MCQ

MCQ 11 Mark

If $x \in R$, the solution set of $6 \leq-3(2 x-4)<12$ is

A
$\{x: x \in R, 0\}$
✓
$\{x: x \in R, 0 \leq x<1\}$
C
$\{0,1\}$
D
none of these

Answer

Correct option: B.

$\{x: x \in R, 0 \leq x<1\}$

$
\begin{aligned}
& x \in R \\
& 6 \leq-3(2 x-4)<12 \\
& \Rightarrow 6 \leq-3(2 x-4) \\
& \Rightarrow 6 \leq-6 x+12 \\
& \Rightarrow 6 \leq 12-6 \\
& \Rightarrow 6 x \leq 6 \\
& \Rightarrow x \leq \frac{6}{6} \\
& \Rightarrow x \leq 1
\end{aligned}
$
and
$
\begin{aligned}
& -3(2 x-4)<12 \\
& \Rightarrow-6 x+12<12 \\
& \Rightarrow-6 x<12-12 \\
& \Rightarrow-6 x<0 \\
& \Rightarrow x<0
\end{aligned}
$
From (i) and (ii),
$
\therefore 0< x \leq 1
$
Solution set $=\{x: x \in R

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MCQ 21 Mark

If $x \in I$, then the solution set of the inequation $1<3 x+5 \leq 11$ is

✓
$\{-1,0,1,2\}$
B
$\{-2,-1,0,1\}$
C
$\{-1,0,1\}$
D
$\left\{x: x \in R ,-\frac{4}{3} < x \leq 2\right\}$

Answer

Correct option: A.

$\{-1,0,1,2\}$

$x ∈ I$
$1 < 3x + 5 ≤ 11$
$⇒ 1 < 3x + 5$
$⇒ 1 – 5 < 3x$
$⇒ –4 < 3x$
$\Rightarrow \frac{-4}{3}$ and
$3 + 5 ≤ 11$
$⇒ 3x ≤ 11 – 5$
$⇒ 3x ≤ 6$
$\Rightarrow x \leq \frac{6}{3} $
$ \Rightarrow x \leq 2 $
$ \therefore \frac{-4}{3}$
Solution set $= \{–1, 0, 1, 2\}.$

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MCQ 31 Mark

If $x \in W$, then the solution set of the inequation $5-4 x \leq 2-3 x$ is

A
$\{1,2,3\}$
B
$\{0,1,2,3\}$
✓
$\{x: x \in R, x \leq 3\}$
D
$\{3,4,5, \ldots\}$

Answer

Correct option: C.

$\{x: x \in R, x \leq 3\}$

x ∈ W ....(Given)
5 – 4x ≤ 2 – 3x
⇒ 5 – 2 ≤ – 3x + 4x
⇒ 3 ≤ x
As, x ∈ W, thus the solution set is {3, 4, 5, ....}.

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MCQ 41 Mark

If $x \in W$, then the solution set of the inequation $3 x+11 \geq x+8$ is

A
$\{-2,-1,0,1,2, \ldots\}$
B
$\{-1,0,1,2, \ldots\}$
✓
$\{0,1,2,3, \ldots\}$
D
$\left\{x: x \in R , x \geq-\frac{3}{2}\right\}$

Answer

Correct option: C.

$\{0,1,2,3, \ldots\}$

$
\begin{aligned}
& x \in W \\
& 3 x+11 \geq x+8 \\
& \Rightarrow 3 x-x \geq 8-11 \\
& \Rightarrow 2 x \geq-3 \\
& \Rightarrow x \geq \frac{-3}{2} \\
& \Rightarrow x \geq-1 \frac{1}{2}
\end{aligned}
$
Solution set $=\{0,1,2,3, \ldots\}$.

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MCQ 51 Mark

If $x \in\{-3,-1,0,1,3,5\}$, then the solution set of the inequation $3 x-2 \leq 8$ is

A
$\{-3,-1,1,3\}$
✓
$\{-3,-1,0,1,3\}$
C
$\{-3,-2,-1,0,1,2,3\}$
D
$\{-3,-2,-1,0,1,2\}$

Answer

Correct option: B.

$\{-3,-1,0,1,3\}$

$
\begin{aligned}
& x \in\{-3,-1,0,1,3,5\} \\
& 3 x-2 \leq 8 \\
& \Rightarrow 3 x \leq 8+2 \\
& \Rightarrow 3 x \leq 10 \\
& \Rightarrow x \leq \frac{10}{3} \\
& \Rightarrow x<3 \frac{1}{3}
\end{aligned}
$
Solution set $=\{-3,-1,0,1,3\}$

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