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Day 424: JEE Mains Maths

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

  1. Question 1

    Three Dimensional Geometry. Asked once: 30 Jan 2024 (same type asked 33 times) See all 33 of this type

    82
    If d1d_{1} is the shortest distance between the lines x+1=2y=−12z,x=y+2=6z−6x+ 1 = 2y= - 12z,x=y+ 2 = 6z- 6 and d2d_{2} is the shortest distance between the lines x−12=y+8−7=z−45,x−12=y−21=z−6−3\frac{x- 1}{2}=\frac{y+ 8}{- 7}=\frac{z- 4}{5},\frac{x- 1}{2}=\frac{y- 2}{1}=\frac{z- 6}{- 3}, then the value of 323d1d2\frac{32\sqrt{3}d_{1}}{d_{2}} is :

  2. Question 2

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

    167
    Let the system of equations x+2y+3z=5,2x+3y+z=9,4x+3y+λz=μx + 2y + 3z = 5,2x + 3y + z = 9,4x + 3y + \lambda z = \mu have infinite number of solutions. Then λ+2μ\lambda + 2\mu is equal to:

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  3. Question 3

    Determinants. Asked once: 2021 Paper 19 (same type asked 19 times) See all 19 of this type

    89
    Let AA be a 3×33 \times 3 real matrix. If det(2Adj(2Adj(Adj(2 A))))=241det(2Adj(2Adj(Adj(2\text{ }A)))) =2^{41}, then the value of det(A2)det\left( A^{2} \right) equal

  4. Question 4

    Vector Algebra. Asked once: 24 Jan 2023 (same type asked 18 times) See all 18 of this type

    177
    Let a→=i^+2j^+λk^,b→=3i^−5j^−λk^,a→⋅c→=7,2b→⋅c→+43=0,a→×c→=b→×c→\overrightarrow{a}=\widehat{i}+ 2\widehat{j}+ \lambda\widehat{k},\overrightarrow{b}= 3\widehat{i}- 5\widehat{j}- \lambda\widehat{k},\overrightarrow{a}\cdot\overrightarrow{c}= 7,2\overrightarrow{b}\cdot\overrightarrow{c}+ 43 = 0,\overrightarrow{a}\times\overrightarrow{c}=\overrightarrow{b}\times\overrightarrow{c}. Then ∣a→⋅b→∣|\overrightarrow{a}\cdot\overrightarrow{b}| is equal to

  5. Question 5

    Differential Equations. Asked once: 31 Jan 2024 (same type asked 41 times) See all 41 of this type

    71
    Let y=y(x)y = y(x) be the solution of the differential equation
    dydx=(tan⁡x)+ysin⁡x(secx−sin⁡xtanx)\frac{dy}{dx}=\frac{(\tan x) +y}{\sin x(secx- \sin xtanx)}
    x∈(0,π2)x \in\left( 0,\frac{\pi}{2} \right) satisfying the condition y(π4)=2y\left( \frac{\pi}{4} \right)= 2. Then, y(π3)y\left( \frac{\pi}{3} \right) is

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