MCQ

MCQ 11 Mark

Mark $(\checkmark)$ against the correct answer of the following: $\Big(\frac{-1}{3}\Big)^{3}=\ ?$

A
$\frac{-1}{9}$
B
$\frac{1}{9}$
✓
$\frac{-1}{27}$
D
$\frac{1}{27}$

Answer

Correct option: C.

$\frac{-1}{27}$

$\Big(\frac{-1}{3}\Big)^{3}$
$=\frac{-1^3}{3^3}$
$=\frac{-1}{27}$

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MCQ 21 Mark

Tick $(\checkmark)$ the correct answer the following:
$0.000367 \times 10^4$ in usual form is:

✓
$3.67$
B
$36.07$
C
$0.367$
D
$0.0367$

Answer

Correct option: A.

$3.67$

$0.000367\times10^4$
$=0.000367\times10000$
$=\frac{367}{1000000}\times10000$
$=\frac{367}{100}$
$=3.67$

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MCQ 31 Mark

Tick $(\checkmark)$ the correct answer the following: $\Big(-\frac{1}{2}\Big)^{3}=\ ?$

A
$\frac{-1}{6}$
B
$\frac{1}{6}$
✓
$\frac{1}{8}$
D
$\frac{-1}{8}$

Answer

Correct option: C.

$\frac{1}{8}$

$\Big(\frac{-1}{2}\Big)^{3}$
$=\Big(\frac{-1}{2}\Big)\times\Big(\frac{-1}{2}\Big)\times\Big(\frac{-1}{2}\Big)$
$=\frac{-1}{8}$

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MCQ 41 Mark

Tick $(\checkmark)$ the correct answer the following:
The value of $(3^{-1} + 4^{-1})^{-1} ÷ 5^{-1}$ is:

A
$\frac{7}{10}$
✓
$\frac{60}{7}$
C
$\frac{7}{5}$
D
$\frac{7}{15}$

Answer

Correct option: B.

$\frac{60}{7}$

$\big(-3^{-1}+4^{-1}\big)\div5^{-1}$
$=\Big(\frac{1}{3}+\frac{1}{4}\Big)^{-1}\div\frac{1}{5}$
$=\Big(\frac{4+3}{12}\Big)^{-1}\div\frac{1}{5}$
$=\Big(\frac{7}{12}\Big)^{-1}\div\frac{1}{5}$
$=\Big(\frac{12}{7}\Big)\div\frac{1}{5}$
$=\Big(\frac{12}{7}\Big)\times{5}$
$=\frac{60}{7}$

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MCQ 51 Mark

Mark $(\checkmark)$ against the correct answer of the following: The value of $(-3)^{-3}$ is:

A
$-27$
B
$9$
✓
$\frac{-1}{27}$
D
$\frac{1}{27}$

Answer

Correct option: C.

$\frac{-1}{27}$

$(-3)^{-3}=\Big(\frac{1}{-3}\Big)^3$
$=\frac{1^3}{-3^3}$
$=\frac{1}{-27}$
$=\frac{1\times-1}{-27\times-1}$
$=\frac{-1}{27}$

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MCQ 61 Mark

Tick $(\checkmark)$ the correct answer the following:
The value of $(-2)^{-5}$ is

A
$-32$
✓
$\frac{-1}{32}$
C
$32$
D
$\frac{1}{32}$

Answer

Correct option: B.

$\frac{-1}{32}$

$(-2)^{-5}$
$=\frac{1}{(-2)^5}$
$=\frac{1}{-32}$
$=\frac{-1}{32}\Big[\because(\text{x})^{-\text{m}}=\frac{1}{\text{x}^{\text{m}}}\Big]$

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MCQ 71 Mark

Tick $(\checkmark)$ the correct answer the following: $\bigg\{\Big(\frac{1}{3}\Big)^{-3}-\Big(\frac{1}{2}\Big)^{-3}\bigg\}\div\Big(\frac{1}{4}\Big)^{-3}=\ ?$

✓
$\frac{19}{64}$
B
$\frac{27}{16}$
C
$\frac{64}{19}$
D
$\frac{16}{25}$

Answer

Correct option: A.

$\frac{19}{64}$

$\bigg\{\Big(\frac{1}{3}\Big)^{-3}-\Big(\frac{1}{2}\Big)^{-3}\bigg\}\div\Big(\frac{1}{4}\Big)^{-3}$
$=\big(3^3-2^3\big)\div(4)^3$
$=(27-8)\div64$
$=\frac{19}{64}$

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MCQ 81 Mark

Tick $(\checkmark)$ the correct answer the following: The value of $x$ for which $\Big(\frac{7}{12}\Big)^{-4}\times\Big(\frac{7}{12}\Big)^{3\text{x}}=\Big(\frac{7}{12}\Big)^5$, is:

A
$-1$
B
$1$
C
$2$
✓
$3$

Answer

Correct option: D.

