MCQ

MCQ 11 Mark

If the replacement set is $\{-5,-3,-1,0,1,3\}$, then the solution set of the inequation $-3 < x <3$ is

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

Answer

Correct option: D.

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

Replacement set $=\{-5,-3,-1,0,1,3\}$
$-3< x <3$
$\therefore x =\{-2,-1,0,1,2\}$ from the replacement set,
Solution set $x=\{-1,0,1\}$

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MCQ 21 Mark

Arjun is twice as old as Shriya. If five years ago his age was three times Shriya’s age, then Arjun’s present age is

A
$10$ years
B
$15$ years
✓
$20$ years
D
$25$ years

Answer

Correct option: C.

$20$ years

Let Shriya’s age $= x$ years
Then Arjun’s age $= 2x$
$5$ years ago,
Age of Shriya was $= (x – 5)$ years
and age of Arjun’s $= (2x – 5)$ years
$\therefore 2x – 5 = 3(x – 5)$
$\Rightarrow 2x – 5 = 3x – 15$
$\Rightarrow 3x – 2x = 15 – 5 = 10$
$\Rightarrow x = 10$
$\therefore$ Arjun’s present age $= 2x = 2 \times 10 = 20$ years

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MCQ 31 Mark

Sum of digits of a two digit number is $8$. If the number obtained by reversing the digits is $18$ more than the original number, then the original number is

✓
$35$
B
$53$
C
$26$
D
$62$

Answer

Correct option: A.

$35$

Sum of digits of a two digit number $=8$
Let unit digit $= x$
Then tens digit $=8- x$
$\therefore$ Number $= x +10(8- x )= x +80-10 x =80-9 x$
By reversing the digits,
Unit digit $=8-x$
and tens digit $=x$
$\therefore$ Number $=8-x+10 x=8+9 x$
$\therefore 8+9 x=80-9 x+18$
$\Rightarrow 9 x+9 x=80+18-8$
$\Rightarrow 18 x=90$
$\Rightarrow x=\frac{90}{18}=5$
$\therefore$ Number $=80-9 x$
$=80-9 \times 5$
$=80-45$
$=35$

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MCQ 41 Mark

What should be added to twice the rational number $\frac{-7}{3}$ to get $\frac{3}{7}$ ?

A
$\frac{58}{21}$
B
$\frac{29}{21}$
C
$\frac{89}{21}$
✓
$\frac{107}{21}$

Answer

Correct option: D.

$\frac{107}{21}$

Let $x$ be added
According to the condition,
$\therefore \frac{-7}{3} \times 2+x=\frac{3}{7}$
$ \frac{-14}{3}+x=\frac{3}{7} $
$\Rightarrow x=\frac{3}{7}+\frac{14}{3}$
$\therefore x=\frac{9+98}{21}=\frac{107}{21}\quad$

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MCQ 51 Mark

If the perimeter of a rectangle is $13 \ cm$ and its Width is $2 \frac{3}{4} \ cm$, then its length is

A
$2 \frac{3}{4} cm$
✓
$3 \frac{3}{4} cm$
C
$4 \frac{3}{4} cm$
D
$5 \frac{3}{4} cm$

Answer

Correct option: B.

$3 \frac{3}{4} cm$

Perimeter of a rectangle $=13 \ cm$
Width $=2 \frac{3}{4}=\frac{11}{4} \ cm$
Let length $=x \ cm$
$\therefore$ Perimeter $=2 ($Length $+$ Breadth$)$
$\Rightarrow 13=2\left(x+\frac{11}{4}\right)$
$\Rightarrow \frac{13}{2}=x+\frac{11}{4}$
$\Rightarrow x=\frac{13}{2}-\frac{11}{4}=\frac{26-11}{4}=\frac{15}{4}$
$\therefore$ Length $=\frac{15}{4}=3 \frac{3}{4} \ cm$

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MCQ 61 Mark

If the sum of three consecutive integers is $51,$ then the largest integer is

A
$16$
B
$17$
✓
$18$
D
$19$

Answer

Correct option: C.

$18$

Let first integers $= x$
Then next two integers $=x+1, x+2$
$\therefore x+x+1+x+2=51$
$\Rightarrow 3 x+3=51$
$\Rightarrow 3 x=51-3=48$
$\Rightarrow x=\frac{48}{3}=16$
$\therefore$ First integer $=16$
and other two integer $=17,18$
Largest integers $=18$

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MCQ 71 Mark

Fifteen years from now Ravi’s age will be four times his present age. What is Ravi’s present age?

