Download App

MATHS Assertion (A) & Reason (B) MCQ

Exponents · Gujarat Board (GSEB) STD 8 (GSEB - English Medium). 7 questions.

Questions

Assertion (A) & Reason (B) MCQ

🎯

Test yourself on this topic

7 questions · timed · auto-graded

MCQ 11 Mark
Assertion (A): $2^{3^4}=2^{12}$.
Reason (R): For any integers $a, m$ and $n$, we have $\left(a^m\right)^n=a^{m \times n}$.
  • A
    Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
  • B
    Both Assertion (A) and Reason (R) are true and Reason (R) is not the correct explanation 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) Assertion (A) is false but Reason (R) is true.
$2^{3^4}=2^{81}$ and $\left(2^3\right)^4=2^{3 \times 4}=2^{12}$. So, $A$ is false
R states the law of exponents. So, R is true.
View full question & answer→
MCQ 21 Mark
Assertion (A): $\frac{2^{-100}}{2^{-101}}=2^{-201}$
Reason (R): For any integers $a, m$ and $n$, we have $\frac{a^m}{a^n}=a^{m-n}$
  • A
    Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
  • B
    Both Assertion (A) and Reason (R) are true and Reason (R) is not the correct explanation 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) Assertion (A) is false but Reason (R) is true.
$\frac{2^{-100}}{2^{-101}}=2^{-100-(-101)}=2^{-100+101}=2^1=2$. So, $A$ is false.
R states the law of exponents. So, $R$ is true.
View full question & answer→
MCQ 31 Mark
Assertion (A): $8^{-2}$ is the same as $2^{-8}$.
Reason (R): If $\frac{a}{b}$ be a rational number and $n$ be a positive integer then $\left(\frac{a}{b}\right)^{-n}=\left(\frac{b}{a}\right)^n$.
  • A
    Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
  • B
    Both Assertion (A) and Reason (R) are true and Reason (R) is not the correct explanation 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) Assertion (A) is false but Reason (R) is true.
$8^{-2}=\frac{1}{8^2}=\frac{1}{64}$ and $2^{-8}=\frac{1}{2^8}=\frac{1}{256}$. So, A is false.
$
\left(\frac{a}{b}\right)^{-n}=\frac{a^{-n}}{b^{-n}}=\frac{\left(\frac{1}{a^n}\right)}{\left(\frac{1}{b^n}\right)}=\frac{b^n}{a^n}=\left(\frac{b}{a}\right)^n
$
So, $R$ is true.
View full question & answer→
MCQ 41 Mark
Assertion (A): The multiplicative inverse of $a^{-n}$ is $a^n$. 
Reason (R): $a^{-n} \times a^n=1$.
  • ✓
    Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
  • B
    Both Assertion (A) and Reason (R) are true and Reason (R) is not the correct explanation 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: A.
Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
(A) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
$a^{-n} \times a^n=\frac{1}{a^n} \times a^n=1$
So, $a^n$ is the multiplicative inverse of $a^{-n}$. Hence, both A and R are true and R is the correct explanation of A .
View full question & answer→
MCQ 51 Mark
Assertion (A): $\frac{2^{-5}}{5^{-2}}=\frac{5^2}{2^5}$.
Reason (R): For any integers $a$ and $n$, we have $a^{-n}=\frac{1}{a^n}$.
  • ✓
    Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
  • B
    Both Assertion (A) and Reason (R) are true and Reason (R) is not the correct explanation 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: A.
Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
(A) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
$\frac{2^{-5}}{5^{-2}}=\frac{\left(\frac{1}{2^5}\right)}{\left(\frac{1}{5^2}\right)}=\frac{5^2}{2^5} \cdot\left[\because \quad a^{-n}=\frac{1}{a^n}\right]$
Clearly. A is true.
R describes the law used in the above calculation. So, R is true and correct explanation of A.
View full question & answer→
MCQ 61 Mark
Assertion (A): $(-10) \times(-10) \times(-10) \times(-10)=10^{-4}$.
Reason (R): For any integer $a$, we have $a \times a \times a \times \ldots n$ times $=a^n$.
  • A
    Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
  • B
    Both Assertion (A) and Reason (R) are true and Reason (R) is not the correct explanation 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) Assertion (A) is false but Reason (R) is true.
$(-10) \times(-10) \times(-10) \times(-10)=(-10)^4$. So, A is false.
R states the basic concept of exponents. So, R is true.
View full question & answer→
MCQ 71 Mark
Assertion (A): $2^5 \times 2^3=2^{15}$.
Reason (R): For any integers $a, m$ and $n$, we have $a^m \times a^n=a^{m+n}$
  • A
    Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
  • B
    Both Assertion (A) and Reason (R) are true and Reason (R) is not the correct explanation 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) Assertion (A) is false but Reason (R) is true.
$2^5 \times 2^3=2^{(5+3)}=2^8$. So, A is false.
R states the law of exponents, So, R is true.
View full question & answer→
Generate Paper FreeAll Exponents topics
Assertion (A) & Reason (B) MCQ - MATHS STD 8 Questions - Vidyadip