Assertion (A) & Reason (B) MCQ

MCQ 11 Mark

Assertion : The roots of the equation $x^2+3 x+7=0$ are imaginary.
Reason : If discriminant (D) of a quadratic equation is less than zero, then the roots of the quadratic equation are imaginary.

✓
Both assertion and reason are correct and reason is the correct explanation of assertion.
B
Both assertion and reason are correct but reason is not the correct explanation of assertion.
C
Assertion is correct but reason is incorrect.
D
Assertion is incorrect but reason is correct.

Answer

Correct option: A.

Both assertion and reason are correct and reason is the correct explanation of assertion.

(a) Both assertion and reason are correct and reason is the correct explanation of assertion.
Explanation :
We have,
$\begin{array}{l}\text { Discriminant }=b^2-4 a c \\ =(3)^2-4 \times 1 \times 7 \\ =9-28 \\ =-19<0\end{array}$
So, the roots of the equation $x^2+3 x+70$ are imaginary.

View full question & answer→

MCQ 21 Mark

Assertion : A natural number, when increased by 12 , equals 160 times its reciprocal. The number is 20 .
Reason : The roots of a quadratic equation $a x^2+b x+c=0$ are given by the formula $x=\frac{-b \pm \sqrt{b^2-4 a c}}{2 a}$.

A
Both assertion and reason are correct and reason is the correct explanation of assertion.
B
Both assertion and reason are correct but reason is not the correct explanation of assertion.
C
Assertion is correct but reason is incorrect.
✓
Assertion is incorrect but reason is correct.

Answer

Correct option: D.

Assertion is incorrect but reason is correct.

(d) Assertion is incorrect but reason is correct.
Explanation:
Let the required natural number be $x$.
Then according to the question,
$\begin{array}{l}(x+12)=\frac{160}{x} \\ \Rightarrow x(x+12)=160 \\ \Rightarrow x^2+12 x-160=0 \\ \Rightarrow x^2+20 x-8 x-160=0 \\ \Rightarrow x(x+20)-8(x+20)=0 \\ \Rightarrow(x-8)(x+20)=0 \\ \Rightarrow x-8=0 \text { or } x+20=0 \\ \Rightarrow x=8 \text { or }-20\end{array}$
Since, $x$ is a natural number.
$\therefore x=8 \text {. }$

View full question & answer→

MCQ 31 Mark

Assertion: The values of $k$ for which the equation $k x^2+1-2(k-1) x+x^2=0$ has equal roots are 0,3 .
Reason : If the roots of a quadratic equation are equal, then its discriminant is greater than zero.

A
Both assertion and reason are correct and reason is the correct explanation of assertion.
B
Both assertion and reason are correct but reason is not the correct explanation of assertion.
✓
Assertion is correct but reason is incorrect.
D
Assertion is incorrect but reason is correct.

Answer

Correct option: C.

Assertion is correct but reason is incorrect.

(c) Assertion is correct but reason is incorrect.
Explanation:
We have,
$\begin{array}{l}k x^2+1-2(k-1) x+x^2=0 \\ \Rightarrow(k+1) x^2-2(k-1) x+1=0\end{array}$
This equation has equal roots.
$\begin{array}{l}\therefore[-2(k-1)]^2-4 \times(k+1) \times 1=0 \\ \Rightarrow 4 k^2-8 k+4-4 k-4=0 \\ \Rightarrow 4 k^2-12 k=0 \\ \Rightarrow 4 k(k-3)=0 \\ \Rightarrow k=0,3\end{array}$

View full question & answer→

Mathematics Assertion (A) & Reason (B) MCQ

Test yourself on this topic