Question

Each of these questions contains two statements, Statement 1(Assertion) and Statement 2(Reason).
State which of the following is correct :
(A) Statement-I is true, Statement-II is true ; Statement-II is correct explanation for Statement-I.
(B) Statement-I is true, Statement-II is true ; Statement-II is NOT a correct explanation for Statement-I
(C) Statement-I is true, Statement-II is false
(D) Statement-I is false, Statement-II is true

Statement -I : The sum of $n$ terms of two arithmetic progressions are in the ratio $(7n+1):(4n+17)$, then the ratio of their $n^{th}$ terms is $7:4$.

Statement-II : If $S_n=a{n}^2+bn+c,$ then $T_n=S_n-S_{n-1}$

• A. A
• B. B
• C. C
• D. D

Answer 1

The correct option is D D

Statement 1:

$\frac{S_n}{S_n^{{}^{\prime }}}=\frac{7n+1}{4n+17}=\frac{\frac{n}{2}\left[7\right(n-1)+7+1]}{\frac{n}{2}\left[4\right(n-1)+4+17]}$

$=\frac{\frac{n}{2}[2\ast 4+7(n-1\left)\right]}{\frac{n}{2}[2\ast 10.5+4(n-1\left)\right]}$

$\frac{T_n}{T_n^{{}^{\prime }}}=\frac{4+7(n-1)}{10.5+4(n-1)}\ne \frac{7}{4}$

Statement 1 $\to$ False

Statement 2:

Whatever is $S_n$ , $T_n=S_n-S_{n-1}$ is always true

Statement 2 $\to$ True