In this blog, I will share the Complex Numbers And Vector Jee Mains Questions with solutions that help crack the Jee main exam. This is a previous year’s question.

## Complex Numbers And Vector Jee Mains Questions

### Complex Numbers Jee Mains Questions

1. Let the complex number z = x + iy be such that (2z-3i/2z+i) is purely imaginary. If x + y2 = 0, then y^{4}+ y^{2} – y is equal to :

(A) 3/2

(B) 2/3

(C) 4/3

(D) 3/4

2. If for z = α + iβ, |z + 2| = z + 4(1 +i), then α + β and αβ are the roots of the equation

(A) x^{2} + 3x – 4 = 0

(B) x^{2} +7x + 12 = 0

(C) x^{2} + x – 12 = 0

(D) x^{2} + 2x – 3 = 0

3. Let α, β be the roots of the equation x^{2} – √2x + 2=0, then α^{14}+β^{14} is equal to

(A) -128√2

(B) -64√2

(C) -128

(D) -64

4. Let p,q∊R and (1 – √3i )^{200} = 2^{199} (p+qi), i=√-1, Then p+q+q^{2} and p-q+q^{2} are roots of the equation.

(A) x^{2}+ 4x – 1 = 0

(B) x^{2} – 4x +1 = 0

(C) x^{2}+ 4x + 1 = 0

(D) x^{2} – 4x – 1 = 0

5. If the centre and radius of the circle are |z-2/z-3| = 2 respectively (α,β)and γ, then 3(α+β+γ) is equal to

(A) 11

(B) 9

(C) 10

(D) 12

6. Let w1 be the point obtained by the rotation of z1 = 5 + 4i about the origin through a right angle in the anticlockwise direction, and w2 be the point obtained by the rotation of z2 = 3 + 5i about the origin through a right angle in the clockwise direction. Then the principal argument of w1 – w2 is equal to :

(A) pi – tan^{-1}(8/9)

(B) – pi + tan^{-1}(8/9)

(C) pi – tan^{-1}(33/5)

(D) – pi + tan^{-1}(33/5)

7. For all z ∈ C on the curve C1 : |z| = 4, let the locus of the point z + 1/ z be the curve C2. Then

(A) The curves C₁ and C₂ intersect at 4 points

(B) The curves C₁ lies inside C₂

(C) The curves C₁ and C₂ intersect at 2 points

(D) The curves C₂ lies inside C₁

8. Let C be the circle in the complex plane with centre z_{0} = 1/2 * (1 + 3i) and radius r = 1. Let z_{1} = 1 + i and the complex number z₂ be outside the circle C such that |z₁ – z_{0} | |z_{2} – z_{0}| = 1 . If z_{0}, z₁ and z₂ are collinear, then the smaller value of |z_{2}|^{2} is equal to

(A) 7/2

(B) 13/2

(C) 5/2

(D) 3/2

9. For two non-zero complex number z₁ and z2, if Re(z_{1}*z_{2}) = 0 and Re(z_{1} + z_{2}) = 0 then which of the following are possible ?

(A) Im(z_{1}) > 0 and Im(z_{2}) > 0

(B) Im(z_{1}) < 0 and Im(z_{2}) > 0

(C) Im(z_{1}) > 0 and Im(z_{2}) < 0

(D) Im(z_{1}) < 0 and Im(z_{2}) < 0 Choose the correct answer from the options given below:

(A) B and D

(B) B and C

(C) A and B

(D) A and C

10. Let z_{1} = 2 + 3i and Z_{2} = 3 + 4i The set S = {z∈ C : |z – z_{1}| ^{2}) – |z – z_{2}|^{2} = |z_{1} – z_{2}| ^{2}} represents a

(A) straight line with sum of its intercepts on the coordinate axes equals 14

(B) hyperbola with the length of the transverse axis 7

(C) a straight line with the sum of its intercepts on the coordinate axes equals -18

(D) hyperbola with eccentricity 2

There are total 97 Complex Numbers Jee Mains previous year Questions and the solution are avilable.

Complex Numbers Jee Mains Questions | Click Here |

### Vector Jee Mains Questions

1. Let |a^{->}| = 2, |b^{->}|= 3 vectors and the angle between the vectors a^{->} and b^{->} be π/4 Then |(a^{->}+2b^{->}) × (2a^{->} – 3b^{->})|^{2 } is equal to

(A) 482

(B) 481

(C) 882

(D) 441

2. Let a^{->} and b^{->} be two vectors. Let |a^{->}|= 1, |b^{->}| = 4 And a^{->}* b^{->} = 2. If c^{->} = (2a^{->} × b^{->}) – 3b^{->}, then the value of b^{->} and c^{->} is

(A) -24

(B) -48

(C) -84

(D) -60

3. if a^{->}=^i+4^j+2^k,b^{->}=3^i−2^j+7^k and c^{->}=2^i−^j+4^k. if a vector d^{->} satisfies d^{->}*b^{->}=c^{->}*b^{->} and d^{->}.a^{->}=24 then |d^{->}|^{2} is equal to

(A) 323

(B) 423

(C) 413

(D) 313

4. a^{->}=2^i+3^j+4^k,b^{->}=^i−2^j-2^k and c^{->}=-^i+4^j+3^k. if d^{->} is a vector perpendicular to both b^{->} and c^{->}, and a^{->}.d^{->} = 18 then |a^{->}*d^{->}| is equal to :

(A) 760

(B) 640

(C) 720

(D) 680

5. Let α ^{->} = 4i + 3j + 5k and β^{->} = i + 2j – 4k Let β_{1} be parallel to α^{->} and β₂^{->} be perpendicular to α^{->} . If β^{->} = β_{1}^{->} +β_{2}^{->} , then the value of 5β_{2}^{->} . (^i + ^j + ^k) is

(A) 6

(B) 11

(C) 7

(D) 9

There are total 124 Vector Jee Mains previous year Questions and the solution are avilable.

Vector Jee Mains Questions | Click Here |

Also read – Binomial Theorem, Sequence And Series Jee Mains Questions