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Day 427: JEE Mains Maths

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

  1. Question 1

    Determinants. Asked once: 13 Apr 2023 (same type asked 26 times) See all 26 of this type

    151
    If the system of equations
    2x+y−z=52x−5y+λz=μx+2y−5z=7\begin{matrix} & 2x + y - z = 5 \\ & 2x - 5y + \lambda z = \mu \\ & x + 2y - 5z = 7 \end{matrix}
    has infinitely many solutions, then (λ+μ)2+(λ−μ)2(\lambda + \mu)^{2}+ (\lambda - \mu)^{2} is equal to

    Tap an option to check your answer.

  2. Question 2

    Vector Algebra. Asked once: 2021 Paper 3 (same type asked 18 times) See all 18 of this type

    88
    Let a→=i^+2j^−k^,b→=i^−j^\overrightarrow{a}=\widehat{i}+ 2\widehat{j}-\widehat{k},\overrightarrow{b}=\widehat{i}-\widehat{j} and c→=i^−j^−k^\overrightarrow{c}=\widehat{i}-\widehat{j}-\widehat{k} be three given vectors. If r→\overrightarrow{r} is a vector such that r→×a→=c→×a→\overrightarrow{r}\times\overrightarrow{a}=\overrightarrow{c}\times\overrightarrow{a} and r→⋅b→=0\overrightarrow{r}\cdot\overrightarrow{b}= 0, then r→⋅a→\overrightarrow{r}\cdot\overrightarrow{a} is equal to

  3. Question 3

    Differential Equations. Asked once: 13 Apr 2023 (same type asked 41 times) See all 41 of this type

    177
    If y=y(x)y = y(x) is the solution of the differential equation dydx+4x(x2−1)y=x+2(x2−1)52,x>1\frac{dy}{dx}+\frac{4x}{\left( x^{2}- 1 \right)}y =\frac{x + 2}{\left( x^{2}- 1 \right)^{\frac{5}{2}}},x > 1 such that y(2)=29log⁡e(2+3)y(2) =\frac{2}{9}\log_{e}(2 +\sqrt{3}) and  y(2)=\ y(\sqrt{2}) = αlog⁡e(α+β)+β−γ,α,β,γ∈N\alpha\log_{e}(\sqrt{\alpha}+ \beta) + \beta -\sqrt{\gamma},\alpha,\beta,\gamma \in N, then αβγ\alpha\beta\gamma is equal to

  4. Question 4

    Three Dimensional Geometry. Asked once: 8 Apr 2023 (same type asked 33 times) See all 33 of this type

    76
    The shortest distance between the lines x−44=y+25=z+33\frac{x - 4}{4}=\frac{y + 2}{5}=\frac{z + 3}{3} and x−13=y−34=z−42\frac{x - 1}{3}=\frac{y - 3}{4}=\frac{z - 4}{2} is

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  5. Question 5

    Determinants. Asked once: 11 Apr 2023 (same type asked 26 times) See all 26 of this type

    158
    If the system of linear equations
    7x+11y+αz=135x+4y+7z=β175x+194y+57z=361\begin{matrix} & 7x + 11y + \alpha z = 13 \\ & 5x + 4y + 7z = \beta \\ & 175x + 194y + 57z = 361 \end{matrix}
    has infinitely many solutions, then α+β+2\alpha + \beta + 2 is equal to

    Tap an option to check your answer.