• # question_answer 80) DIRECTION (Qs. 80): Each of these questions contains two statements: Statement-1 (Assertion) and Statement-2 (Reason). Choose the correct answer (ONLY ONE option is correct) from the following- Let${{I}_{n}}=\int\limits_{I}^{e}{{{(\ell nx)}^{n}}dx,\,\,n\in N}$ Statement-1: ${{I}_{1}},\,\,\,{{I}_{2}},\,\,{{I}_{3}},...$is an increasing sequence. Statement-2: $\ln \,\,\,x$ is an increasing function. A)  Statement-1 is false, Statement-2 is true.B)  Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.C)  Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.D)  Statement-1 is true, Statement-2 is false.

Statement-II is true, as if$f(x)=\ln x$, then $f'(x)=\frac{1}{x}>0$(as$x>0$, so that$f(x)$is defined) Statement-I is not true as $0<\ln x<1,\,\,\forall x\in (1,\,\,e)$and hence ${{(\ln x)}^{n}}$ decreases as $n$ is increasing. So that ${{I}_{n}}$ is a decreasing sequence.