A
$4$ years
✓
$5$ years
C
$6$ years
D
$3$ years

Answer

Correct option: B.

$5$ years

Let present age of Ravi $= x$ years
After $15$ years, his age will be $=(x+5)$ years
$\therefore x+15=4 x$
$\Rightarrow 15=4 x-x=3 x$
$\Rightarrow x=\frac{15}{3}=5$
$\therefore$ His present age $=5$ years

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MCQ 81 Mark

If we subtract $\frac{1}{2}$ from a number and multiply the result by $\frac{1}{2}$, we get $\frac{1}{8}$, then the number is

A
$\frac{1}{2}$
✓
$\frac{3}{4}$
C
$\frac{1}{4}$
D
none of these

Answer

Correct option: B.

$\frac{3}{4}$

Let number be $x$, then
$\left(x-\frac{1}{2}\right) \frac{1}{2}=\frac{1}{8}$
$\Rightarrow x-\frac{1}{2}=\frac{1}{8} \times \frac{2}{1}=\frac{1}{4}$
$\Rightarrow x=\frac{1}{4}+\frac{1}{2}=\frac{3}{4}$
$\therefore x=\frac{3}{4} \quad$

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MCQ 91 Mark

The solution of the equation $\frac{8 x-3}{3 x}=2$ is

A
$\frac{1}{2}$
B
$\frac{2}{3}$
✓
$\frac{3}{2}$
D
$\frac{1}{3}$

Answer

Correct option: C.

$\frac{3}{2}$

$\text { Solution of } \frac{8 x-3}{3 x}=2$
$8 x-3=6 x $
$\Rightarrow 8 x-6 x=3$
$\Rightarrow 2 x=3 $
$\Rightarrow x=\frac{3}{2}$

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MCQ 101 Mark

The solution of the equation $\frac{x}{2}-\frac{1}{5}=\frac{x}{3}+\frac{1}{4}$ is

✓
$2.7$
B
$1.8$
C
$2.9$
D
$1.7$

Answer

Correct option: A.

$2.7$

The solution of the equation
$\frac{x}{2}-\frac{1}{5}=\frac{x}{3}+\frac{1}{4}$
$\Rightarrow \frac{x}{2}-\frac{x}{3}=\frac{1}{4}+\frac{1}{5}$
$\Rightarrow \frac{3-2}{6} x=\frac{5+4}{20}$
$ \Rightarrow \frac{1}{6} x=\frac{9}{20}$
$ x=\frac{9}{20} \times \frac{6}{1}=\frac{27}{10}=2.7 \quad$

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MCQ 111 Mark

The solution of the equation $\frac{3 x}{5}+1=\frac{4 x}{15}$ is $+7$ is

A
$12$
B
$14$
C
$16$
✓
$18$

Answer

Correct option: D.

$18$

$\frac{3 x}{5}+1=\frac{4 x}{15}+7$
$\frac{3 x}{5}-\frac{4 x}{15}=7-1$
$=\frac{9 x-4 x}{15}=6 $
$\Rightarrow \frac{5 x}{15}=6$
$x=\frac{6 \times 15}{5}=18 $
$\Rightarrow x=18 $

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MCQ 121 Mark

The solution of the equation $4 z+3=6+2 z$ is

A
$1$
✓
$\frac{3}{2}$
C
$2$
D
$3$

Answer

Correct option: B.

$\frac{3}{2}$

Solution of equation $4 z+3=6+2 z$
$\Rightarrow 4 z-2 z=6-3$
$ \Rightarrow 2 z=3 $
$\Rightarrow z=\frac{3}{2}$

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MCQ 131 Mark

The solution of the equation $\frac{2}{3} x+1=\frac{15}{9}$ is

✓
$1$
B
$\frac{3}{2}$
C
$2$
D
$\frac{2}{3}$

Answer

Correct option: A.

$1$

The solution of the equation
$\frac{2}{3} x+1=\frac{15}{9}$
$\Rightarrow \frac{2}{3} x=\frac{15}{9}-1=\frac{15-9}{9}=\frac{6}{9}$
$ x=\frac{6}{9} \times \frac{3}{2}=1$
$ x=1 \quad$

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MCQ 141 Mark

Which of the following is not a linear equation in one variable?

A
$3x + 2 = 0$
B
$2y – 4 = y$
✓
$x + 2y = 7$
D
$2(x – 3) + 7 = 0$

Answer

Correct option: C.

$x + 2y = 7$

$x + 2y = 7$ is not a linear equation in one variable
as there are two variables $x$ and $y.$

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