PYQ Vault
EbooksTutor

Day 375: JEE Mains Maths

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

  1. Question 1

    Three Dimensional Geometry. Asked once: 3 Apr 2025 (same type asked 33 times) See all 33 of this type

    70
    Line L1L_{1} passes through the point (1,2,3)(1,2,3) and is parallel to zz-axis. Line L2L_{2} passes through the point (λ,5,6)(\lambda,5,6) and is parallel to yy-axis. Let for λ=λ1,λ2,λ2<λ1\lambda=\lambda_{1},\lambda_{2},\lambda_{2}<\lambda_{1}, the shortest distance between the two lines be 3 . Then the square of the distance of the point (λ1,λ2,7)\left( \lambda_{1},\lambda_{2},7 \right) from the line L1L_{1} is.

    Tap an option to check your answer.

  2. Question 2

    Determinants. Asked once: 2 Apr 2025 (same type asked 26 times) See all 26 of this type

    133
    If the system of equation
    2x+λy+3z=52x+\lambda y+ 3z= 5
    3x+2y−z=73x+ 2y-z= 7
    4x+5y+μz=94x+ 5y+\mu z= 9
    has infinitely many solutions, then (λ2+μ2)\left( \lambda^{2}+\mu^{2} \right) is equal to :

    Tap an option to check your answer.

  3. Question 3

    Three Dimensional Geometry. Asked once: 9 Apr 2024 (same type asked 19 times) See all 19 of this type

    177
    The square of the distance of the image of the point (6,1,5)(6,1,5) in the line x−13=y2=z−24\frac{x- 1}{3}=\frac{y}{2}=\frac{z- 2}{4}, from the origin is

  4. Question 4

    Differential Equations. Asked once: 30 Jan 2023 (same type asked 19 times) See all 19 of this type

    167
    The solution of the differential equation dydx=−(x2+3y23x2+y2),y(1)=0\frac{dy}{dx}= -\left( \frac{x^{2}+ 3y^{2}}{3x^{2}+y^{2}} \right),y(1) = 0 is

    Tap an option to check your answer.

  5. Question 5

    Determinants. Asked once: 5 Apr 2024 (same type asked 19 times) See all 19 of this type

    71
    Let AA and BB be two square matrices of order 3 such that ∣A∣=3|A| = 3 and ∣B∣=2|B| = 2. Then ∣ATA(adj(2 A))−1(adj(4 B))(adj(AB))−1AAT∣\left| A^{T}A(adj(2\text{ }A))^{- 1}(adj(4\text{ }B))(adj(AB))^{- 1}AA^{T} \right| is equal to :

    Tap an option to check your answer.