M.C.Q. [1 Marks Each]

MCQ 2011 Mark

The value of $\Big(\frac{2}{5}\Big)^{-2}$ is:

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

Answer

Correct option: C.

$\frac{25}{4}$

Using law of exponents, $\text{a}^{-\text{m}}=\frac{1}{\text{a}^\text{m}} [\because$ a is non$-$integer$]$
$\therefore \Big(\frac{2}{5}\Big)^{-2}=\frac{1}{\Big(\frac{2}{5}\Big)^{2}}$
$=\frac{1}{\frac{4}{25}}$
$=\frac{25}{4}$

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MCQ 2021 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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MCQ 2031 Mark

$3^{-2} \times 3^{-5}$ is equal to:

A
$3^{-3}$
B
$3^{-10}$
C
$3^{7}$
✓
$3^{-7}$

Answer

Correct option: D.

$3^{-7}$

D. $3^{-7}$
Solution:
$3^{-2} × 3^{-5} = \frac{1}{3^2}\times \frac{1}{3^5}$
$=\frac{1}{3^{2+5}}$
$=\frac{1}{3^7}$
$=3^{-7}$

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MCQ 2041 Mark

For any two non$-$zero rational nmbers a and b, $\text{a}^{4}\div\text{b}^4$ is equal to:

A
$(\text{a}\times\text{b})^0$
B
$(\text{a}\times\text{b})^{10}$
✓
$(\text{a}\times\text{b})^5$
D
$(\text{a}\times\text{b})^{25}$

Answer

Correct option: C.

$(\text{a}\times\text{b})^5$

$\text{a}^{\text{n}}\times\text{b} ^{\text{n}}=(\text{a}\times{\text{b}} )^\text{n}$
Hence,
$\text{a}^\text{5}\times\text{b}^5=(\text{a}\times\text{b} )^5$

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MCQ 2051 Mark

The value of $\log^{\text{x}^{2}\text{yz}}_\text{xyz}+\log^{\text{xy}^{2}\text{z}}_\text{xyz}+\log^{\text{xyz}^{2}}_\text{xyz}$ is equal to:

A
$2$
B
$1$
✓
$4$
D
Not

Answer

Correct option: C.

$4$

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MCQ 2061 Mark

$a^m \times b^m$ is equal to:

✓
$(ab)^m$
B
$(ab)^{-m}$
C
$a^mb$
D
$ab^m$

Answer

Correct option: A.

$(ab)^m$

A. $(ab)^m$

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MCQ 2071 Mark

In standard form $56700000$ is written as ______.

✓
$5.67 \times 10^7$
B
$567 \times 10^7$
C
$5.67 \times 10^5$
D
$567 \times 100000$

Answer

Correct option: A.

$5.67 \times 10^7$

A. $5.67 \times 10^7$

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MCQ 2081 Mark

The value of $2^{-2}$ is:

A
$4$
B
$\frac{1}{2}$
C
$2$
✓
$\frac{1}{4}$

Answer

Correct option: D.

$\frac{1}{4}$

D. $\frac{1}{4}$
Solution:
$2^{-2} = \frac{1}{2^2} = \frac{1}{4}$

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MCQ 2091 Mark

The value of $\text{log}108-\text{log}54-\text{log}2$ is:

A
$1$
B
$2$
C
$3$
✓
$0$

Answer

Correct option: D.

$0$

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MCQ 2101 Mark

Expand $1256.249$ using exponents.

✓
$1 \times 10^3+2 \times 10^2+5 \times 10^1+6 \times 10^0$$+2 \times 10^{-1}+4 \times 10^{-2}+9 \times 10^{-3} $
B
$1 \times 10^5+2 \times 10^2+5 \times 10^1+6 \times 10^0$$+2 \times 10^{-1}+4 \times 10^{-2}+9 \times 10^{-3} $
C
$1 \times 10^4+2 \times 10^2+5 \times 10^2+6 \times 10^1$$+2 \times 10^3+4 \times 10^{-1}+9 \times 10^{-2}$
D
None of these.

Answer

Correct option: A.

$1 \times 10^3+2 \times 10^2+5 \times 10^1+6 \times 10^0$$+2 \times 10^{-1}+4 \times 10^{-2}+9 \times 10^{-3} $

A. $1 \times 10^3+2 \times 10^2+5 \times 10^1+6 \times 10^0$$+2 \times 10^{-1}+4 \times 10^{-2}+9 \times 10^{-3} $

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MCQ 2111 Mark

$\frac{5^7}{6^7}$ will give the value:

✓
$(\frac{5}{6})^7$
B
$(\frac{5}{6})^0$
C
$(\frac{5}{6})^{-7}$
D
$(\frac{6}{5})^{-7}$

Answer

Correct option: A.

$(\frac{5}{6})^7$

By exponent law,
$\frac{\text{a}^\text{m}}{\text{b}^\text{m}}= \big(\frac{\text{a}}{\text{b}}\big)^\text{m}$
$\frac{5^7}{6^7} = \big(\frac{5}{7}\big)^7$

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MCQ 2121 Mark

$(2^\circ + 4^{-1}) \times 2^2$is equal to.

A
$2$
B
$3$
C
$4$
✓
$5$

Answer

Correct option: D.

$5$

D. $5$
Solution:
$(2^\circ+4^{-1})\times2^2$
$=\big(1+\frac{1}{4}\big)\times4$
$=\frac{5}{4}\times4 = 5$

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MCQ 2131 Mark

If y be any non-zero integer, then $y^0$ is equal to:

✓
$1$
B
$0$
C
$-1$
D
Not defined

Answer

Correct option: A.

$1$

A. $1$
Solution:
Using law of exponents,
$a^0 = 1$ [$\because$ a is non-zero integer]
Similarly,
$y^0 = 1$

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MCQ 2141 Mark

The multiplicative inverse of $10^{10}$ is:

A
$10$
B
$\frac{1}{10}$
C
$10^{-10}$
✓
$10^{10}$

Answer

Correct option: D.

$10^{10}$

D. $10^{10}$
Solution:
$10^{-10}\times10^{10} = 10^{-10+10} = 10^\circ= 1$

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MCQ 2151 Mark

$\Big(\frac{3}{4}\Big)^{5}\div\Big(\frac{5}{3}\Big)^{5}$ is equal to:

✓
$\Big(\frac{3}{4}\div\frac{5}{3}\Big)^5$
B
$\Big(\frac{3}{4}\div\frac{5}{3}\Big)^1$
C
$\Big(\frac{3}{4}\div\frac{5}{3}\Big)^0 $
D
$\Big(\frac{3}{4}\div\frac{5}{3}\Big)^{10} $

Answer

Correct option: A.

$\Big(\frac{3}{4}\div\frac{5}{3}\Big)^5$

We have:
$\Big(\frac{3}{4}\Big)^{5}\div\Big(\frac{5}{3}\Big)^{5}$
$=\Big( \frac{3}{4}\div\frac{5}{3}\Big)^5$

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MATHS M.C.Q. [1 Marks Each]