MCQ

MCQ 11 Mark

$\log (1 \times 2 \times 3)$ is equal to

✓
$\log 1+\log 2+\log 3$
B
$\log 3$
C
$\log 2$
D
none of these

Answer

Correct option: A.

$\log 1+\log 2+\log 3$

(A) $\log 1+\log 2+\log 3$
Explanation : Since, $\log _a(m n)=\log _a m+\log _a n$
One extending this rule for three variables, we get$
\log _a(m n p)=\log _a m+\log _a n+\log _a p
$
Therefore, $\log (1 \times 2 \times 3)=\log 1+\log 2+\log 3$.

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MCQ 21 Mark

$\log \left(\frac{32}{4}\right)$ is equal to

A
$\frac{\log 32}{\log 4}$
✓
$\log 32-\log 4$
C
$2^3$
D
none of these

Answer

Correct option: B.

$\log 32-\log 4$

(B) $\log 32-\log 4$
Explanation : We know that,
$
\log _a\left(\frac{m}{n}\right)=\log _a m-\log _a n
$
Therefore, $\log \left(\frac{32}{4}\right)=\log 32-\log 4$

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MCQ 31 Mark

$\log _2 8$ is equal to

A
2
B
8
✓
3
D
none of these

Answer

Correct option: C.

(C) 3
Explanation: $\log _2 8=\log _2\left(2^3\right)=3 \log _2 2=3$
[Applying rules $\log _a m^n=n \log _a m$ and $\log _a a=1$ ]

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MCQ 41 Mark

$\log 6+\log 5$ is expressed as

A
$\log 11$
✓
$\log 30$
C
$\log \frac{5}{6}$
D
none of these

Answer

Correct option: B.

$\log 30$

(B) $\log 30$
Explanation : We know that
$\log _a(m n)=\log _a m+\log _a n$
Therefore, $\log 6+\log 5=\log (6 \times 5)=\log 30$

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MCQ 51 Mark

Which is true?

A
$2^0>\left(\frac{1}{2}\right)^0$
B
$2^0<\left(\frac{1}{2}\right)^0$
✓
$2^0=\left(\frac{1}{2}\right)^0$
D
none of these

Answer

Correct option: C.

$2^0=\left(\frac{1}{2}\right)^0$

(C) $2^0=\left(\frac{1}{2}\right)^0$
Explanation : According to zero index rule,$
\begin{aligned}
& 2^0=1 \text { and }\left(\frac{1}{2}\right)^0=1 \\
\therefore & 2^0=\left(\frac{1}{2}\right)^0
\end{aligned}
$

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MCQ 61 Mark

$3.2^{1 / 2} \cdot 4^{3 / 4}$ is equal to

A
a fraction
✓
a positive integer
C
a negative integer
D
none of these

Answer

Correct option: B.

a positive integer

(B) a positive integer
Explanation : $2^{\frac{1}{2}} \cdot 4^{\frac{3}{4}}=2^{\frac{1}{2}} \cdot\left(2^2\right)^{3 / 4}$
$\begin{array}{r}=2^{\frac{1}{2}} \cdot 2^{2 \times \frac{3}{4}} \\ \quad\left[ U \operatorname{sing}\left(a^{m}\right)^n=a^{m n}\right]\end{array}$
$\begin{array}{l}=2^{\frac{1}{2}} \cdot 2^{\frac{3}{2}} \\ =2^{\frac{1}{2}+\frac{3}{2}}=2^{\frac{4}{2}}=2^2=4 \\ \quad\left[\text { Using } a^m \times a^n=a^{m+n}\right]\end{array}$

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MCQ 71 Mark

The value of $8^{1 / 3}$ is

A
$\sqrt[3]{2}$
B
4
✓
2
D
none of these

Answer

Correct option: C.

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MCQ 81 Mark

$4 x^{-1 / 4}$ is expressed as

A
$-4 x^{1 / 4}$
B
$x^{-1}$
✓
$\frac{4}{x^{1 / 4}}$
D
none of these

Answer

Correct option: C.

$\frac{4}{x^{1 / 4}}$

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Applied Maths MCQ

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