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Day 287: JEE Mains Maths

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

  1. Question 1

    Binomial Theorem. Asked once: 2021 Paper 7 (same type asked 3 times) See all 3 of this type

    70
    If the fourth term in the expansion of (x+xlog⁡2x)7\left( x+x^{\log_{2}x} \right)^{7} is 4480, then the value of xx where x∈Nx\in N is equal to:

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  2. Question 2

    Three Dimensional Geometry. Asked once: 2021 Paper 5 (same type asked 3 times) See all 3 of this type

    73
    Let PP be a plane lx+my+nz=0lx + my + nz = 0 containing the line, 1−x1=y+42=z+23\frac{1 -x}{1}=\frac{y+ 4}{2}=\frac{z+ 2}{3}. If plane PP divides the line segment ABAB joining points A(−3,−6,1)A( - 3, - 6,1) and B(2,4,−3)B(2,4, - 3) in ratio k:1k:1 then the value of kk is equal to:

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  3. Question 3

    Application of Integrals. Asked once: 28 Jun 2022 (same type asked 3 times) See all 3 of this type

    69
    The area of the region S={(x,y):y2≤8x,y≥2x,x≥1}S =\left\{ (x,y):y^{2}\leq 8x,y \geq\sqrt{2}x,x \geq 1 \right\} is

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  4. Question 4

    Matrices. Asked once: 2021 Paper 2 (same type asked 3 times) See all 3 of this type

    76
    Let AA and BB be 3×33 \times 3 real matrices such that AA is symmetric matrix and BB is skew-symmetric matrix. Then the system of linear equations (A2B2−B2A2)X=O\left( A^{2}B^{2}-B^{2}A^{2} \right)X=O, where XX is a 3×13 \times 1 column matrix of unknown variables and OO is a 3×13 \times 1 null matrix, has:

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  5. Question 5

    Conic Sections. Asked once: 2021 Paper 10 (same type asked 3 times) See all 3 of this type

    75
    Let a tangent be drawn to the ellipse x227+y2=1\frac{x^{2}}{27}+y^{2}= 1 at (33cos⁡θ,sin⁡θ)(3\sqrt{3}\cos\theta,\sin\theta) where θ∈(0,π2)\theta \in\left( 0,\frac{\pi}{2} \right). Then the value of θ\theta such that the sum of intercepts on axes made by this tangent is minimum is equal to:

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