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Day 376: JEE Mains Maths

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

  1. Question 1

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

    88
    Let a→=9i^−13j^+25k^,b→=3i^+7j^−13k^\overrightarrow{a}= 9\widehat{i}- 13\widehat{j}+ 25\widehat{k},\overrightarrow{b}= 3\widehat{i}+ 7\widehat{j}- 13\widehat{k} and c→=17i^−2j^+k^\overrightarrow{c}= 17\widehat{i}- 2\widehat{j}+\widehat{k} be three given vectors. If r→\overrightarrow{r} is a vector such that r→×a→=(b→+c→)×a→\overrightarrow{r}\times\overrightarrow{a}= (\overrightarrow{b}+\overrightarrow{c}) \times\overrightarrow{a} and r→⋅(b→−c→)=0\overrightarrow{r}\cdot (\overrightarrow{b}-\overrightarrow{c}) = 0, then ∣593r→+67a→∣2(593)2\frac{|593\overrightarrow{r}+ 67\overrightarrow{a}|^{2}}{(593)^{2}} is equal to

  2. Question 2

    Limits and Continuity. Asked once: 4 Apr 2024 (same type asked 16 times) See all 16 of this type

    61
    Let f:R→Rf:R \rightarrow R be a function given by
    f(x)={1−cos⁡2xx2,x<0α,x=0, where α,β∈R. If β1−cos⁡xx,x>0f(x) =\left\{ \begin{matrix} \frac{1 - \cos2x}{x^{2}} & ,x < 0 \\ \alpha & ,x = 0,\text{~where~}\alpha,\beta \in R\text{. If~} \\ \frac{\beta\sqrt{1 - \cos x}}{x} & ,x > 0 \end{matrix} \right.
    ff is continuous at x=0x = 0, then α2+β2\alpha^{2}+\beta^{2} is equal to:

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  3. Question 3

    Three Dimensional Geometry. Asked once: 26 Jul 2022 (same type asked 15 times) See all 15 of this type

    177
    The plane passing through the line L:lx−y+3(1−l)L:\mathcal{l}x - y + 3(1 -\mathcal{l)} z=1,x+2y−z=2z = 1,x + 2y - z = 2 and perpendicular to the plane 3x+2y+z=63x + 2y + z = 6 is 3x−8y+7z=43x - 8y + 7z = 4. If θ\theta is the acute angle between the line LL and the yy-axis, then 415 cos⁡2θ\cos^{2}\theta is equal to

  4. Question 4

    Determinants. Asked once: 28 Jun 2022 (same type asked 14 times) See all 14 of this type

    63
    If the system of linear equations
    2x+3y−z=−22x + 3y - z = - 2
    x+y+z=4x + y + z = 4
    x−y+∣λ∣z=4λ−4x - y + |\lambda|z = 4\lambda - 4
    where λ∈R\lambda \in R, has no solution, then

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  5. Question 5

    Statistics. Asked once: 8 Apr 2023 (same type asked 13 times) See all 13 of this type

    90
    Let the mean and variance of 8 numbers x,y,10x,y,10, 12,6,12,4,812,6,12,4,8, be 9 and 9.25 respectively. If x>yx > y, then 3x−2y3x - 2y is equal to