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Day 285: JEE Mains Maths

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

  1. Question 1

    Three Dimensional Geometry. Asked once: 24 Jan 2023 (same type asked 3 times) See all 3 of this type

    80
    The distance of the point (7,−3,−4)(7, - 3, - 4) from the plane passing through the points (2,−3,1),(−1,1,−2)(2, - 3,1),( - 1,1, - 2) and (3,−4,2)(3, - 4,2) is :

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  2. Question 2

    Conic Sections. Asked once: 28 Jun 2022 (same type asked 3 times) See all 3 of this type

    90
    Let the lines y+2x=11+77y+ 2x=\sqrt{11}+ 7\sqrt{7} and 2y+x=211+672y+x= 2\sqrt{11}+ 6\sqrt{7} be normal to a circle C:(x−h)2+(y−k)2=r2C:(x-h)^{2}+ (y-k)^{2}=r^{2}. If the line 11y−3x=5773+11\sqrt{11}y- 3x=\frac{5\sqrt{77}}{3}+ 11 is tangent to the circle CC, then the value of (5h−8k)2+5r2(5h- 8k)^{2}+ 5r^{2} is equal to

  3. Question 3

    Definite Integration. Asked once: 2021 Paper 4 (same type asked 3 times) See all 3 of this type

    83
    The value of ∫−22∣3x2−3x−6∣dx\int_{- 2}^{2} \left| 3x^{2}- 3x- 6 \right|dx is

  4. Question 4

    Quadratic Equations. Asked once: 2021 Paper 11 (same type asked 3 times) See all 3 of this type

    46
    If α\alpha and β\beta are the distinct roots of the equation x2+(3)1/4x+31/2=0x^{2}+ (3)^{1/4}x+3^{1/2}= 0, then the value of α96(α12−1)+β96(β12−1)\alpha^{96}\left( \alpha^{12}- 1 \right)+\beta^{96}\left( \beta^{12}- 1 \right) is equal to:

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  5. Question 5

    Differentiation. Asked once: 2021 Paper 5 (same type asked 3 times) See all 3 of this type

    69
    Let the functions f:R→Rf:\mathbb{R}\rightarrow\mathbb{R} and g:R→Rg:\mathbb{R}\rightarrow\mathbb{R} be defined as f(x)={x+2,x<0x2,x≥0f(x)=\begin{cases} x+2, & x<0 \\ x^2, & x\geq 0 \end{cases} and g(x)={x3,x<13x−2,x≥1g(x)=\begin{cases} x^3, & x<1 \\ 3x-2, & x\geq 1 \end{cases}. Then the number of points in R\mathbb{R} where (f∘g)(x)(f\circ g)(x) is NOT differentiable is equal to:

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