Assertion (A) & Reason (B) MCQ

MCQ 11 Mark

Assertion (A): The proper measure of dispersion about the mean of a set of observations i.e. standard deviation is expressed as positive square root of the variance.
Reason (R): The units of individual observations $x _{ i }$ and the unit of their mean are different that of variance.

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) Both A and R are true and R is the correct explanation of A .
Explanation: Assertion: In the calculation of variance, we find that the units of individual observations $x _{ i }$ and the unit of their mean $\bar{x}$ are different from that of variance, since variance involves the sum of squares of ( $x _{ i }-\bar{x}$ ).
For this reason, the proper measure of dispersion about the mean of a set of observations is expressed as positive square-root of the variance and is called standard deviation.

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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 $A.$

$(1+(-1))^{n}=n_{c_0} 1^n+n_{c_1}(1)^{n-1}(-1)^1+n_{c_2}(1)^{n-2}(-1)^2+\ldots+{ }^n c_n(1)^{n-n}(-1)^n$
$=n_{c_8}-n_{c_1}+n_{c_2}-n_{c_3}+\ldots(-1)^{n} n_{c_n}$
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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