Assertion (A) & Reason (B) MCQ

MCQ 11 Mark

Assertion (A): The sum of first 6 terms of the GP 4, 16, 64, ... is equal to 5460.
Reason (R): Sum of first n terms of the G.P is given by $S _{ n }=\frac{a\left(r^n-1\right)}{r-1}$, where a = first term r = common ratio and
|r| > 1.

✓
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: Given GP 4, 16, 64, ...
$\therefore a =4, r =\frac{16}{4}=4>1$
$\therefore S_6=\frac{4\left((4)^6-1\right)}{4-1}=\frac{4(4095)}{3}=5460$
Hence, Assertion and Reason both are true and Reason is the correct explanation of Assertion.

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MCQ 21 Mark

Assertion (A): The variance of 10 observations is 6. If each observation is multiplied by 3, then new variance is 54.
Reason (R): If $\sigma^2$ is the variance of $n$ observations $x _1, x _2, \ldots, x _{ n }$, then variance of the observations $ax _1, ax _2 \ldots$, $ax _{ n }$ is $a ^2 \sigma^2$.

✓
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: We know that if each observation is multiplied by a non-zero real number a, then variance is multiplied by $a ^2$.
$\therefore R$ is true.
Now, given that variance of 10 observations is 6 and each observation is multiplied by 3. So, new variance is $3^2 \times 6$ i.e. 54.
$\therefore A$ is true and $R$ is the correct explanation of $A$.

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

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