MCQ 11 Mark
Assertion (A): If the numbers $\frac{-2}{7}, K, \frac{-7}{2}$ are in GP, then $k = \pm 1$.
Reason (R): If $a_1, a_2, a_3$ are in GP, then $\frac{a_2}{a_1}=\frac{a_3}{a_2}$.
Reason (R): If $a_1, a_2, a_3$ are in GP, then $\frac{a_2}{a_1}=\frac{a_3}{a_2}$.
- ABoth A and R are true and R is the correct explanation of A.
- BBoth A and R are true but R is not the correct explanation of A.
- CA is true but R is false.
- DA is false but R is true.
Answer
View full question & answer→(a) Both A and R are true and R is the correct explanation of A.
Explanation: Assertion: If $\frac{-2}{7}, K, \frac{-7}{2}$ are in G.P.
Then, $\frac{a_2}{a_1}=\frac{a_3}{a_2}$
$\left[\because\right.$ common ratio $\left.( r )=\frac{a_2}{a_1}=\frac{a_3}{a_2}=\frac{a_4}{a_3}=\ldots\right]$
$\therefore \frac{k}{\frac{-2}{7}}=\frac{\frac{-7}{2}}{k}$
$\begin{array}{l}\Rightarrow \frac{7}{-2} k=\frac{-7}{2} \times \frac{1}{k} \\ \Rightarrow 7 k \times 2 k =-7 \times(-2) \\ \Rightarrow 14 k ^2=14 \\ \Rightarrow k ^2=1 \Rightarrow k = \pm 1\end{array}$
Hence, Assertion and Reason both are true and Reason is the correct explanation of Assertion.
Explanation: Assertion: If $\frac{-2}{7}, K, \frac{-7}{2}$ are in G.P.
Then, $\frac{a_2}{a_1}=\frac{a_3}{a_2}$
$\left[\because\right.$ common ratio $\left.( r )=\frac{a_2}{a_1}=\frac{a_3}{a_2}=\frac{a_4}{a_3}=\ldots\right]$
$\therefore \frac{k}{\frac{-2}{7}}=\frac{\frac{-7}{2}}{k}$
$\begin{array}{l}\Rightarrow \frac{7}{-2} k=\frac{-7}{2} \times \frac{1}{k} \\ \Rightarrow 7 k \times 2 k =-7 \times(-2) \\ \Rightarrow 14 k ^2=14 \\ \Rightarrow k ^2=1 \Rightarrow k = \pm 1\end{array}$
Hence, Assertion and Reason both are true and Reason is the correct explanation of Assertion.