CUET UG Mathematics Applied Inequation Previous Year Questions (PYQs)
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The system of linear inequalities $2x-1 \ge 3$ and $x-3>5$ has solution:
1
2
3
4
Solution
First inequality:
$2x-1 \ge 3$
$2x \ge 4$
$x \ge 2$
Second inequality:
$x-3>5$
$x>8$
Common solution:
$x>8$
So solution set is
$(8,\infty)$
The values of $x$ which satisfied $|3x| \ge |6-3x|$
A. $(0,1]$
B. $[1,4]$
C. $(4,\infty)$
D. $(-1,0)$
E. $(-\infty,0)$
Choose the correct answer from the options given below:
1
2
3
4
Solution
Given
$|3x| \ge |6-3x|$
$3|x| \ge 3|2-x|$
Divide by 3:
$|x| \ge |2-x|$
Square both sides:
$x^2 \ge (2-x)^2$
$x^2 \ge 4-4x+x^2$
Cancel $x^2$:
$0 \ge 4-4x$
$4x \ge 4$
$x \ge 1$
So solution set:
$[1,\infty)$
From given intervals:
B: $[1,4]$ ✔
C: $(4,\infty)$ ✔
CUET UG Mathematics Applied
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CUET UG Mathematics Applied
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and More.
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