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Day 404: JEE Mains Maths

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

  1. Question 1

    Three Dimensional Geometry. Asked once: 2021 Paper 22 (same type asked 15 times) See all 15 of this type

    64
    Let the equation of the plane, that passes through the point (1,4,−3)(1,4,-3) and contains the line of intersection of the planes 3x−2y+4z−7=03x- 2y+ 4z- 7 = 0 and x+5y−2z+9=0x + 5y - 2z + 9 = 0, be αx+βy+γz+3=0\alpha x +\beta y +\gamma z + 3 = 0, then α+β+γ\alpha+\beta+\gamma is equal to:

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  2. Question 2

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

    154
    The system of equations
    −kx+3y−14z=25- kx + 3y - 14z = 25
    −15x+4y−kz=3- 15x + 4y - kz = 3
    −4x+y+3z=4- 4x + y + 3z = 4
    is consistent for all kk in the set

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  3. Question 3

    Statistics. Asked once: 2021 Paper 19 (same type asked 13 times) See all 13 of this type

    88
    Let the mean and variance of four numbers 3,7,x3,7,x and y(x>y)y(x>y) be 5 and 10 respectively. Then the mean of four numbers 3+2x,7+2y,x+y3 + 2x,7 + 2y,x+y and x−yx - y is

  4. Question 4

    Vector Algebra. Asked once: 28 Jun 2022 (same type asked 13 times) See all 13 of this type

    169
    Let a→\overrightarrow{a} be a vector which is perpendicular to the vector 3i^+12j^+2k^3\widehat{i}+\frac{1}{2}\widehat{j}+ 2\widehat{k}. If a→×(2i^+k^)=2i^−13j^−4k^\overrightarrow{a}\times (2\widehat{i}+\widehat{k}) = 2\widehat{i}- 13\widehat{j}- 4\widehat{k}, then the projection of the vector a→\overrightarrow{a} on the vector 2i^+2j^+k^2\widehat{i}+ 2\widehat{j}+\widehat{k} is

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  5. Question 5

    Differential Equations. Asked once: 29 Jan 2023 (same type asked 13 times) See all 13 of this type

    65
    Let y=f(x)y = f(x) be the solution of the differential equation y(x+1)dx−x2dy=0,y(1)=ey(x + 1)dx -x^{2}dy = 0,y(1) = e. Then lim⁡x→0+f(x)\lim_{x \rightarrow0^{+}} f(x) is equal to

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