Math Chapter Wise

EnglishTGT 2013

Q181.i z e θ = then find the value of 2 z 1 − +:

Aitanθ Btanθ Cicotθ D2/isec θ

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EnglishTGT 2013

Q182.What is the nature triangle whose vertices (imaginary numbers) are 3+4i, 8-6i and 13+9i?

AEquilateral triangle BRight Angled Triangle CAcute angle Triangle DObtuse angle Triangle

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EnglishTGT 2013

Q183.If 6i -3i 1 4 3i -1 = x + iy 20 3 i then find the value of x and y?

Ax = 0, y = 0 Bx = 0, y =1 Cx = 0, y = –1 Dx = 1, y = –1

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EnglishTGT 2013

Q184.The value of 4 cos isin icos sin θ + θ + θ + θ + θ + θ + θ + θ + θ will be:

Acos4 isin 4/θ + θ Bcos8 isin8/θ + θ Ccos8 isin8/θ − θ Dcos4 isin 4/θ − θ

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EnglishTGT 2013

Q185.If x = cosα + isinα and y = cosβ + isinβ then the value of x – y x + y will be:

Atan α β Btan 2 α −β Ci tan 2 α −β Ditan( )/α −β

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EnglishTGT 2013

Q186.If i z3 + z2 – z + i = 0 then the value of |z|:

A1 B2 C–1 D3

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EnglishTGT 2013

Q187.If ω is the unit cube root, then the value of (1 – ω + ω2) (1 + ω – ω2) will be:

A1 B–1 C4 D–4

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EnglishTGT 2013

Q188.If a ib x iy c id + + = + then the value of x2 + y2 will be:

A2 2 a b c d + B2 2 a b c d + Cad bc Da ib − +

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EnglishUP PCS (Pre) 1997

Q189.If the imaginary part of 2z 1 iz 1 + is –2, then the locus of a point representing z, is a:

ACircle BStraight line CParabola DNone of these

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EnglishUP PCS (Pre) 1997

Q190.If 35 200 1 3 1 3 z i i 2 2 2 2 = − + + − − = − + + − − = − + + − − = − + + − − then:

ARe (z)<0 BRe(z) = 0 CRe(z) > 0 DNone of these

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EnglishUP PCS (Pre) 1997

Q191.Theproductoftwocomplexnumbers(a,b)and(c,d)is:

A(ac+bd, ad+bc) B(ac–bd, ad+bc) C(ac+bd, ad–bc) D(ad+bc, ac–bd)

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EnglishTGT 2010

Q192.The conjugate of a complex number is 1 i 1 −. Then complex number is

A−1/i 1 B1 i 1 + C1 i 1 − + D−1/i 1

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EnglishTGT 2009

Q193.If 1 2cos x x θ= + θ= + and 1 2cos y, y φ= + φ= + then the value of m n n m x y y x + + is:

A2 cos (mθ – nφ) B2 sin (mθ – nφ) C2 cos (mθ + nφ) D2 sin (mθ + nφ)

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EnglishTGT 2009

Q194.(()) (()) n 1 sin icos 1 sin icos + θ+ θ + θ+ θ + θ+ θ + θ+ θ = + θ− θ + θ− θ + θ− θ + θ− θ

An n cos n isin n 2 2 π − θ + − θ Bn n cos n isin n 2 2 π + θ + + θ Cn n sin n icos n 2 2 π − θ + − θ Dcos n 2 isin n 2 2 2 π + θ + + θ

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EnglishTGT 2009

Q195.Given (((()))) 100 Z 1 i 3, = + = + then the value of (()) (()) Re z Im z will be equal to:

A2100 B250 C1/3 D3

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EnglishTGT 2009

Q196.If (x+iy)1/3 = a + ib then the value of x y a b + + will be:

A4(a2 + b2) B4(a2 –b2) C4(b2 – a2) DNone of these

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EnglishTGT 2009

Q197.If Z1 and Z2 are two complex numbers such that |Z1| = |Z2| + |Z1 – Z2| then

A1 2 Z Im 0 Z = B1 2 Z Re 0 Z = C1 1 2 2 Z Z Re Im Z Z = DNone of these

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EnglishTGT 2009

Q198.The least positive integer of n for (1+i)3n =(1–i)3n is:

A2 B4 C5 D6

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EnglishTGT 2009

Q199.The value of (((()))) 4 2 3 3 +ω+ ω +ω+ ω +ω+ ω +ω+ ω is:

A16ω B16ω2 Cω DNone of these

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EnglishTGT 2004

Q200.If z is a complex number such that z-i z + i = 1 then z will be located in:

AOn a straight line BOn an ellipse COn a circle DOn a hyperbola

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