Assertion (A) & Reason (B) MCQ

MCQ 11 Mark

Assertion (A): The collection of all natural numbers less than 100' is a set.
Reason (R): A set is a well-defined collection of the distinct objects.

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 The collection of all natural numbers less than 100', is a well-defined collection. So, it is a set.

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MCQ 21 Mark

Assertion (A): If the sum of first two terms of an infinite GP is 5 and each term is three times the sum of the succeeding terms, then the common ratio is $\frac{1}{4}$.
Reason (R): In an AP 3, 6, 9, 12 ......... the 10 th term is equal to 33.

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

(c) A is true but R is false.
Explanation: Assertion Let a be the first term and r(|r| < 1) be the common ratio of the GP.
$\therefore$ The GP is $a , ar ^2, ar ^2, \ldots$
According to the question,
$T_1+T_2=5 \Rightarrow a+a r=5 \Rightarrow a(1+r)=5$
and $T_n=3\left(T_{n+1}+T_{n+2}+T_{n+3}+\ldots\right)$
$\begin{array}{l}\Rightarrow a r^{n-1}=3\left(a r^n+a r^{n+1}+a r^{n+2}+\ldots\right) \\ \Rightarrow a r^{n-1}=3 a r^n\left(1+r+r^2+\ldots\right) \\ \Rightarrow 1=3 r\left(\frac{1}{1-r}\right) \\ \Rightarrow 1=r=3 r \\ \Rightarrow r=\frac{1}{4}\end{array}$
Reason: Given, 3, 6, 9, 12 ...
Here, a = 3, d = 6 - 3 = 3
$\therefore T _{10}= a +(10-1) d$
$\begin{array}{l}=3+9 \times 3 \\
=3+27=30\end{array}$

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MATHS Assertion (A) & Reason (B) MCQ

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