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Test: Inequalities- 2 - CAT MCQ


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13 Questions MCQ Test - Test: Inequalities- 2

Test: Inequalities- 2 for CAT 2024 is part of CAT 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 course for CAT & Test: Inequalities- 2 solutions in Hindi for CAT 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 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

Hence, option D is correct

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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