Complex Numbers And Vector Jee Mains Questions

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 y4+ y2 – 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) x2 + 3x – 4 = 0
(B) x2 +7x + 12 = 0
(C) x2 + x – 12 = 0
(D) x2 + 2x – 3 = 0

3. Let α, β be the roots of the equation x2 – √2x + 2=0, then α1414 is equal to
(A) -128√2
(B) -64√2
(C) -128
(D) -64

4. Let p,q∊R and (1 – √3i )200 = 2199 (p+qi), i=√-1, Then p+q+q2 and p-q+q2 are roots of the equation.
(A) x2+ 4x – 1 = 0
(B) x2 – 4x +1 = 0
(C) x2+ 4x + 1 = 0
(D) x2 – 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 z0 = 1/2 * (1 + 3i) and radius r = 1. Let z1 = 1 + i and the complex number z₂ be outside the circle C such that |z₁ – z0 | |z2 – z0| = 1 . If z0, z₁ and z₂ are collinear, then the smaller value of |z2|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(z1*z2) = 0 and Re(z1 + z2) = 0 then which of the following are possible ?
(A) Im(z1) > 0 and Im(z2) > 0
(B) Im(z1) < 0 and Im(z2) > 0
(C) Im(z1) > 0 and Im(z2) < 0
(D) Im(z1) < 0 and Im(z2) < 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 z1 = 2 + 3i and Z2 = 3 + 4i The set S = {z∈ C : |z – z1| 2) – |z – z2|2 = |z1 – z2| 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 QuestionsClick 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 β1 be parallel to α-> and β₂-> be perpendicular to α-> . If β-> = β1->2-> , then the value of 5β2-> . (^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 QuestionsClick Here

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