﻿ IIT - JEE Main Important Questions of Complex Numbers and Quadratic Equations | Zigya

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# Complex Numbers and Quadratic Equations

#### Multiple Choice Questions

1.

The sum of all real values of x satisfying the equation
is:

• 3

• -4

• 6

• 6

654 Views

2.

A complex number z is said to be unimodular, if |z|= 1. suppose z1 and z2 are complex numbers such that  is unimodular and z2 is not unimodular. Then, the point z1 lies on a

• straight line parallel to X -axis

• straight line parallel to Y -axis

264 Views

3.
Let α and  β be the roots of equations x2-6x-2 = 0. If ann- βn, for n≥1, the value of a10-2a8/2a9 is equal to
• 6

• -6

• 3

• 3

856 Views

4.

The normal to the curve x2 + 2xy-3y2 =0 at (1,1)

• does not meet the curve again

• meets the curve again in the second quadrant

• meets the curve again in the third quadrant

• meets the curve again in the third quadrant

247 Views

5.

If z is a complex number such that |z|≥2, then the minimum value of

• is equal to 5/2

• lies in the interval (1,2)

• is strictly greater than 5/2

• is strictly greater than 5/2

287 Views

6.

Let α and β be the roots of equation px2 +qx r =0 p ≠0. If p,q and r are in AP and  = 4, then the value of |α- β| is

220 Views

7.

If the coefficients of x3 and x4 in the expansion of (1+ax+bx2)(1-2x)18 in powers of x are both zero, then (a,b) is equal to

246 Views

8.

If [a x b b x c c x a] = λ[a b c]2, then λ is equal to

• 0

• 1

• 2

• 2

261 Views

9.

The real number k for which the equation, 2x3 +3x +k = 0 has two distinct real roots in [0,1]

• lies between 1 and 2

• lies between 2 and 3

• lies between -1 and 0

• lies between -1 and 0

183 Views

10.

If the equations x2 + 2x + 3 = 0 and ax2 + bx + c = 0, a, b, c ∈ R, have a common root, then a : b : c is

• 1:2:3

• 3:2:1

• 1:3:2

• 1:3:2

177 Views