Complex Numbers and Quadratic Equations (KVPY Stream-SA (Class 11) Math): Questions 7 - 11 of 27

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Question number: 7

» Complex Numbers and Quadratic Equations » Quadratic Equations in Real and Complex Number System

Appeared in Year: 2013

MCQ▾

Question

In an acute-angled triangle ABC, the altitudes from A, B, C when extended intersect the circle again at points A1, B1, C1, respectively. If ∠ABC = 45° then ∠A1B1C1 equals.

Choices

Choice (4) Response

a.

135°

b.

45°

c.

60°

d.

90°

Question number: 8

» Complex Numbers and Quadratic Equations » Relation Between Roots and Coefficients

Appeared in Year: 2012

MCQ▾

Question

Let f(x) be a quadratic polynomial with f(2)=10 and f(2)=2 . Then the coefficient of x in f(x) is

Choices

Choice (4) Response

a.

1

b.

4

c.

2

d.

3

Question number: 9

» Complex Numbers and Quadratic Equations » Complex Numbers as Ordered Pairs of Reals

Appeared in Year: 2012

MCQ▾

Question

How many ordered pairs of (m, n) integers satisfy m12=12n ?

Choices

Choice (4) Response

a.

30

b.

10

c.

15

d.

12

Question number: 10

» Complex Numbers and Quadratic Equations » Nature of Roots

Appeared in Year: 2013

MCQ▾

Question

Let a, b be non-zero real numbers. Which of the following statements about the quadratic equation.

ax2+(a+b)x+b=0

Is necessarily true?

(I) It has at least one negative root

(III) Both roots are negative

(II) Both its roots are real.

(IV) It has at least one positive root.

Select the correct option,

Choices

Choice (4) Response

a.

(III) and (IV) are correct

b.

(I) and (II) are correct

c.

(I), (II) and (III) are correct

d.

(I) and (III) are correct

Question number: 11

» Complex Numbers and Quadratic Equations » Formation of Quadratic Equations With Given Roots

Appeared in Year: 2014

MCQ▾

Question

Let p(x)=x25x+a and q(x)=x23x+b , where a and b are positive integers. Suppose hcf(p(x),q(x))=x1 and k(x)=lcm(p(x),q(x)) . If the coefficient of the highest degree term of k (x) is 1, the sum of the roots of (x1)+k(x) is

Choices

Choice (4) Response

a.

6

b.

5

c.

4

d.

7

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