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Day 359: JEE Mains Maths

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

  1. Question 1

    Vector Algebra. Asked once: 29 Jan 2025 (same type asked 18 times) See all 18 of this type

    55
    Let a→=2i^−j^+3k^,b→=3i^−5j^+k^\overrightarrow{a}= 2\widehat{i}-\widehat{j}+ 3\widehat{k},\overrightarrow{b}= 3\widehat{i}- 5\widehat{j}+\widehat{k} and c→\overrightarrow{c} be a vector such that a→×c→=c→×b→\overrightarrow{a}\times\overrightarrow{c}=\overrightarrow{c}\times\overrightarrow{b} and (a→+c→)⋅(b→+c→)=168(\overrightarrow{a}+\overrightarrow{c}) \cdot (\overrightarrow{b}+\overrightarrow{c}) = 168. Then the maximum value of ∣c→∣2|\overrightarrow{c}|^{2} is :

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  2. Question 2

    Limits and Continuity. Asked once: 23 Jan 2025 (same type asked 16 times) See all 16 of this type

    53
    If the function
    f(x)={2x{sin⁡(k1+1)x+sin⁡(k2−1)x},x<04x=02xlog⁡e(2+k1x2+k2x)x>0f(x) =\left\{ \begin{matrix} \frac{2}{x}\left\{ \sin\left( k_{1}+ 1 \right)x + \sin\left( k_{2}- 1 \right)x \right\} & ,x < 0 \\ 4 & x = 0 \\ \frac{2}{x}\log_{e}\left( \frac{2 +k_{1}x}{2 +k_{2}x} \right) & x > 0 \end{matrix} \right.
    is continuous at x=0x = 0, then k1 2+k2 2k_{1}\ ^{2}+k_{2}\ ^{2} is equal to

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  3. Question 3

    Three Dimensional Geometry. Asked once: 24 Jan 2023 (same type asked 15 times) See all 15 of this type

    162
    Let the plane containing the line of intersection of the planes P1:x+(λ+4)y+z=1P1:x + (\lambda + 4)y + z = 1 and P2:2x+y+P2:2x + y + z=2z = 2 pass through the points (0,1,0)(0,1,0) and (1,0,1)(1,0,1). Then the distance of the point (2λ,λ,−λ)(2\lambda,\lambda, - \lambda) from the plane P2P2 is

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  4. Question 4

    Determinants. Asked once: 25 Jul 2022 (same type asked 14 times) See all 14 of this type

    152
    The number of real values λ\lambda, such that the system of linear equations
    2x−3y+5z=92x - 3y + 5z = 9
    x+3y−z=−18x + 3y - z = - 18
    3x−y+(λ2−∣λ∣)z=163x - y +\left( \lambda^{2}- |\lambda| \right)z = 16
    has no solution, is:-

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  5. Question 5

    Statistics. Asked once: 29 Jan 2024 (same type asked 13 times) See all 13 of this type

    87
    If the mean and variance of the data 65,68,58,4465,68,58,44, 48,45,60,α,β,6048,45,60,\alpha,\beta,60 where α>β\alpha > \beta are 56 and 66.2 respectively, then α2+β2\alpha^{2}+\beta^{2} is equal to