Framing Algebraic Expressions — Multiple Choice Questions

Perimeter of a regular pentagon is $x$ m, its each side is :

1. $5x$ m

2. $(x - 5)$ m

3. $\dfrac{5}{x}$ m

4. $\dfrac{x}{5}$ m

Answer

A regular pentagon has 5 equal sides.

∴ Each side = $\dfrac{\text{Perimeter}}{5} = \dfrac{x}{5}$ m

Hence, option 4 is the correct option.

$x - [y - {z - (x - \overline{y - z})}]$ is :

1. 0

2. $-z$

3. $-x$

4. $-y$

Answer

Solving,

$\Rightarrow x - [y - {z - (x - \overline{y - z})}] \\[1em] \Rightarrow x - [y - {z - (x - y + z)}] \\[1em] \Rightarrow x - [y - {z - x + y - z}] \\[1em] \Rightarrow x - [y - {y - x}] \\[1em] \Rightarrow x - [y - y + x] \\[1em] \Rightarrow x - x = 0.$

Hence, option 1 is the correct option.

If $a = 2$ and $b = 1, a^b - b^a$ is equal to :

1. 3

2. –1

3. 0

4. 1

Answer

Substituting $a$ = 2 and $b$ = 1,

$\Rightarrow a^{b} - b^{a} = 2^{1} - 1^{2} \\[1em] \Rightarrow 2 - 1 = 1.$

Hence, option 4 is the correct option.

If $a = 3, b = -3$ and $c = 1$, then $2a - b + 3c$ is equal to :

1. 6

2. 3

3. 12

4. 9

Answer

Substituting $a$ = 3, $b$ = −3 and $c$ = 1,

$\Rightarrow 2a - b + 3c = 2(3) - (-3) + 3(1) \\[1em] \Rightarrow 6 + 3 + 3 = 12.$

Hence, option 3 is the correct option.

If $x = 3$ and $y = 2$, then the value of $x^2y \div xy^2$ is :

1. 6

2. $\dfrac{2}{3}$

3. $\dfrac{3}{2}$

4. none of these

Answer

Solving,

$\Rightarrow x^{2}y \div xy^{2} \\[1em] \Rightarrow \dfrac{x^{2}y}{xy^{2}} \\[1em] \Rightarrow \dfrac{x}{y} \\[1em] \Rightarrow \dfrac{3}{2}.$

Hence, option 3 is the correct option.

If $3x - 2 = 7$, the value of $x$ is :

1. $\dfrac{5}{3}$

2. 3

3. 0

4. none of these

Answer

Solving,

$\Rightarrow 3x - 2 = 7 \\[1em] \Rightarrow 3x = 7 + 2 \\[1em] \Rightarrow 3x = 9 \\[1em] \Rightarrow x = 3.$

Hence, option 2 is the correct option.

If $\dfrac{x}{3} + 7 = 11$, the value of $x$ is :

1. 25

2. –12

3. 12

4. –10

Answer

Solving,

$\Rightarrow \dfrac{x}{3} + 7 = 11 \\[1em] \Rightarrow \dfrac{x}{3} = 11 - 7 \\[1em] \Rightarrow \dfrac{x}{3} = 4 \\[1em] \Rightarrow x = 4 \times 3 = 12.$

Hence, option 3 is the correct option.

The equation for a number multiplied by 3 and the result divided by 2 is 12, is :

1. $\dfrac{x \times 3}{2}$ = 12

2. $\dfrac{x \times 2}{3}$ = 12

3. $\dfrac{x \times 3}{3}$ = 12

4. none of these

Answer

Let the number be $x$.

The number multiplied by 3 = $x \times 3$

This result divided by 2 = $\dfrac{x \times 3}{2}$

∴ The required equation is $\dfrac{x \times 3}{2} = 12$.

Hence, option 1 is the correct option.

If $9.5 = x - 4.7$, then $x$ is equal to :

1. 4.8

2. 14.2

3. 4.2

4. –4.8

Answer

Solving,

$\Rightarrow 9.5 = x - 4.7 \\[1em] \Rightarrow 9.5 + 4.7 = x \\[1em] \Rightarrow x = 14.2.$

Hence, option 2 is the correct option.

The sum of three consecutive integers is 21, integers are :

1. 6, 7 and 8

2. 5, 6 and 10

3. 4, 8 and 9

4. 8, 10 and 3

Answer

Let the three consecutive integers be $x, x + 1$ and $x + 2$.

$\Rightarrow x + (x + 1) + (x + 2) = 21 \\[1em] \Rightarrow 3x + 3 = 21 \\[1em] \Rightarrow 3x = 18 \\[1em] \Rightarrow x = 6.$

∴ The integers are 6, 7 and 8.

Hence, option 1 is the correct option.

The difference of two natural numbers is 2 and their sum is 14, the numbers are :

1. 4 and 10

2. 6 and 8

3. 5 and 9

4. 7 and 9

Answer

Let the smaller number be $x$, then the larger number = $x$ + 2.

$\Rightarrow x + (x + 2) = 14 \\[1em] \Rightarrow 2x + 2 = 14 \\[1em] \Rightarrow 2x = 12 \\[1em] \Rightarrow x = 6.$

∴ The numbers are 6 and 6 + 2 = 8.

Hence, option 2 is the correct option.

A number $x$ is decreased by 12 and then the new number obtained is multiplied by 2; the result is 30. The equation for this statement is :

1. $x - 12 \times 2 = 30$

2. $\dfrac{x}{2} - 12 = 30$

3. $(x - 12) \times 2 = 30$

4. $x - 12 \div 2 = 30$

Answer

The number $x$ decreased by 12 = ($x$ − 12)

This new number multiplied by 2 = ($x$ − 12) × 2

∴ The required equation is ($x$ − 12) × 2 = 30.

Hence, option 3 is the correct option.