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Day 387: JEE Mains Maths

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

  1. Question 1

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

    64
    If the system of linear equations
    3x+y+βz=32x+αy−z=−3x+2y+z=4\begin{matrix} & 3x+y+\beta z= 3 \\ & 2x+\alpha y-z= - 3 \\ & x+ 2y+z= 4 \end{matrix}
    has infinitely many solutions, then the value of 22β−9α22\beta- 9\alpha is :

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  2. Question 2

    Three Dimensional Geometry. Asked once: 8 Apr 2024 (same type asked 19 times) See all 19 of this type

    174
    Let P(α,β,γ)P(\alpha,\beta,\gamma) be the image of the point Q(1,6,4)Q(1,6,4) in the line x1=y−12=z−23\frac{x}{1}=\frac{y- 1}{2}=\frac{z- 2}{3}. Then 2α+β+γ2\alpha+\beta+\gamma is equal to

  3. Question 3

    Differential Equations. Asked once: 24 Jan 2023 (same type asked 19 times) See all 19 of this type

    155
    Let y=y(x)y = y(x) be the solution of the differential equation (x2−3y2)dx+3xydy=0,y(1)=1\left( x^{2}- 3y^{2} \right)dx + 3xydy = 0,y(1) = 1. Then 6y2(e)6y^{2}(e) is equal to

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  4. Question 4

    Determinants. Asked once: 31 Jan 2024 (same type asked 19 times) See all 19 of this type

    175
    Let AA be a 3×33 \times 3 matrix and det(A)=2det(A) = 2. If n=det⁡(adj(adj(…(adj A)…)))n = \det(\mathrm{adj}(\mathrm{adj}(\ldots(\mathrm{adj}\,A)\ldots))), where adj is applied 2024 times, then the remainder when nn is divided by 9 is equal to

  5. Question 5

    Vector Algebra. Asked once: 8 Apr 2024 (same type asked 18 times) See all 18 of this type

    163
    Let a→=4i^−j^+k^,b→=11i^−j^+k^\overrightarrow{a}= 4\widehat{i}-\widehat{j}+\widehat{k},\overrightarrow{b}= 11\widehat{i}-\widehat{j}+\widehat{k} and c→\overrightarrow{c} be a vector such that (a→+b→)×c→=c→×(−2a→+3b→)(\overrightarrow{a}+\overrightarrow{b}) \times\overrightarrow{c}=\overrightarrow{c}\times ( - 2\overrightarrow{a}+ 3\overrightarrow{b}). If (2a→+3b→)⋅c→=1670(2\overrightarrow{a}+ 3\overrightarrow{b}) \cdot\overrightarrow{c}= 1670, then ∣c→∣2|\overrightarrow{c}|^{2} is equal to:

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