 2 n 1 1 Z 1 Z.............. 1 Z − − − − − − − − − − − − − − is equal to?

A0 B1 Cn Dn2

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EnglishPGT 2013

Q94.i is equal to:

A–1 B1 2 + i C1 DNone of these

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EnglishPGT 2013

Q95.The smallest positive integer value of n for which ((()) 1+ + n i is a pure imaginary:

A1 B2 C4 D6

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EnglishPGT 2013

Q96.If P represents a variable complex point Z such that 2 1 2 − = Z Z. Then what will be the locus of P?

AStraight line BCircle CEllipsoid DHyperbola

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EnglishPGT 2010

Q97.Which of the following is correct where i 1? = −

A1+i>2–i B2+i>1+i C2–i>1+i DNone of these

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EnglishPGT 2010

Q98.The locus of the point z satisfying the condition |z–3i|= 2 is

ACircle BParabola CEllipse Dx-axis

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EnglishPGT 2010

Q99.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

Q100.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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