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IIT - JEE 2015 Practise Test MARKS: 45 Time: 50 Min Topic: Location of Roots DATE: 02/08/13 Single Choice Questions (+3, - 1)

This document contains a practice test for IIT-JEE 2015 on the topic of location of roots. The test has 15 multiple choice questions regarding finding the values of parameters for which quadratic equations have real or imaginary roots within certain intervals. The test provides the questions, options for each question, and information on marks and date. It also lists various exam centers across India where the exam may be held.

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Sarvesh Dubey
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208 views2 pages

IIT - JEE 2015 Practise Test MARKS: 45 Time: 50 Min Topic: Location of Roots DATE: 02/08/13 Single Choice Questions (+3, - 1)

This document contains a practice test for IIT-JEE 2015 on the topic of location of roots. The test has 15 multiple choice questions regarding finding the values of parameters for which quadratic equations have real or imaginary roots within certain intervals. The test provides the questions, options for each question, and information on marks and date. It also lists various exam centers across India where the exam may be held.

Uploaded by

Sarvesh Dubey
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF, TXT or read online on Scribd
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ANDHERI / BORIVALI / DADAR / CHEMBUR / THANE / MULUND/ NERUL / POWAI

IIT JEE 2015


TIME: 50 MIN

PRACTISE TEST
TOPIC: LOCATION OF ROOTS

MARKS: 45
DATE: 02/08/13

Single Choice Questions (+3, 1)


1.

Find the values of a for which x 2 ax 4 is negative for at least one value of x
(a) a , 4 4,
(b) a 4, 4
(c) a , 4 4,

2.

(d) None of these

Find the values of m for which both roots of x 2 4 m x 4m 0 are greater than 4
(a) a 4,

(b) a 5,

(c) a 4,

(d) None of these

3.

If x 2 abx 1 0 has real roots. Then the minimum values of a 2 b 2 is


(a) 4
(b) 8
(c) 2
(d) 1

4.

Find the values of a so that sin 2 2a sin 3 0 has no roots


(a) a ,
(b) a , 1 1,
(d) a 1,1

(c) none of these


5.

Find

the

values

of

for

which

both

roots

, 0,3

of

the

equation

m 3 x 2 2 m 2 x m 1 0 : , 0,3
(a) m 1,
(b) m ,
(c) m ,1 3,
(d) m ,1 4,
6.

2 cos
sin
(a) , 2 2,

(b) cannot be determined

(c) ,

(d) , 3

Find the range of

3,

7.

If x 2 3ax 1 0 has imaginary roots then the number of integral values of a are
(a) 2
(b) 1
(c) 3
(d) 4

8.

If the equation ax 2 3bx 9c 0 has imaginary roots, then a 2 c2 b 2 2ac


(a) Always positive
(b) Always Negative
(c) zero
(d) cannot be determined

9.

For what values of m R do both roots of the equation x 2 6mx 9m 2 2m 2 0 exceed 3.


11
11
(a) m ,1
(b) m ,
(c) m 1,
(d) m 1,
9

10.

The values of m for which both roots of the equation x 2 2mx m2 1 0 lies in the interval (2, 4)
(a) m 2, 4
(b) m 4,
(c) m 1,3
(d) m , 2 4,

CENTERS: MUMBAI / DELHI / AKOLA / KOLKATA / LUCKNOW / NASHIK / GOA

11.

The values of a for which the inequality a9 x 4 a 1 3x a 1 is satisfied for all real values of x.
[The range of 3x is 0, ]
4
(a) a 1,
3

(b) a 1,
6

12.

13.

(c) x 5, 1

(d) none of these

Find the values of a for which roots of x 2 ax 3x a 2 0 lie in the interval (2,3)

8
(b) a 1,
3

(c) a 3, 7

(d) none of these

x 1 2a x 4 x 2 1 3 x 2 x 1 0 is an equation. Find values of a for which all 4

roots are real. [Given that the range of

3,
(c) a , 3
(a) a

15.

4
(d) a ,1 ,
3

x 1 x 5 0
Solve for x:
x 1
(a) x 5, 1
(b) x 5, 1

(a) a ,

14.

(c) a 1,

3,

1
x2 x 1
is between and 3]
2
x x 1
3
(b) a 3,3

(d) a

3, 2

Find values of a for which x 2 a 2 x a 2 0 for all x R


2

(a) a , 2,
3

(c) a , 2,
3

(b) a

2
(d) a , 2 ,
3

CENTERS: MUMBAI / DELHI / AKOLA / KOLKATA / LUCKNOW / NASHIK / GOA

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