PYQ Vault
EbooksTutor

Day 423: JEE Mains Maths

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

  1. Question 1

    Three Dimensional Geometry. Asked once: 31 Jan 2024 (same type asked 33 times) See all 33 of this type

    170
    The shortest distance between lines L1L_{1} and L2L_{2}, where L1:x−12=y+1−3=z+42L_{1}:\frac{x - 1}{2}=\frac{y + 1}{- 3}=\frac{z + 4}{2} and L2L_{2} is the line passing through the points A(−4,4,3)⋅B(−1,6,3)A( - 4,4,3) \cdot B( - 1,6,3) and perpendicular to the line x−3−2=y3=z−11\frac{x - 3}{- 2}=\frac{y}{3}=\frac{z - 1}{1}, is

    Tap an option to check your answer.

  2. Question 2

    Determinants. Asked once: 1 Feb 2024 (same type asked 26 times) See all 26 of this type

    72
    If the system of equations
    2x+3y−z=52x + 3y - z = 5
    x+αy+3z=−4x + \alpha y + 3z = - 4
    3x−y+βz=73x - y + \beta z = 7
    has infinitely many solutions, then 13αβ13\alpha\beta is equal to

    Tap an option to check your answer.

  3. Question 3

    Determinants. Asked once: 26 Jun 2022 (same type asked 19 times) See all 19 of this type

    63
    Let AA be a 3×33 \times 3 invertible matrix. If ∣adj(24 A)∣=∣adj(3adj(2 A))∣|adj(24\text{ }A)| = |adj(3adj(2\text{ }A))|, then ∣A∣2|A|^{2} is equal to:

    Tap an option to check your answer.

  4. Question 4

    Vector Algebra. Asked once: 29 Jan 2023 (same type asked 18 times) See all 18 of this type

    156
    If a→=ı^+2k^,b→=ı^+ȷ^+k^,c→=7ı^−3ȷ^+4k^,r→×b→+b→×c→=0→\overrightarrow{a}=\widehat{\imath}+ 2\widehat{k},\overrightarrow{b}=\widehat{\imath}+\widehat{\jmath}+\widehat{k},\overrightarrow{c}= 7\widehat{\imath}- 3\widehat{\jmath}+ 4\widehat{k},\overrightarrow{r}\times\overrightarrow{b}+\overrightarrow{b}\times\overrightarrow{c}=\overrightarrow{0} and r→⋅a→=0\overrightarrow{r}\cdot\overrightarrow{a}= 0. Then r→⋅c→\overrightarrow{r}\cdot\overrightarrow{c} is equal to

    Tap an option to check your answer.

  5. Question 5

    Differential Equations. Asked once: 1 Feb 2024 (same type asked 41 times) See all 41 of this type

    81
    If x=x(t)x = x(t) is the solution of the differential equation (t+1)dx=(2x+(t+1)4)dt,x(0)=2(t+ 1)dx=\left( 2x+ (t+ 1)^{4} \right)dt,x(0) = 2, then, x(1)x(1) equals