Assertion (A) & Reason (B) MCQ

MCQ 11 Mark

Assertion (A): There are infinite number of lines which passes through $(2,14)$.
Reason (R): A linear equation in two variables has infinitely many solutions.

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

(b) Both A and R are true but R is not the correct explanation of A .
Explanation: Through a point infinite lines can be drawn. Through $(2,14)$ infinite number of lines can be drawn. Also a line has infinite points on it hence a linear equation representing a line has infinite solutions.

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MCQ 21 Mark

Assertion $(A): $The perimeter of a right angled triangle is $60 \ cm$ and its hypotenuse is $26 \ cm .$ The other sides of the triangle are $10 \ cm$ and $24 \ cm .$ Also, area of the triangle is $120 \ cm^2$.
Reason $(R):(\text { Base })^2+(\text { Perpendicular })^2=(\text { Hypotenuse })^2$

✓
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 $A.$

$a + b + c = 60$
$a + b + 26 = 60$
$a + b = 34 ...(i)$
Now, $26^2=a^2+b^2 \ldots( ii)$
Squaring $(1)$ both sides, we get
$(a+b)^2=(34)^2$
$a^2+b^2+2 a b=34 \times 34$
$(26)^2+2 ab =1156[$ From $ii)]$
$2 ab =1156-676$
$2 ab =480$
$ab =240 \ldots ...(iii)$
Now, $a+\frac{240}{a}=34[$ From $(i)$ and $(iii)]$
$a^2-24 a-10 a+240=0$
$a(a-24)-10(a-24)=0$
$a=10,24$
Now, other sides are $10 \ cm$ and $24 \ cm$
$ s =\frac{26+10+24}{2}=30 \ cm$
$\text { Area of triangle }=\sqrt{30(30-26)(30-10)(30-24)}$
$=\sqrt{30 \times 4 \times 20 \times 6}$
$=120 \ cm^2$

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Maths Assertion (A) & Reason (B) MCQ

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