Math Chapter Wise

EnglishUP PCS (Pre) 2002

Q161.The equation 2 z z = has:

Ano solution Btwo solutions Cfour solutions Dinfinit number of solutions

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EnglishUP PCS (Pre) 2002

Q162.The point z in Argand's plane moves such that Re iz +1 = 2 iz -1 where z = x+iy, the locus of is:

AA straight line Ba circle Can ellipse Da hyperbola

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EnglishUP PCS (Pre) 2002

Q163.If 2 z - = 6 z, then the greatest value |z| is:

A36 B11 C3 11/+ D3 11

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EnglishUP PCS (Pre) 2002

Q164.If ω ≠1 is a cube root of unity, then the value of the expression (1+2ω+2ω2)10 +(2+ω+2ω2)10 + (2+2ω+ω2)10 is

A0 B1 Cω Dω2

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EnglishUP PCS (Pre) 2002

Q165.() θ − θ 4 3 (sin + i cos) is equal to: cos i sin

Acos θ – i sin θ Bcos θ + i sin θ Csin θ – i cos θ Dsin θ + i cos θ

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EnglishUP PCS (Pre) 2003

Q166.If is an imaginary cube root of unity, then the value of– 2 10 2 10 (1 3 3) (3 3) + ω + ω + + ω + ω + ω + ω + + ω + ω + ω + ω + + ω + ω + ω + ω + + ω + ω 2 10 (3 3) + + ω + ω + + ω + ω + + ω + ω + + ω + ω is-

A0 B1 C1 D2/1

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EnglishUP PCS (Pre) 2004

Q167.If a + ib is a zero of a real polynomial, then the correct statement is–

Aib is also zero B–ib is also zero Ca is also zero Da –ib is also zero

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EnglishUP PCS (Pre) 2005

Q168.If x = 3 + i, then the value of the expression x3 – 3x2 –8x+15

A0 B–15 C3 D–8

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EnglishUP PCS (Pre) 1998, 2005

Q169.If arg − z 1 π = z +1 4, the locus of z is:

Astraight line Bcircle Cellipse Dhyperbola

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EnglishUP PCS (Pre) 2005

Q170.If the complex numbers Z1, Z2, Z3 represent the vertices of an equilateral triangle, such that 1 2 3 Z = Z = Z then the value of Z1 + Z2+Z3 is:

A1 B–1 C0 D3

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EnglishUP PCS (Pre) 2007

Q171.If w is an imaginary cube root of unity, then the common roots of the equations z3 + 2z2 + 2z + 1 = 0 and z1985 + z100 + 1 = 0 are

A1, w Bw, w2 C1, w2 Dnone of the above

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EnglishUP PCS (Pre) 2007

Q172.If w is an imaginary cube root of unity and x=a+b, y=aw+bw2, z=aw2 +bw, then x3 +y3 +z3 is equal to

Aa3/+ b3 B0 C2(a3 + b3) D3(a3 + b3)

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English

Q173.If 398 1 i + − =x+iy, then (x, y) is equal to

A(–1,0) B(1,0) C(0,–1) D(0,1)

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English(GIC) Lecturer 2015

Q174.If z is a purely real number such that Re(z)<0, then arg(z) is equal to

A–π/2 B0 Cπ/2 Dπ

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English(GIC) Lecturer, 2015

Q175.The sum of nth roots of unity is

A0 B1 C2 DNone of the above

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English(GIC) Lecturer 2015

Q176.Radius of the circle z – 3 = 2 z + 3 is

A2 B3 C4 D5

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English(GIC) Lecturer 2015

Q177.If 3+4i is a root of the equation x2 +px+q = 0, then

Ap = 6, q = 25 Bp = 6, q = –15 Cp = –6, q = –7 Dp = –6, q = 25

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English(GIC) Lecturer, 2015

Q178.If 1 2 1 2 z 3z 1, 3 z z − = − − 2 z 1, then the value of 1 z is

A3 B1/3 C0 DNone of these

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English(GIC) Lecturer 2015

Q179.If 30 15 3 i 3 3 (A iB), 2 2 then (A,B)

A(0, 1) B(–1, 0) C(1, 0) D(0, –1)

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English(GIC) Lecturer 2015

Q180.If n is a positive integer, then– n n 3 i 3 i is equal to –

An 1 n 2 cos 6 Bn n 2 cos 6 Cn 1 n 2 cos 6 DNone of the above

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