Assertion (A) & Reason (B) MCQ

MCQ 11 Mark

Assertion $(A):$ The mean deviation about the mean for the data $4, 7, 8, 9, 10, 12, 13, 17$ is $3.$
Reason $(R):$ The mean deviation about the mean for the data $38, 70, 48, 40, 42, 55, 63, 46, 54, 44$ is $8.5.$

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 $A.$
✓
$A$ is true but $R$ is false.
D
$A$ is false but $R$ is true.

Answer

Correct option: C.

$A$ is true but $R$ is false.

Assertion: Mean of the given series
$\overline{\bar{x}}=\frac{\text { Sum of terms }}{\text { Number of terms }}=\frac{\sum x_i}{n}$
$=\frac{4+7+8+9+10+12+13+17}{8}=10$

$xi$	$\| x i -\bar{x}\|$
$4$	$\|4-10\|=6$
$7$	$\|7-10\|=3$
$8$	$\|8-10\|=2$
$9$	$\|9-10\|=1$
$10$	$\|10-10\|=0$
$12$	$\|12-10\|=2$
$13$	$\|13-10\|=3$
$17$	$\|17-10\|=7$
$\sum x_i=80$	$\sum\left\|x_i-\bar{x}\right\|=24$

$\therefore$ Mean deviation about mean
$=\frac{\Sigma\left|x_i-\bar{x}\right|}{n}=\frac{24}{8}=3$
Reason Mean of the given series
$\bar{x}=\frac{\text { Sum of terms }}{\text { Number of terms }}=\frac{\sum x_i}{n}$
$=\frac{38+70+48+40+42+55}{+63+46+54+44}=50$
$\therefore$ Mean deviation about mean
$=\frac{\Sigma\left|x_i-\bar{x}\right|}{n}$
$=\frac{84}{10}=8.4$
Hence, Assertion is true and Reason is false.

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MCQ 21 Mark

Assertion $(A):$ The expansion of $(1+ x )^{ n }=n_{c_0}+n_{c_1} x+n_{c_2} x^2 \ldots+n_{c_n} x^n$.
Reason $(R):$ If $x=-1$, then the above expansion is zero.

A
Both $A$ and $R$ are true and $R$ is the correct explanation of $A.$
✓
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: B.

Both $A$ and $R$ are true but $R$ is not the correct explanation of $A.$

Assertion $: (1+x)^n=n_{c_0}+n_{c_1} x+n_{c_2} x^2 \ldots+n_{c_n} x^n$
Reason $:(1+(-1))^{n}=n_{c_0} 1^n+n_{c_1}(1)^{n-1}(-1)^1+n_{c_2}(1)^{n-2}(-1)^2+\ldots+{ }^n c_n(1)^{n-n}(-1)^n$
$=n_{c_8}-n_{c_1}+n_{c_2}-n_{c_3}+\ldots(-1)^{n} n_{c_n}$
Each term will cancel each other
$\therefore(1+(-1))^{ n }=0$
Reason is also the but not the correct explanation of Assertion.

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Maths Assertion (A) & Reason (B) MCQ

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