MODULOUS Question for CAT 2

Introduction

Tackling the Common Admission Test (CAT) can be an intimidating endeavor, particularly when it involves mastering quantitative aptitude. A crucial concept that often appears in the exam is the modulus function. Grasping how to handle modulus questions is vital for achieving a high score in this section. In this blog, we will delve into various modulus questions aimed at challenging your problem-solving abilities and deepening your understanding of this significant topic. Whether you're taking the test for the first time or aiming to boost your score, these practice questions will equip you with the necessary tools for success. Let's explore the realm of modulus and enhance your CAT exam preparation!

MODULOUS Question for CAT

Q1.For what value of k would the equation, |2x – 1| + |x + 2| = k, have exactly one solution.

a.0.5

b.1

c.2

d.2.5

Q2.Find the number of solution to x² – 3 |x – 2| - 34 = 0.

a.0

b.1

c.2

d.3

Q3.How many integral values of x will satisfy the inequality |x + 1| + |x – 2| + |x + 3| < 15.

a.8

b.10

c.16

d.20

Q4.The number of integers satisfying the inequality |x² – 8x| = 12 is

a.0

b.1

c.2

d.3

Q5.Find the least value of |x – 9| + |x – 8| + …… + |x – 1| + |x| + |x + 1|.

a.60

b.30

c.46

d.90

Q6.What is the minimum value of the function, P(x) = |x - 3| + 3|x - 4| + 2|x - 5| + 3|x - 7|.

a.5

b.7

c.9

d.11

Q7.How many integral values of x satisfy the relation |x² – 5x| < 6.

a.2

b.4

c.5

d.8

Q8.Solve for x; |2x + 6| + |3x – 6| < 12.

a.x < 0

b.x > 3

c.x < 0 or x > 3

d.0 < x < 2.4

Q9.Solve for x: |x + 3| + |x – 2| + |x + 5| = 15.

a.3

b.-7

c.3 or -7

d.No solution

Q10.How many integral values of x will satisfy |x² – 26| < 10.

a.0

b.1

c.2

d.4

Q11.How many Non Negative integral values of x will satisfy (x² − 5x − 6)/|x − 3| ≤ 0.

a.2

b.3

c.5

d.6

Q12.Find the minimum value of |2x - 3| + |x + 5|

a.1.5

b.6.5

c.10

d.12

Q13.For what value of x does the expression |3x – 6| + |2x + 4| assume the least value?

a.-2

b.2

c.2 or -2

d.-2 ≤ x ≤ 2

Q14.Find the minimum value of |x – 2| + |x – 5| + |x + 2|

a.0

b.7

c.10

d.11

Q15.f(x) = |x – 2| + |x – 5| + |x – 9|, Find the value of x at which f(x) attains a minimum value.

a.3

b.4

c.5

d.6

Q16.For which of the following values of x, does the expression f(x) = |x – 2| + |x| + |x + 1| + |x + 3| assume the least value?I. x = 0

II. x = –1

III. x = –0.5

IV. x = 0.5

1. (III)

2. Both (I )and (II)

3. (I), (II) and (III)

4. All four

Q17.f(x) = |x – 3| + |x – 2| + |x – 1| + |x| + |x + 1| + |x + 2| + |x + 3|. For what value of x will f(x) be least? Also find the least value of f(x).

a.x = 0; 6

b.x = 0; 12

c.–3 ≤ x ≤ 3; 6

d.–3 ≤ x ≤ 3; 12

Q18.Find the least value of given expression: |x – 1| + |x – 2| + |x – 3| + |x – 4| + ...... + |x – 99|.

a.0

b.50

c.1225

d.2450

Q19.Solve for x, |x – 1| – |x – 2| = 10.

a.13/2

b.10

c.Both (a) and (b)

d.No solution

Q20.Find the number of non-zero integral solutions of the equation |x| + |y| = 10.

a.20

b.36

c.40

d.48

Q21.Find the number of integral solutions of the equation |x| + |y| = 20.

a.40

b.76

c.80

d.84

Q22.Find the number of integral solutions to |x| + |y| < 7.

a.60

b.61

c.72

d.85

Q23.If |b| ≥ 1 and x = – |a| b, then which one of the following is necessarily true?

a.a – xb < 0

b.a – x b ≥ 0

c,a – xb > 0

d.a – xb ≤ 0

Q24.Find the range of x where ||x - 3| - 4| > 3?

a.(-∞, -4)

b.(-∞, -4) or ( 10, ∞)

c.( -∞, -4) or (2, 4) or ( 10, ∞)

Q25.For how many of the following value of k does the equation |x – 2| + |x – 5| + |x + 4| = k have exactly two integral solutions.

I. k = 9           II. k = 2             III. k = 10           IV. k = 16           V. k = 18

a.0

b.1

c.2

d.3

ANSWERS 

1	2	3	4	5	6	7	8	9	10
D	C	B	C	B	D	B	D	C	C
11	12	13	14	15	16	17	18	19	20
D	B	B	B	C	C	B	D	D	B
21	22	23	24	25
C	D	B	D	C