Assertion (A) & Reason (B) MCQ

MCQ 11 Mark

Assertion (A): A function $f : N \rightarrow N$ be defined by $f(n)=\left\{\begin{array}{ll}\frac{n}{2} & \text { if } n \text { is even } \\ \frac{(n+1)}{2} & \text { if } n \text { is odd }\end{array}\right.$ for all $n \in N$; is one-one
Reason (R): A function $f: A \rightarrow B$ is said to be injective if $a \neq b$ then $f(a) \neq f(b)$.

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 is false because distinct elements in N has equal images.
for example $f(1)=\frac{(1+1)}{2}=1$
$f(2)=\frac{2}{2}=1$
Reason is true because for injective function if elements are not equal then their images should be unequal.

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MCQ 21 Mark

Assertion $(A):$ Minimum value of $(x-5)(x-7)$ is $-1 .$
Reason $(R):$ Minimum value of $ax ^2+ bx + c$ is $\frac{4 a c-b^2}{4 a}$.

✓
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

Correct option: A.

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

We have,$ (x - 5)(x - 7)$
$\Rightarrow x^2-12 x+35$
We know that, $ax ^2+ bx + c$ has minimum value $\frac{4 a c-b^2}{4 a}$.
Here, $a = 1 b = - 12$ and $c = 35$
$\therefore$ Minimum value of $(x-5)(x-7)=\frac{4.1 \cdot 35-(-12)^2}{4.1}$
$=\frac{140-144}{4}$
$=-\frac{4}{4}=-1$

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Mathematics Assertion (A) & Reason (B) MCQ

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