MCQ

MCQ 11 Mark

If $\left(\frac{12}{13}\right)^4 \times\left(\frac{13}{12}\right)^{-8}=\left(\frac{12}{13}\right)^{2 x}$, then the value of $x$ is

A
$-2$
✓
$6$
C
$2$
D
$-6$

Answer

Correct option: B.

$6$

$\left(\frac{12}{13}\right)^4 \times\left(\frac{13}{12}\right)^{-8}=\left(\frac{12}{13}\right)^{2 x}$
$\Rightarrow \left(\frac{12}{13}\right)^4 \times\left(\frac{12}{13}\right)^8=\left(\frac{12}{13}\right)^{2 x}$
$\Rightarrow \left(\frac{12}{13}\right)^{4+8}=\left(\frac{12}{13}\right)^{2 x} $
$\Rightarrow\left(\frac{12}{13}\right)^{12}=\left(\frac{12}{13}\right)^{2 x}$
Comparing, $ 2 x=12 $
$\Rightarrow x=\frac{12}{2}=6$
$\therefore x=6$

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MCQ 21 Mark

$2^0+3^0+\left(\frac{1}{4}\right)^0$ is equal to

A
$\frac{21}{4}$
B
$0$
C
$9$
✓
$3$

Answer

Correct option: D.

$3$

$2^0+3^0+\left(\frac{1}{4}\right)^0=1+1+1=3 \quad\left(\because a^0=1\right)$

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MCQ 31 Mark

Multiplicative inverse of $\left(\frac{-2}{3}\right)^4$ is

A
$\frac{16}{81}$
B
$\frac{-16}{81}$
✓
$\frac{81}{16}$
D
$\frac{-81}{16}$

Answer

Correct option: C.

$\frac{81}{16}$

Multiplicative inverse of $\left(\frac{-2}{3}\right)^4$ or $\frac{-2}{3} \times \frac{-2}{3} \times \frac{-2}{3} \times \frac{-2}{3}$ or $\frac{16}{81}$ is $\frac{81}{16}$

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MCQ 41 Mark

The usual form of $3.67 \times 10^5$ is

A
$3670000$
✓
$367000$
C
$36700$
D
$3670$

Answer

Correct option: B.

$367000$

$3.67 \times 10^5=367000$

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MCQ 51 Mark

Standard form of $0.000000789$ is

A
$78.9 \times 10^{-8}$
B
$789 \times 10^{-9}$
✓
$7.89 \times 10^{-7}$
D
None

Answer

Correct option: C.

$7.89 \times 10^{-7}$

$0.000000789=7.89 \times 10^{-7}$

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MCQ 61 Mark

$\left(\frac{-4}{3}\right)^7 \times\left(\frac{-4}{3}\right)^8 \div\left(\frac{-3}{4}\right)^{-5}$ is equal to

A
$\left(\frac{-4}{3}\right)^{20}$
✓
$\left(\frac{-4}{3}\right)^{10}$
C
$\left(\frac{-3}{4}\right)^{10}$
D
$\left(\frac{-3}{4}\right)^{20}$

Answer

Correct option: B.

$\left(\frac{-4}{3}\right)^{10}$

$\left(\frac{-4}{3}\right)^7 \times\left(\frac{-4}{3}\right)^8 \div\left(\frac{-3}{4}\right)^{-5}$
$=\left(\frac{-4}{3}\right)^7 \times\left(\frac{-4}{3}\right)^8 \div\left(\frac{4}{-3}\right)^5$
$=\left(\frac{-4}{3}\right)^{7+8-5}$
$=\left(\frac{-4}{3}\right)^{10}$

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MCQ 71 Mark

The value of $\left(\frac{729}{4096}\right)^{\frac{-1}{3}}$ is

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

Answer

Correct option: A.

$\frac{16}{9}$

$\left(\frac{729}{4096}\right)^{\frac{-1}{3}}=\left(\frac{4096}{729}\right)^{\frac{1}{3}}=\left(\frac{16^3}{9^3}\right)^{\frac{1}{3}}$
$=\frac{16^{3 \times \frac{1}{3}}}{9^{3 \times \frac{1}{3}}}$
$=\frac{16}{9}$

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MCQ 81 Mark

If $2^4 \times 4^3 = 4^x,$ then the value of $x$ is

✓
$5$
B
$7$
C
$4$
D
$-5$

Answer

Correct option: A.

$5$

$2^4 \times 4^3 = 4^x$
$\Rightarrow 2^4 \times (2^2)^3 = (2^2)^x$
$\Rightarrow 2^4 \times 2^6 = 2^{2x}$
$\Rightarrow 2^{10} = 2^{2x}$
$2x = 10$
$\Rightarrow x = 5$

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MCQ 91 Mark

The value of $\left[\left(\frac{1}{4}\right)^{-2}+\left(\frac{1}{3}\right)^{-2}\right] \div\left(\frac{1}{5}\right)^{-2}$ is

A
$0$
B
$-1$
✓
$1$
D
$\frac{7}{5}$

Answer

Correct option: C.

$1$

$\left(\left(\frac{1}{3}\right)^{-2}+\left(\frac{1}{4}\right)^{-2}\right) \div\left(\frac{1}{5}\right)^{-2}$
$\quad=\left[(3)^2+(4)^2\right] \div\left(5^2\right)$
$\quad=(9+16) \div 25$
$\quad=25 \div 25$
$\quad=1$

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MCQ 101 Mark

$\left(\frac{1}{2}\right)^{-5}$ is equal to

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

Answer

Correct option: A.

$32$

$\left(\frac{1}{2}\right)^{-5}=(2)^5=2 \times 2 \times 2 \times 2 \times 2=32$

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