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This mock test of Test: Complex Numbers for JEE helps you for every JEE entrance exam.
This contains 30 Multiple Choice Questions for JEE Test: Complex Numbers (mcq) to study with solutions a complete question bank.
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QUESTION: 1

Number of values `p' for which the equation (p^{2} – 3p + 2) x^{2} – (p^{2} – 5p + 4)x + p – p^{2} = 0 possess more than two roots, is

Solution:

QUESTION: 2

The roots of the equation (b – c) x^{2} + (c – a) x + (a – b) = 0 are

Solution:

QUESTION: 3

If a, b are the roots of quadratic equation x^{2} + px + q = 0 and g, d are the roots of x^{2} + px – r = 0, then (a – g) . (a - d) is equal to

Solution:

QUESTION: 4

Two real numbers a & b are such that a + b = 3 & |a - b| = 4, then a & b are the roots of the quadratic equation

Solution:

QUESTION: 5

If a, b, c are integers and b^{2} = 4(ac + 5d^{2}), d ∈ N, then roots of the equation ax^{2} + bx + c = 0 are

Solution:

b^{2} = 4(ac + 5d^{2})

b^{2} = 4ac + 20d^{2}

b^{2} – 4ac = 20d^{2}

D = 20d^{2 }

As D > 0, roots of the equation ax^{2} + bx + c = 0 are real.

D^{1/2} = 2*(5^{1/2}) *d

D^{1/2} is irrational.

As a, b, c are integers, roots of the equation are irrational.

QUESTION: 6

Let a, b and c are real numbers such that 4a + 2b + c = 0 and ab > 0. Then the equation ax^{2} + bx + c = 0 has

Solution:

QUESTION: 7

Which of the following graph represents expression f(x) = ax^{2} + bx + c (a < 0) when a > 0, b < 0 & c < 0 ?

Solution:

QUESTION: 8

The expression y = ax^{2} + bx + c has always the same sign as of `a' if

Solution:

For the quadratic curve to always have the same sign, it must never cut the X-axis, i i.e. it must not have any real roots.

So, b^{2} – 4ac < 0

4ac > b^{2}

QUESTION: 9

If a, b ∈ R, a < 0 and the quadratic equation ax^{2} – bx + 1 = 0 has imaginary roots then a + b + 1 is

Solution:

**The correct option is A.**

**Error in the question : a is not less than zero. It should be a0**

**We have D0**

**(-b)2-4a0a0**

**So the parabola formed is open upwards**

**f(-1)=a+b+10 as for negative values of x , y is always positive**

QUESTION: 10

If a and b are the non–zero distinct roots of x^{2} + ax + b = 0, then the least value of x^{2} + ax + b is

Solution:

QUESTION: 11

If y = –2x^{2} – 6x + 9, then

Solution:

QUESTION: 12

The number of the integer solutions of x^{2} + 9 < (x + 3)^{2} < 8x + 25 is

Solution:

QUESTION: 13

If both roots of the quadratic equation (2 – x) (x + 1) = p are distinct & positive, then p must lie in the interval

Solution:

QUESTION: 14

The equatiobn π^{x} = –2x^{2} + 6x – 9 has

Solution:

The RHS of the expression has a<0 which means the graph will lie below the x-axis and π^{x} lies above the x-axis.Therefore,no solution.

QUESTION: 15

Let a > 0, b > 0 and c > 0. Then both the roots of the equation ax^{2} + bx + c = 0

Solution:

QUESTION: 16

The set of all solutions of the inequality < 1/4 contains the set

Solution:

QUESTION: 17

Consider y =, where x is real, then the range of expression y^{2} + y – 2 is

Solution:

QUESTION: 18

The values of k, for which the equation x^{2} + 2(k – 1) x + k + 5 = 0 possess atleast one positive root, are

Solution:

QUESTION: 19

If > 4, then least and the highest values of 4x^{2} are

Solution:

QUESTION: 20

If coefficients of the equation ax^{2} + bx + c = 0, a < 0 are real and roots of the equation are non–real complex and a + c + b < 0, then

Solution:

QUESTION: 21

If the roots of the equation x^{2} + 2ax + b = 0 are real and distinct and they differ by at most 2m, then b lies in the interval

Solution:

QUESTION: 22

If the roots of the quadratic equation x^{2} + px + q = 0 are tan 30º and tan 15º respectively, then the value of 2 + q – p is

Solution:

QUESTION: 23

If (1 – p) is root of quadratic equation x^{2} + px + (1 – p) = 0, then its roots are

Solution:

QUESTION: 24

The values of x and y besides y can satisfy the equation (x, y ∈ real numbers) x^{2}– xy + y^{2} – 4x – 4y + 16 = 0

Solution:

QUESTION: 25

For what value of a and b the equation x^{4} – 4x^{3} + ax^{2} + bx + 1 = 0 has four real positive roots ?

Solution:

QUESTION: 26

If a, b are roots of the equation ax^{2} + bx + c = 0, then the value of a^{3} + b^{3} is

Solution:

QUESTION: 27

If z_{1} = 2 + i, z_{2} = 1 + 3i, then Re ( z_{1} - z_{2}) =

Solution:

The numbers in the questions are not very clear.

z_{1} = 2 + i

z_{2} = 1+3i

z_{1} – z_{2} = (2 – 1) + i (1 – 3)

= 1 – 2i

QUESTION: 28

If a, b are roots of the equation ax^{2} + bx + c = 0 then the equation whose roots are 2a + 3b and 3a + 2b is

Solution:

QUESTION: 29

If S is the set of all real x such that is positive, then S contains

Solution:

QUESTION: 30

If the roots of the equation x^{2} - 5x + 16 = 0 are a, b and the roots of the equation x^{2} + px + q = 0 are (a^{2} + b^{2}) and , then-

Solution:

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