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Day 396: JEE Mains Maths

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

  1. Question 1

    Determinants. Asked once: 24 Jan 2025 (same type asked 26 times) See all 26 of this type

    70
    If the system of equations
    2x−y+z=45x+λy+3z=12100x−47y+μz=212\begin{matrix} & 2x - y + z = 4 \\ & 5x + \lambda y + 3z = 12 \\ & 100x - 47y + \mu z = 212 \end{matrix}
    has infinitely many solutions, then μ−2λ\mu - 2\lambda is equal to

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  2. Question 2

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

    159
    Let (α,β,γ)(\alpha,\beta,\gamma) be the image of the point (8,5,7)(8,5,7) in the line x−12=y+13=z−25\frac{x - 1}{2} = \frac{y + 1}{3} = \frac{z - 2}{5}. Then α+β+γ\alpha + \beta + \gamma is equal to

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  3. Question 3

    Differential Equations. Asked once: 25 Jul 2022 (same type asked 19 times) See all 19 of this type

    71
    The general solution of the differential equation (x−y2)dx+y(5x+y2)dy=0\left( x -y^{2} \right)dx + y\left( 5x +y^{2} \right)dy = 0 is :

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  4. Question 4

    Determinants. Asked once: 15 Apr 2023 (same type asked 19 times) See all 19 of this type

    69
    Let the determinant of a square matrix AA of order mm be m−nm - n, where mm and nn satisfy 4m+n=224m + n = 22 and 17 m+4n=9317\text{ }m + 4n = 93. If det (nadj(adj(mA)))=(nadj(adj(mA))) = 3a5b6c3^{a}5^{b}6^{c}. then a+b+ca + b + c is equal to:

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  5. Question 5

    Vector Algebra. Asked once: 5 Apr 2024 (same type asked 18 times) See all 18 of this type

    88
    Let a→=i^−3j^+7k^, b→=2i^−j^+k^\overrightarrow{a}=\widehat{i}- 3\widehat{j}+ 7\widehat{k},\ \overrightarrow{b}= 2\widehat{i}-\widehat{j}+\widehat{k} and c→\overrightarrow{c} be a vector such that (a→+2b→)×c→=3(c→×a→)(\overrightarrow{a}+ 2\overrightarrow{b}) \times\overrightarrow{c}= 3(\overrightarrow{c}\times\overrightarrow{a}). If a→⋅c→=130\overrightarrow{a}\cdot\overrightarrow{c}= 130, then b→⋅c→\overrightarrow{b}\cdot\overrightarrow{c} is equal to