JEE Main & Advanced Sample Paper JEE Main Sample Paper-19

  • question_answer 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.

    Correct Answer: A

    Solution :

     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.

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