$3$

$\Big(\frac{7}{12}\Big)^{-4}\times\Big(\frac{7}{12}\Big)^{3\text{x}}=\Big(\frac{7}{12}\Big)^5$
$\Rightarrow\Big(\frac{7}{12}\Big)^{3\text{x}-4}$
$=\Big(\frac{7}{12}\Big)^5$
$=3\text{x}-4=5$
$=3\text{x}=5+4=9$
$\Rightarrow\text{x}=\frac{9}{3}$
$=3$

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MCQ 91 Mark

Tick $(\checkmark)$ the correct answer the following:
$3670000$ in standard form is:

A
$367 \times 10^4$
B
$36.7 \times 10^5$
✓
$3.67 \times 10^6$
D
None of these.

Answer

Correct option: C.

$3.67 \times 10^6$

$3670000 = 3.670000 \times 1000000$
$=3.67 \times 10^6$

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MCQ 101 Mark

Tick $(\checkmark)$ the correct answer the following: $\Big(\frac{-3}{4}\Big)^{2}=\ ?$

A
$\frac{-9}{16}$
✓
$\frac{9}{16}$
C
$\frac{16}{9}$
D
$\frac{-16}{9}$

Answer

Correct option: B.

$\frac{9}{16}$

$\Big(\frac{-3}{4}\Big)^{2}$
$=\Big(\frac{-3}{4}\Big)\times\Big(\frac{-3}{4}\Big)$
$=\frac{9}{16}$

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MCQ 111 Mark

Mark $(\checkmark)$ against the correct answer of the following: The value of $\Big(\frac{3}{4}\Big)^{-3}$ is:

A
$\frac{-27}{64}$
✓
$\frac{64}{27}$
C
$\frac{-9}{4}$
D
$\frac{27}{64}$

Answer

Correct option: B.

$\frac{64}{27}$

$=\Big(\frac{3}{4}\Big)^{-3}$
$=\Big(\frac{4}{3}\Big)^{3}$
$=\frac{4^3}{3^3}$
$=\frac{64}{27}$

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MCQ 121 Mark

Tick $(\checkmark)$ the correct answer the following: $0.0000463$ in standard form is:

A
$463 \times 10^{-7}$
✓
$4.63 \times 10^{-5}$
C
$4.63 \times 10^{-9}$
D
$46.3 \times 10^{-6}$

Answer

Correct option: B.

$4.63 \times 10^{-5}$

$0.0000463$
$=\frac{463}{10000000}$
$=\frac{463}{10^2\times10^5}$
$=\frac{4.63}{10^5}$
$=4.63\times10^{-5}$

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MCQ 131 Mark

Tick $(\checkmark)$ the correct answer the following: $\Big(\frac{-5}{3}\Big)^{-1}=\ ?$

A
$\frac{5}{3}$
B
$\frac{3}{5}$
✓
$\frac{-3}{5}$
D
None of these.

Answer

Correct option: C.

$\frac{-3}{5}$

$\Big(\frac{-5}{3}\Big)^{-1}=\Big(\frac{-3}{5}\Big)^{1}$
$=\frac{-3}{5}\ \bigg\{\because\Big(\frac{1}{\text{x}}\Big)^{-\text{m}}=\text{x}^\text{m}\bigg\}$

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MCQ 141 Mark

Tick $(\checkmark)$ the correct answer the following: $\big(2^{-5}\div2^{−2}\big) = ?$

A
$\frac{1}{128}$
B
$\frac{-1}{128}$
C
$-\frac{1}{8}$
✓
$\frac{1}{8}$

Answer

Correct option: D.

$\frac{1}{8}$

$\big(2^{-5}\div2^{-2}\big)$
$=2^{-5-(-2)}$
$=2^{-5+2}$
$=2^{-3}\{\because\text{a}^\text{m}\div\text{a}^\text{n}=\text{a}^{\text{m-n}}\}$
$=\frac{1}{2^3}$
$=\frac{1}{8}$

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MCQ 151 Mark

Tick $(\checkmark)$ the correct answer the following:
If $\left(2^{3 x-1}+10\right) \div 7=6$, then $x$ is equal to:

A
$-2$
B
$0$
C
$1$
✓
$2$

Answer

Correct option: D.

