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

  • question_answer DIRECTION (Qs. 83): 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-
    Statement-1: Slope of tangents drawn from \[(4,\,\,10)\]) to parabola\[{{y}^{2}}=9x\]are\[\frac{1}{4},\,\,\frac{9}{4}\]
    Statement-2: Every parabola is symmetric about its directrix

    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: D

    Solution :

    \[y=mx+\frac{a}{m}\] \[10=4m-1\frac{9/4}{m}\Rightarrow 16{{m}^{2}}-40m+9=0\]                 \[{{m}_{1}}+{{m}_{2}}=\frac{40}{16}=\frac{5}{2};\,\,{{m}_{1}}{{m}_{2}}=\frac{9}{16}\] \[\Rightarrow \]               \[{{m}_{1}}=\frac{1}{4},\,\,{{m}_{2}}=\frac{9}{4}\] every parabola is symmetric about its axis only Statement 1 is true.

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