Assertion (A) & Reason (B) MCQ

MCQ 11 Mark

Assertion (A): $\left(\frac{2}{3}\right)^4$ is the reciprocal of $\left(\frac{3}{2}\right)^{-4}$.
Reason (R): If $\left(\frac{a}{b}\right)$ is a nonzero rational number and $m$ is a nonzero integer then $\left(\frac{b}{a}\right)^m$ is the reciprocal of $\left(\frac{a}{b}\right)^m$

A
Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanatton of Assertion (A).
B
Both Assertion (A) and Reason (R) are true and Reason (R) Is not the correct explanatlon
of Assertion (A).
C
Assertion (A) is true but Reason (R) is false.
✓
Assertion (A) is false but Reason (R) is true.

Answer

Correct option: D.

Assertion (A) is false but Reason (R) is true.

(d): The reciprocal of $\left(\frac{3}{2}\right)^{-4}$ is $\left(\frac{2}{3}\right)^{-4}$ or $\left(\frac{3}{2}\right)^4$.
$\therefore A$ is false.
The reciprocal of $\left(\frac{a}{b}\right)^m$ is $\left(\frac{b}{a}\right)^m$.
$\therefore R$ is true.

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MCQ 21 Mark

Assertion (A): $\left(\frac{2}{3}\right)^2 \times\left(\frac{2}{3}\right)^3=\left(\frac{2}{3}\right)^5$
Reason (R): For any rational number $\frac{a}{b}$, we have $\left\{\left(\frac{a}{b}\right)^m\right\}^n=\left(\frac{a}{b}\right)^{m n}$.

A
Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanatton of Assertion (A).
✓
Both Assertion (A) and Reason (R) are true and Reason (R) Is not the correct explanatlon
of Assertion (A).
C
Assertion (A) is true but Reason (R) is false.
D
Assertion (A) is false but Reason (R) is true.

Answer

Correct option: B.

Both Assertion (A) and Reason (R) are true and Reason (R) Is not the correct explanatlon
of Assertion (A).

(b): A is true since $\left(\frac{a}{b}\right)^m \times\left(\frac{a}{b}\right)^n=\left(\frac{a}{b}\right)^{m+n}$ for any rational number $\left(\frac{a}{b}\right)$ and positive integers $m$ and $n . R$ is clearly true by the laws of exponents.
$\therefore A$ and R are both true but R is not the correct explanation of A .

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MCQ 31 Mark

Assertion (A): $\left(\frac{3}{5}\right)^2+\left(\frac{4}{5}\right)^2=1$
Reason (R): For any rational number $\frac{a}{b}$, we have $\left(\frac{a}{b}\right)^m+\left(\frac{a}{b}\right)^n=\left(\frac{a}{b}\right)^{m+n}$.

A
Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanatton of Assertion (A).
B
Both Assertion (A) and Reason (R) are true and Reason (R) Is not the correct explanatlon
of Assertion (A).
✓
Assertion (A) is true but Reason (R) is false.
D
Assertion (A) is false but Reason (R) is true.

Answer

Correct option: C.

Assertion (A) is true but Reason (R) is false.

(c): $\left(\frac{3}{5}\right)^2+\left(\frac{4}{5}\right)^2=\frac{3^2}{5^2}+\frac{4^2}{5^2}=\frac{9}{25}+\frac{16}{25}=\frac{25}{25}=1$.
$\therefore A$ is true.
We have, $\left(\frac{2}{3}\right)^2+\left(\frac{2}{3}\right)^3=\frac{2^2}{3^2}+\frac{2^3}{3^3}=\frac{4}{9}+\frac{8}{27}=\frac{12+8}{27}=\frac{20}{27}$.
But, $\left(\frac{2}{3}\right)^5=\frac{2^5}{3^5}=\frac{32}{243}$.
Thus. $\left(\frac{2}{3}\right)^2+\left(\frac{2}{3}\right)^3 \neq\left(\frac{2}{3}\right)^5$.
So, $\left(\frac{a}{b}\right)^m+\left(\frac{a}{b}\right)^n \neq\left(\frac{a}{b}\right)^{m+n}$.
$\therefore R$ is false.

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MCQ 41 Mark

Assertion (A): $2^0+3^0=1$
Reason (R): For any nonzero integer $a$, the value of $a^{\circ}$ is 1

A
Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanatton of Assertion (A).
B
Both Assertion (A) and Reason (R) are true and Reason (R) Is not the correct explanatlon
of Assertion (A).
C
Assertion (A) is true but Reason (R) is false.
✓
Assertion (A) is false but Reason (R) is true.

Answer

Correct option: D.

Assertion (A) is false but Reason (R) is true.

(d): $2^0+3^0=1+1=2$.
$\therefore A$ is false. R is clearly true.

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MCQ 51 Mark

Assertion (A): $(-2)^3=-8$.
Reason (R): For any negative integer $x$ and any natural number $n, x^n$ is always negative.

A
Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanatton of Assertion (A).
B
Both Assertion (A) and Reason (R) are true and Reason (R) Is not the correct explanatlon
of Assertion (A).
✓
Assertion (A) is true but Reason (R) is false.
D
Assertion (A) is false but Reason (R) is true.

Answer

Correct option: C.

Assertion (A) is true but Reason (R) is false.

(c): $(-2)^3=(-2) \times(-2) \times(-2)=-8$.
$\therefore A$ is true.
Now, $(-2)^4=(-2) \times(-2) \times(-2) \times(-2)=16$.
$\therefore R$ is false.
Note: For a negative integer $x, x^n$ is positive if $n$ is an even natural number.

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MATHS Assertion (A) & Reason (B) MCQ

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