$2$

$\big[2^{3\text{x}-1}+10\big]\div7=6$
$=2^{3\text{x}-1}+10=6\times7$
$=2^{3\text{x}-1}+10=42 $
$\Rightarrow2^{3\text{x}-1}=42-10$
$\Rightarrow2^{3\text{x}-1}=32$
$\Rightarrow2^{3\text{x}-1}=(2)^5$
$\therefore3\text{x}-1=5$
$\Rightarrow3\text{x}=5+1$
$\Rightarrow3\text{x}=6$
$\Rightarrow\text{x}=\frac{6}{3}$
$\Rightarrow\text{x}=2$

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MCQ 161 Mark

Mark $(\checkmark)$ against the correct answer of the following:
$\left(3^{-6} \div 3^4\right)=?$

A
$3^{-2}$
B
$3^2$
✓
$3^{-10}$
D
$3^{10}$

Answer

Correct option: C.

$3^{-10}$

$=\big(3^{-6}\div3^4\big)$
$=\Big(\frac{1}{3^{-6}}\div3^4\Big)$
$=\frac{1}{3^6}\times\frac{1}{3^4}$
$=\frac{1}{3^{(6+4)}}$
$=\frac{1}{3^{10}}$
$=3^{-10}$

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MCQ 171 Mark

Mark $(\checkmark)$ against the correct answer of the following: $\Big(\frac{3}{5}\Big)^{0}=\ ?$

A
$\frac{5}{3}$
B
$\frac{3}{5}$
✓
$1$
D
$0$

Answer

Correct option: C.

$1$

Using the law of exponents, which says $\Big(\frac{\text{a}}{\text{b}}\Big)^0=1$,
We get, $\Big(\frac{3}{5}\Big)^{0}$

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MCQ 181 Mark

Tick $(\checkmark)$ the correct answer the following:
The value of $(-3)^{-4}$ is:

A
$12$
B
$81$
C
$-\frac{1}{12}$
✓
$\frac{1}{81}$

Answer

Correct option: D.

$\frac{1}{81}$

$(-3)^{-4}$
$=\Big(\frac{1}{-3}\Big)^{-4}$
$=\frac{1}{(-3)\times(-3)\times(-3)\times(-3)}$
$=\frac{1}{81}$

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MCQ 191 Mark

Tick $(\checkmark)$ the correct answer the following: $\Big(\frac{2}{3}\Big)^0=\ ?$

A
$\frac{3}{2}$
B
$\frac{2}{3}$
✓
$1$
D
$0$

Answer

Correct option: C.

$1$

$\Big(\frac{2}{3}\Big)^0=1\ \big(\because\text{x}^0=1\big)$

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MCQ 201 Mark

Tick $(\checkmark)$ the correct answer the following: $\Big(\frac{1}{2}\Big)^{-2}+\Big(\frac{1}{3}\Big)^{-2}+\Big(\frac{1}{4}\Big)^{-2}$

A
$\frac{61}{144}$
B
$\frac{144}{61}$
✓
$29$
D
$\frac{1}{29}$

Answer

Correct option: C.

$29$

$\Big(\frac{1}{2}\Big)^{-2}+\Big(\frac{1}{3}\Big)^{-2}+\Big(\frac{1}{4}\Big)^{-2}$
$=(2)^2+(3)^2+(4)^2$
$=4+9+16\ \because\Big(\frac{1}{\text{x}}\Big)^{-\text{m}}=\text{x}^\text{m}$
$=29$

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MCQ 211 Mark

Tick $(\checkmark)$ the correct answer the following: The value of $\Big(\frac{2}{5}\Big)^{-3}$ is:

A
$-\frac{8}{125}$
B
$\frac{25}{4}$
✓
$\frac{125}{8}$
D
$-\frac{2}{5}$

Answer

Correct option: C.

$\frac{125}{8}$

$\Big(\frac{2}{5}\Big)^{-3}$
$=\Big(\frac{5}{2}\Big)^3$
$=\frac{5\times5\times5}{2\times2\times2}$
$=\frac{125}{8}$

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MCQ 221 Mark

Mark $(\checkmark)$ against the correct answer of the following: $\Big(\frac{-6}{5}\Big)^{-1}=\ ?$

A
$\frac{6}{5}$
B
$\frac{-6}{5}$
C
$\frac{5}{6}$
✓
$\frac{-5}{6}$

Answer

Correct option: D.

$\frac{-5}{6}$

$\Big(\frac{-6}{5}\Big)^{-1}$
$=\Big(\frac{5}{-6}\Big)^{1}$
$=\frac{5}{-6}$
$=\frac{5\times-1}{-6\times-1}$
$=\frac{-5}{6}$

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