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Day 192: JEE Mains Maths

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

  1. Question 1

    Conic Sections. Asked once: 30 Jan 2023 (same type asked 3 times) See all 3 of this type

    67
    Let y=x+2,4y=3x+6y = x + 2,4y = 3x + 6 and 3y=4x+13y = 4x + 1 be three tangent lines to the circle (x−h)2+(y−(x - h)^{2}+ (y - k)2=r2k)^{2}=r^{2}. Then h+kh + k is equal to:

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  2. Question 2

    Definite Integration. Asked once: 24 Jan 2023 (same type asked 3 times) See all 3 of this type

    90
    The value of 12∫03∣x2−3x+2∣dx12\int_{0}^{3} \left| x^{2}- 3x + 2 \right|dx is

  3. Question 3

    Quadratic Equations. Asked once: 2021 Paper 16 (same type asked 3 times) See all 3 of this type

    45
    If α\alpha and β\beta are the roots of equation x2+2014x+512=0x^{2}+20^{\frac{1}{4}}x +5^{\frac{1}{2}}= 0, then find (α8+β8)\left( \alpha^{8}+\beta^{8} \right)

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  4. Question 4

    Differentiation. Asked once: 26 Jun 2022 (same type asked 3 times) See all 3 of this type

    67
    Let f,g:R→Rf,g:R \rightarrow R be two real valued functions defined as f(x)={−∣x+3∣, x<0ex, x≥0f(x) =\left\{ \begin{matrix} - |x + 3| & ,\ x < 0 \\ e^{x} & ,\ x \geq 0 \end{matrix} \right. and g(x)={x2+k1x, x<04x+k2, x≥0g(x) =\left\{ \begin{matrix} x^{2}+k_{1}x & ,\ x < 0 \\ 4x +k_{2} & ,\ x \geq 0 \end{matrix} \right., where k1k_{1} and k2k_{2} are real constants. If (gof) is differentiable at x=0x = 0, then (gof) (−4)+( - 4) + (gof) (4) is equal to:

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  5. Question 5

    Three Dimensional Geometry. Asked once: 6 Apr 2023 (same type asked 3 times) See all 3 of this type

    89
    Let the image of the point P(1,2,3)P(1,2,3) in the plane 2x2x −y+z=9- y + z = 9 be QQ. If the coordinates of the point RR are (6,10,7)(6,10,7), then the square of the area of the triangle PQRPQR is