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Day 65: JEE Mains Maths

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

  1. Question 1

    Application of Derivatives. This type asked 3 times: 30 Jan 2024, 8 Apr 2024, 24 Jan 2025. This one: 24 Jan 2025 See all 3 of this type

    62
    Consider the region R={(x,y):x≤y≤9−113x2,x≥0}R =\left\{ (x,y):x \leq y \leq 9 -\frac{11}{3}x^{2},x \geq 0 \right\}. The area, of the largest rectangle of sides parallel to the coordinate axes and inscribed in RR, is :

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  2. Question 2

    Definite Integration. This type asked 3 times: 2021 Paper 26, 5 Apr 2024, 24 Jan 2025. This one: 24 Jan 2025 See all 3 of this type

    52
    In I(m,n)=∫01xm−1(1−x)n−1dx,m,n>0I(m,n) =\int_{0}^{1} x^{m - 1}(1 - x)^{n - 1}dx,m,n > 0, then I(9,14)+I(10,13)I(9,14) + I(10,13) is

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  3. Question 3

    Probability. This type asked 3 times: 29 Jun 2022, 11 Apr 2023, 24 Jan 2025. This one: 24 Jan 2025 See all 3 of this type

    144
    Let A=[aij]A=\left\lbrack a_{ij} \right\rbrack be a square matrix of order 2 with entries either 0 or 1 . Let E be the event that A is an invertible matrix. Then the probability P(E)P(E) is :

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  4. Question 4

    Complex Numbers. This type asked 3 times: 25 Jan 2023, 1 Feb 2023, 23 Jan 2025. This one: 23 Jan 2025 See all 3 of this type

    60
    Let ∣zˉ−i2z‾+i∣=13,z∈C\left| \frac{\bar{z}- i}{2\overline{z}+ i} \right|=\frac{1}{3},z \in\mathbb{C}, be the equation of a circle with center at C . If the area of the triangle, whose vertices are at the points (0,0),C(0,0),C and (α,0)(\alpha,0) is 11 square units, then α2\alpha^{2} equals

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  5. Question 5

    Indefinite Integration. This type asked 3 times: 2021 Paper 22, 8 Apr 2024, 23 Jan 2025. This one: 23 Jan 2025 See all 3 of this type

    52
    Let I(x)=∫dx(x−11)1113(x+15)1513I(x) = \int\frac{dx}{(x - 11)^{\frac{11}{13}}(x + 15)^{\frac{15}{13}}}. If I(37)−I(24)=14(1b113−1c113),b,c∈NI(37) - I(24) =\frac{1}{4}\left( \frac{1}{b^{\frac{1}{13}}}-\frac{1}{c^{\frac{1}{13}}} \right),b,c \in N, then 3(b+c)3(b + c) is equal to

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