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Day 504: JEE Mains Maths

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

  1. Question 1

    Application of Derivatives. Asked once: 5 Apr 2024

    65
    For the function f(x)=sin⁡x+3x−2π(x2+x)f(x) = \sin x + 3x -\frac{2}{\pi}\left( x^{2}+ x \right), where x∈[0,π2]x \in\left\lbrack 0,\frac{\pi}{2} \right\rbrack, consider the following two statements: (I) ff is increasing in (0,π2)\left( 0,\frac{\pi}{2} \right). (II) f′f^{'} is decreasing in (0,π2)\left( 0,\frac{\pi}{2} \right). Between the above two statements,

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  2. Question 2

    Application of Integrals. Asked once: 24 Jan 2025

    142
    The area of the region enclosed by the curves y=ex,y=∣ex−1∣y=e^{x},y=\left| e^{x}- 1 \right| and yy-axis is:

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  3. Question 3

    Binomial Theorem. Asked once: 15 Apr 2023

    68
    Let (a+bx+cx2)10=∑i=020pixi,a,b,c∈N\left( a + bx + cx^{2} \right)^{10}=\sum_{i = 0}^{20} p_{i}x^{i},a,b,c \in N. If p1=20p_{1}= 20 and p2=210p_{2}= 210, then 2(a+b+c)2(a + b + c) is equal to

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  4. Question 4

    Complex Numbers. Asked once: 8 Apr 2024

    75
    Let zz be a complex number such that ∣z+2∣=1|z+ 2| = 1 and Im(z+1z+2)=15Im\left( \frac{z+ 1}{z+ 2} \right)=\frac{1}{5}. Then the value of ∣Re(z+2‾)∣|Re(\overline{z+ 2})| is:

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  5. Question 5

    Conic Sections. Asked once: 2 Apr 2026 S2

    62
    Let the parabola y=x2+px+qy =x^{2}+ px + q passing through the point (1,−1)(1, - 1) be such that the distance between its vertex and the x -axis is minimum. Then the value of p2+q2p^{2}+q^{2} is :

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