Assertion (A) & Reason (B) MCQ

MCQ 11 Mark

Assertion (A): If 5 th term of a G.P. is 9 and 11 th term is 16 , then 8 th term is 12 .
Reason (R): In a G.P., $\mathrm{a}_{\mathrm{n}}=\frac{a_{n-k}+a_{n+k}}{2}, \mathrm{n}, \mathrm{k} \in \mathrm{N}$.

A
Both A and R are true and R is the correct explanation of A .
B
Both A and R are true but R is not the correct explanation of A.
C
$A$ is true but $R$ is false.
D
A is false but $R$ is true.

Answer

A is true but R is false.
Explanation: We know that in a G.P.
$a_{n}=\sqrt{a_{n-k} \cdot a_{n+k}}$
$\therefore$ Reason is false.
Given $\mathrm{a}_{5}=9$ and $\mathrm{a}_{11}=16$.
So, $a_{8}=\sqrt{a_{8-3} \times a_{8+3}}$
$\Rightarrow a_{8}=\sqrt{9 \times 16}=\sqrt{144} \Rightarrow a_{8}=12$
$\therefore$ Assertion is true.

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MCQ 21 Mark

Assertion(A): For a distribution, if $\Sigma x_{i}^{2}=232, \Sigma x_{i}=16$ and $n=8$, then standard deviation (S.D.) is 5 .
Reason(R): Standard deviation (S.D.) $=\sqrt{\frac{\Sigma x_{i}^{2}}{n}-\left(\frac{\Sigma x_{i}}{n}\right)^{2}}$.

✓
Both A and R are true and R is the correct explanation of A .
B
Both A and R are true but R is not the correct explanation of A .
C
A is true but R is false.
D
A is false but $R$ is true.

Answer

Correct option: A.

Both A and R are true and R is the correct explanation of A .

(a) Both A and R are true and R is the correct explanation of A .
Explanation: Assertion (A): $\sum x_{i}^{2}=232$
$\sum x_{i}=16, \mathrm{x}=8$
Standard deviation $(\sigma)=\sqrt{\frac{\sum x_{i}^{2}}{n}-\left(\frac{\sum x_{i}}{n}\right)^{2}}$
$\sigma=\sqrt{\frac{232}{8}-\left(\frac{16}{8}\right)^{2}}$
$=\sqrt{29-4}$
$=\sqrt{25}$
$\sigma=5$
Hence, A is correct.
Reason (R): Standard deviation (S.D)
$=\sqrt{\frac{\sum x_{i}^{2}}{x}-\left(\frac{\sum x_{i}}{x}\right)^{2}}$
R is also true.
Hence, Both A and R are true and R is the correct explanation of A .

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Applied Maths Assertion (A) & Reason (B) MCQ

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