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Day 421: JEE Mains Maths

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

  1. Question 1

    Determinants. Asked once: 2021 Paper 1 (same type asked 14 times) See all 14 of this type

    80
    The system of linear equations
    3x−2y−kz=103x- 2y-kz= 10
    2x−4y−2z=62x- 4y- 2z= 6
    x+2y−z=5mx+ 2y-z= 5m
    is inconsistent if:

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  2. Question 2

    Differential Equations. Asked once: 4 Apr 2024 (same type asked 41 times) See all 41 of this type

    168
    Let y=y(x)y = y(x) be the solution of the differential equation (x2+4)2dy+(2x3y+8xy−2)dx=0\left( x^{2}+ 4 \right)^{2}dy +\left( 2x^{3}y + 8xy - 2 \right)dx = 0. If y(0)=0y(0) = 0 then y(2)y(2) is equal to

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  3. Question 3

    Three Dimensional Geometry. Asked once: 1 Feb 2024 (same type asked 33 times) See all 33 of this type

    80
    If the shortest distance between the lines x−λ−2=y−21=z−11\frac{x - \lambda}{- 2}=\frac{y - 2}{1}=\frac{z - 1}{1} and x−31=y−1−2=z−21\frac{x -\sqrt{3}}{1}=\frac{y - 1}{- 2}=\frac{z - 2}{1} is 1 , then the sum of all possible values of λ\lambda is :

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  4. Question 4

    Determinants. Asked once: 5 Apr 2024 (same type asked 26 times) See all 26 of this type

    66
    If the system of equations
    11x+y+λz=−511x + y + \lambda z = - 5
    2x+3y+5z=32x + 3y + 5z = 3
    8x−19y−39z=μ8x - 19y - 39z = \mu
    has infinitely many solutions, then λ4−μ\lambda^{4}- \mu is equal to:

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  5. Question 5

    Three Dimensional Geometry. Asked once: 2021 Paper 12 (same type asked 19 times) See all 19 of this type

    52
    Consider the line LL given by the equation x−32=y−11=z−21\frac{x - 3}{2}=\frac{y - 1}{1}=\frac{z - 2}{1}. Let QQ be the mirror image of the point (2,3,−1)(2,3, - 1) with respect to LL. Let a plane PP be such that it passes through QQ, and the line LL is perpendicular to PP. Then which of the following points is on the plane PP?

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