Assertion (A) & Reason (B) MCQ

MCQ 11 Mark

Let R be any relation in the set A of human beings in a town at a particular time.
Assertion (A): If $R=\{(x, y): x$ is wife of $y\}$, then $R$ is reflexive.
Reason (R): If $R=\{(x, y): x$ is father of $y\}$, then R is neither reflexive nor symmetric nor transitive.

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.
✓
A is false but R is true.

Answer

Correct option: D.

A is false but R is true.

(d) A is false but R is true.
Explanation: Assertion: Here R is not reflexive: as x cannot be wife of x.
Reason: Here, R is not reflexive; as x cannot be father of x, for any x. R is not symmetric as if x is father of y, then y cannot be father of x. R is not transitive as if x is father of y and y is father of z, then x is grandfather (not father) of z.

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MCQ 21 Mark

Assertion $(A):$ A particle moving in a straight line covers a distance of $x \ cm$ in $t$ second, where $x=t^3+3 t^2-6 t +18$ The velocity of particle at the end of $3$ seconds is $39 \ cm/s.$
Reason $(R):$ Velocity of the particle at the end of $3$ seconds is $\frac{d x}{d t}$ at $t =3$

✓
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 $A.$

We have,
$ x = t ^3+3 t ^2-6 t +18$
Velocity, $v=\frac{d z}{u}=3 t^2+6 t-6$
Thus, velocity of the particle at the end of $3$ seconds is
$\left(\frac{d x}{d t}\right)_{t=3}=3(3)^2+6(3)-6$
$=27+18-6=39 \ cm / s $

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Maths Assertion (A) & Reason (B) MCQ

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