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Day 619: JEE Mains Maths

5 questions. Try each one first, then open its answer.

  1. Question 1

    Application of Derivatives. Asked once: 2021 Paper 2

    62
    Let ff be a twice differentiable function defined on RR such that f(0)=1,f′(0)=2f(0) = 1,f^{'}(0) = 2 and f′(x)≠0f^{'}(x) \neq 0 for all x∈Rx\in R. If ∣f(x)f′(x)f′(x)f′′(x)∣=0\left| \begin{matrix} f(x) & f^{'}(x) \\ f^{'}(x) & f^{''}(x) \end{matrix} \right|= 0, for all x∈Rx\in R then the value of f(1)f(1) lies in the interval:

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  2. Question 2

    Complex Numbers. Asked once: 2021 Paper 3

    71
    Let the lines (2−i)z=(2+i)zˉ(2 -i)z= (2 +i)\bar{z} and (2+i)z+(i−2)zˉ−4i=0(2 +i)z+ (i- 2)\bar{z}- 4i= 0, (here  i2=−1)\left. \ i^{2}= - 1 \right) be normal to a circle CC. If the line iz+zˉ+1+i=0iz+\bar{z}+ 1 +i= 0 is tangent to this circle CC, then its radius is:

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  3. Question 3

    Conic Sections. Asked once: 5 Apr 2024

    166
    Let ABCDABCD and AEFGAEFG be squares of side 4 and 2 units, respectively. The point EE is on the line segment ABAB and the point FF is on the diagonal ACAC. Then the radius rr of the circle passing through the point FF and touching the line segments BCBC and CDCD satisfies :

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  4. Question 4

    Definite Integration. Asked once: 24 Jan 2023

    159
     ∫324334489−4x2dx\ \int_{\frac{3\sqrt{2}}{4}}^{\frac{3\sqrt{3}}{4}} \frac{48}{\sqrt{9 - 4x^{2}}}dx is equal to

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  5. Question 5

    Sequences and Series. Asked once: 26 Jul 2022

    179
    Different A.P.'s are constructed with the first term 100, the last term 199, And integral common differences. The sum of the common differences of all such, A. P's having at least 3 terms and at most 33 terms is.