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Day 547: JEE Mains Maths

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

  1. Question 1

    Probability. Asked once: 26 Jul 2022

    77
    Let E1,E2,E3E_{1},E_{2},E_{3} be three mutually exclusive events such that P(E1)=2+3p6,P(E2)=2−p8P\left( E_{1} \right)=\frac{2 + 3p}{6},P\left( E_{2} \right)=\frac{2 - p}{8} and (E3)\left( E_{3} \right) =1−p2=\frac{1 - p}{2}. If the maximum and minimum values of pp are p1p_{1} and p2p_{2}, then (p1+p2)\left( p_{1}+p_{2} \right) is equal to:

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  2. Question 2

    Quadratic Equations. Asked once: 31 Jan 2023

    78
    The number of real roots of the equation x2−4x+3+x2−9=4x2−14x+6\sqrt{x^{2}- 4x + 3}+\sqrt{x^{2}- 9}=\sqrt{4x^{2}- 14x + 6}, is :

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  3. Question 3

    Relations and Functions. Asked once: 31 Jan 2023

    73
    If the domain of the function f(x)=[x]1+x2f(x) =\frac{\lbrack x\rbrack}{1 +x^{2}}, where [x]\lbrack x\rbrack is greatest integer ≤x\leq x, is [2,6)\lbrack 2,6), then its range is

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  4. Question 4

    Sequences and Series. Asked once: 6 Apr 2024

    151
    Let ABCABC be an equilateral triangle. A new triangle is formed by joining the middle points of all sides of the triangle ABCABC and the same process is repeated infinitely many times. If PP is the sum of perimeters and QQ is be the sum of areas of all the triangles formed in this process, then:

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  5. Question 5

    Straight Lines. Asked once: 29 Jan 2024

    164
    Let AA be the point of intersection of the lines 3x+2y=14, 5x−y=63x+2y=14,\ 5x-y=6 and BB be the point of intersection of the lines 4x+3y=8, 6x+y=54x+3y=8,\ 6x+y=5. The distance of the point P(5,−2)P(5, - 2) from the line ABAB is

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