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Test: Inequalities- 2 - CAT MCQ


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13 Questions MCQ Test Quantitative Aptitude (Quant) - Test: Inequalities- 2

Test: Inequalities- 2 for CAT 2024 is part of Quantitative Aptitude (Quant) preparation. The Test: Inequalities- 2 questions and answers have been prepared according to the CAT exam syllabus.The Test: Inequalities- 2 MCQs are made for CAT 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test: Inequalities- 2 below.
Solutions of Test: Inequalities- 2 questions in English are available as part of our Quantitative Aptitude (Quant) for CAT & Test: Inequalities- 2 solutions in Hindi for Quantitative Aptitude (Quant) course. Download more important topics, notes, lectures and mock test series for CAT Exam by signing up for free. Attempt Test: Inequalities- 2 | 13 questions in 15 minutes | Mock test for CAT preparation | Free important questions MCQ to study Quantitative Aptitude (Quant) for CAT Exam | Download free PDF with solutions
Test: Inequalities- 2 - Question 1
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3x2 - 7x + 4 ≤ 0

Detailed Solution for Test: Inequalities- 2 - Question 1

At x = 0, inequality is not satisfied. Thus, option (c) is rejected. Also x = 0 is not a solution of the equation. Since, this is a continuous function, the solution cannot start from 0. Thus options (a) and (b) are not right. Further, we see that the given function is quadratic with real roots. Hence, option (d) is also rejected.

Test: Inequalities- 2 - Question 2
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3x2 - 7x + 6 < 0

Detailed Solution for Test: Inequalities- 2 - Question 2

At x = 0, inequality is not satisfied.
Hence, options (b), (c) and (d) are rejected. At x = 2, inequality is not satisfied. Hence, option (a) is rejected.
Thus, option (d) is correct.

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Test: Inequalities- 2 - Question 3
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X2 - 14x - 15 > 0

Detailed Solution for Test: Inequalities- 2 - Question 3

Test: Inequalities- 2 - Question 4
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For all integral values of x,

|x - 4| x< 5
Detailed Solution for Test: Inequalities- 2 - Question 4

At x = 0 inequality is satisfied, option (b) is rejected.

At x = 2, inequality is satisfied, option (c) is rejected.

At x = 5, LHS = RHS.

Thus, option (d) is correct.

Test: Inequalities- 2 - Question 5
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|x2 - 2x| < x
Detailed Solution for Test: Inequalities- 2 - Question 5

At x = 1 and x = 3 LHS = RHS.
At x = 2 inequality is satisfied.
At x = 0.1 inequality is not satisfied.
At x = 2.9 inequality is satisfied.
At x = 3.1 inequality is not satisfied.
Thus, option (a) is correct.

Test: Inequalities- 2 - Question 6
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x2 - 7x + 12 < | x - 4 |
Detailed Solution for Test: Inequalities- 2 - Question 6

At x = 0, inequality is not satisfied, option (a) is rejected.

At x = 5, inequality is not satisfied, option (b) is rejected.
At x = 2 inequality is not satisfied.
Options (d) are rejected.
Option (c) is correct.

Test: Inequalities- 2 - Question 7
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|x - 6| > x2 - 5x + 9
Detailed Solution for Test: Inequalities- 2 - Question 7

At x = 2, inequality is satisfied.
At x = 0, inequality is not satisfied.
At x = 1, inequality is not satisfied but LHS = RHS. At x = 3, inequality is not satisfied but LHS = RHS. Thus, option (b) is correct.
Solve other questions of LOD I and LOD II in the same fashion.

Test: Inequalities- 2 - Question 8
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3x2 – 7x – 6 < 0
Detailed Solution for Test: Inequalities- 2 - Question 8

At x = 0, inequality is satisfied. Hence, options (b) and (c) are rejected. x = 3 gives LHS = RHS.
and x = – 0.66 also does the same. Hence. roots of the equation are 3 and – 0.66.
Thus, option (a) is correct.

Test: Inequalities- 2 - Question 9
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x2 – 14x – 15 > 0
Detailed Solution for Test: Inequalities- 2 - Question 9

At x = 0 inequality is not satisfied. Thus option (d) is rejected.
x = –1 and x = 15 are the roots of the quadratic equation. Thus, option (c) is correct.

Test: Inequalities- 2 - Question 10
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|x2 + x| – 5 < 0
Test: Inequalities- 2 - Question 11
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|x2 – 2x – 3| < 3x – 3
Detailed Solution for Test: Inequalities- 2 - Question 11

x2 - 2x - 3 ≥ 0
(x-3) (x+1) ≥ 0
x belongs to (-∞,-3]∪[3,∞)
Therefore, x belongs to (-1,3)
=> x2 - 2x - 3 > 0
x2 - 2x - 3< 3x - 3
x2 - 5x < 0
x(x-5) < 0
x belongs to (0,5)........(1)
x2 - 2x - 3 < 0
x2 - 2x - 3 < 3x - 3
x2 + x - 6 > 0
(x+3)(x-2) > 0
x belongs to (-∞,-3]∪[2,∞)
x belongs to (2,3)........(2)
Taking intersection of (1) and (2)
we get,
x belongs to (2,5)
 

Test: Inequalities- 2 - Question 12
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x2 – 7x + 12 < |x – 4|
Detailed Solution for Test: Inequalities- 2 - Question 12

At x = 0, inequality is not satisfied, option (a) is rejected.
At x = 5, inequality is not satisfied, option (b) is rejected.
At x = 2 inequality is not satisfied.
Options (d) are rejected.
Option (c) is correct

Test: Inequalities- 2 - Question 13
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|x – 6| > x2 – 5x + 9
Detailed Solution for Test: Inequalities- 2 - Question 13

At x = 2, inequality is satisfied.
At x = 0, inequality is not satisfied.
At x = 1, inequality is not satisfied but LHS = RHS.
At x = 3, inequality is not satisfied but LHS = RHS.
Thus, option (b) is correct.
Solve other questions of LOD I and LOD II in the same fashion.

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Inequalities- 2 MCQs with Answers

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