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Day 164: JEE Mains Maths

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

  1. Question 1

    Differentiation. Asked once: 30 Jan 2024 (same type asked 4 times) See all 4 of this type

    164
    Let aa and bb be real constants such that the function ff defined by f(x)={x2+3x+a,x≤1bx+2,x>1f(x) =\left\{ \begin{matrix} x^{2}+ 3x+a & ,x\leq 1 \\ bx+ 2 & ,x> 1 \end{matrix} \right. be differentiable on RR. Then, the value of ∫−22f(x)dx\int_{- 2}^{2} f(x)dx equals

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  2. Question 2

    Permutations and Combinations. Asked once: 29 Jan 2025 (same type asked 4 times) See all 4 of this type

    74
    The number of 6 -letter words, with or without meaning, that can be formed using the letters of the word MATHS such that any letter that appears in the word must appear at least twice, is 4  ______\ \_\_\_\_\_\_

  3. Question 3

    Three Dimensional Geometry. Asked once: 27 Jun 2022 (same type asked 4 times) See all 4 of this type

    74
    If two straight lines whose direction cosines are given by the relations l+m−n=0, 3l2+m2+cnl=0l + m - n = 0,\ 3l^{2}+m^{2}+ cnl = 0 are parallel, then the positive value of cc is:

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  4. Question 4

    Three Dimensional Geometry. Asked once: 29 Jan 2023 (same type asked 4 times) See all 4 of this type

    81
    Let the co-ordinates of one vertex of △ABC\bigtriangleup ABC be A(0,2,α)A(0,2,\alpha) and the other two vertices lie on the line x+α5=y−12=z+43\frac{x + \alpha}{5}=\frac{y - 1}{2}=\frac{z + 4}{3}. For α∈Z\alpha \in Z, if the area of △ABC\bigtriangleup ABC is 21 sq. units and the line segment BCBC has length 2212\sqrt{21} units, then α2\alpha^{2} is equal to

  5. Question 5

    Conic Sections. Asked once: 4 Apr 2025 (same type asked 4 times) See all 4 of this type

    142
    The Centre of a circle C is at the Centre of the ellipse E:x2a2+y2b2=1,a>bE:\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}= 1,a>b. Let CC pass through the foci F1F_{1} and F2F_{2} of EE such that the circle CC and the ellipse E intersect at four points. Let P be one of these four points. If the area of the triangle PF1 F2PF_{1}{\text{ }F}_{2} is 30 and the length of the major axis of E is 17 , then the distance between the foci of E is :

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