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Day 545: JEE Mains Maths

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

  1. Question 1

    Application of Derivatives. Asked once: 29 Jan 2023

    166
    Let ff and gg be twice differentiable functions on RR such that
    f′′(x)=g′′(x)+6xf′(1)=4g′(1)−3=9f(2)=3g(2)=12\begin{matrix} & f^{''}(x) =g^{''}(x) + 6x \\ & f^{'}(1) = 4g^{'}(1) - 3 = 9 \\ & f(2) = 3g(2) = 12 \end{matrix}
    Then which of the following is NOT true?

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  2. Question 2

    Application of Integrals. Asked once: 31 Jan 2024

    65
    The area of the region
    {(x,y):y2≤4x,x<4,xy(x−1)(x−2)(x−3)(x−4)>0,x≠3}\left\{ (x,y):y^{2}\leq 4x,x< 4,\frac{xy(x- 1)(x- 2)}{(x- 3)(x- 4)}> 0,x\neq 3 \right\}
    is

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  3. Question 3

    Binomial Theorem. Asked once: 28 Jul 2022

    174
    If 1+(2+ 49C1+ 49C2+…..+ 49C49)( 50C2+ 50C4+1 +\left( 2 +\ ^{49}C_{1}+\ ^{49}C_{2}+ \ldots.. +\ ^{49}C_{49} \right)\left( \ ^{50}C_{2}+\ ^{50}C_{4}+ \right. + 50C50+\ ^{50}C_{50} ) is equal to 2n⋅m2^{n}\cdot m, where mm is odd, then nn +m+ m is equal to

  4. Question 4

    Complex Numbers. Asked once: 11 Apr 2023

    174
    Let  S={z∈C−{i,2i}:z2+8iz−15z2−3iz−2∈R}.\ S =\left\{ \mathbf{z \in C - \{ i,2i\}:}\frac{z^{2}+ 8iz - 15}{z^{2}- 3iz - 2}\in R \right\}. If α−1311i∈S,α∈R−{0}\alpha -\frac{13}{11}\mathbf{i \in S,\alpha \in R - \{ 0\}}, then 242α2242\alpha^{2} is equal to

  5. Question 5

    Conic Sections. Asked once: 4 Apr 2025

    132
    The axis of a parabola is the line y=xy=x and its vertex and focus are in the first quadrant at distances 2\sqrt{2} and 222\sqrt{2} units from the origin, respectively. If the point (1,k)(1,k) lies on the parabola, then a possible value of kk is :-

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