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Day 171: JEE Mains Maths

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

  1. Question 1

    Quadratic Equations. Asked once: 27 Jun 2022 (same type asked 4 times) See all 4 of this type

    82
    If the sum of all the roots of the equation e2x−11ex−45e−x+812=0e^{2x}- 11e^{x}- 45e^{-x}+\frac{81}{2}= 0 is log⁡eP\log_{e}P, then pp is equal to

  2. Question 2

    Definite Integration. Asked once: 8 Apr 2023 (same type asked 4 times) See all 4 of this type

    171
    Let [t] denote the greatest integer function. If ∫02.4[x2]dx=α+β2+γ3+δ5\int_{0}^{2.4} \left\lbrack x^{2} \right\rbrack dx = \alpha + \beta\sqrt{2}+ \gamma\sqrt{3}+ \delta\sqrt{5}, then α+β+γ+\alpha + \beta + \gamma + δ\delta is equal to

  3. Question 3

    Conic Sections. Asked once: 13 Apr 2023 (same type asked 4 times) See all 4 of this type

    73
    Let PQPQ be a focal chord of the parabola y2=36xy^{2}= 36x of length 100, making an acute angle with the positive xx-axis. Let the ordinate of PP be positive and MM be the point on the line segment PQPQ such that PM:MQ=3:1PM:MQ = 3:1. Then which of the following points does NOT lie on the line passing through MM and perpendicular to the line PQPQ?

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  4. Question 4

    Matrices. Asked once: 8 Apr 2023 (same type asked 4 times) See all 4 of this type

    168
    If A=[15λ10],A−1=αA+βIA =\begin{bmatrix} 1 & 5 \\ \lambda & 10 \end{bmatrix},A^{- 1}= \alpha A + \beta I and α+β=−2\alpha + \beta = - 2, then 4α2+β2+λ24\alpha^{2}+\beta^{2}+\lambda^{2} is equal to:

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  5. Question 5

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

    81
    A group of 40 students appeared in an examination of 3 subjects - Mathematics, Physics & Chemistry. It was found that all students passed in at least one of the subjects, 20 students passed in Mathematics, 25 students passed in Physics, 16 students passed in Chemistry, at most 11 students passed in both Mathematics and Physics, at most 15 students passed in both Physics and Chemistry, at most 15 students passed in both Mathematics and Chemistry. The maximum number of students passed in all the three subjects is