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Day 538: JEE Mains Maths

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

  1. Question 1

    Application of Integrals. Asked once: 1 Feb 2024

    70
    The area enclosed by the curves xy+4y=16xy+ 4y= 16 and x+y=6x + y = 6 is equal to :

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  2. Question 2

    Binomial Theorem. Asked once: 24 Jan 2023

    175
    Let the sum of the coefficients of the first three terms in the expansion of (x−3x2)n,x≠0.n∈N\left( x -\frac{3}{x^{2}} \right)^{n},x \neq 0.n \in N, be 376. Then the coefficient of x4x^{4} is

  3. Question 3

    Complex Numbers. Asked once: 13 Apr 2023

    83
    Let ω=zz‾+k1z+k2iz+λ(1+i),k1,k2∈R\omega = z\overline{z}+k_{1}z +k_{2}iz + \lambda(1 + i),k_{1},k_{2}\in R. Let Re(ω)=0Re(\omega) = 0 be the circle CC of radius 1 in the first quadrant touching the line y=1y = 1 and the yy-axis. If the curve Im(ω)=0Im(\omega) = 0 intersects CC at A and B, then 30(AB)230(AB)^{2} is equal to

  4. Question 4

    Conic Sections. Asked once: 21 Jan 2026 S1

    65
    Let PQ and MN be two straight lines touching the circle x2+y2−4x−6y−3=0x^{2}+y^{2}- 4x - 6y - 3 = 0 at the points A and B respectively. Let O be the centre of the circle and ∠AOB=π/3\angle AOB = \pi/3. Then the locus of the point of intersection of the lines PQ and MN is:

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  5. Question 5

    Definite Integration. Asked once: 28 Jan 2025

    137
    Let f:R→Rf:R\rightarrow R be a twice differentiable function such that f(2)=1f(2) = 1. If F(x)=xf(x)F(x) = xf(x) for all x∈Rx \in R, ∫02xF′(x)dx=6\int_{0}^{2} xF^{'}(x)dx= 6 and ∫02x2F′′(x)dx=40\int_{0}^{2} x^{2}F^{''}(x)dx= 40, then F′(2)+∫02F(x)dxF^{'}(2) +\int_{0}^{2} F(x)dx is equal to :

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