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Day 59: JEE Mains Maths

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

  1. Question 1

    Trigonometric Identities. This type asked 3 times: 2021 Paper 17, 9 Apr 2024, 23 Jan 2026 S2. This one: 23 Jan 2026 S2 See all 3 of this type

    63
    The least value of (cos⁡2θ−6sin⁡θcos⁡θ+3sin⁡2θ+2)\left( \cos^{2}\theta - 6\sin\theta \cos\theta + 3\sin^{2}\theta + 2 \right) is

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  2. Question 2

    Application of Integrals. This type asked 3 times: 13 Apr 2023, 8 Apr 2024, 23 Jan 2026 S1. This one: 23 Jan 2026 S1 See all 3 of this type

    72
    Let the area of the region bounded by the curve y=max⁡{sin⁡x,cos⁡x}y = \max\{ \sin x,\cos x\}, the lines x=0,x=3π2x = 0,x = \frac{3\pi}{2} and the xx-axis be A. Then, A+A2A + A^{2} is equal to

  3. Question 3

    Binomial Theorem. This type asked 3 times: 4 Apr 2024, 24 Jan 2025, 23 Jan 2026 S1. This one: 23 Jan 2026 S1 See all 3 of this type

    64
    The sum of all possible values of n∈Nn \in N, so that the coefficients of x,x2x,x^{2} and x3x^{3} in the expansion of (1+x2)2(1+x)n\left( 1 +x^{2} \right)^{2}(1 + x)^{n}, are in arithmetic progression is :

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  4. Question 4

    Indefinite Integration. This type asked 3 times: 27 Jun 2022, 22 Jan 2025, 23 Jan 2026 S1. This one: 23 Jan 2026 S1 See all 3 of this type

    52
    Let f(x)=∫ (2−x2)⋅ex(1+x)(1−x)3/2dxf(x) =\int_{}^{}\ \frac{\left( 2 -x^{2} \right)\cdot e^{x}}{(\sqrt{1 + x})(1 - x)^{3/2}}dx. If f(0)=0f(0) = 0, then f(12)f\left( \frac{1}{2} \right) is equal to :

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  5. Question 5

    Probability. This type asked 3 times: 31 Jan 2023, 30 Jan 2024, 23 Jan 2026 S1. This one: 23 Jan 2026 S1 See all 3 of this type

    74
    From the first 100 natural numbers, two numbers first a and then b are selected randomly without replacement. If the probability that a−b≥10a - b \geq 10 is mn,gcd(m,n)=1\frac{m}{n},gcd(m,n) = 1, then m+nm + n is equal to ____\_\_\_\_ .