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Day 29: JEE Mains Maths

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

  1. Question 1

    Quadratic Equations. This type asked 5 times: 2021 Paper 3, 2021 Paper 18, 2021 Paper 21, 31 Jan 2024, 29 Jan 2025. This one: 29 Jan 2025 See all 5 of this type

    126
    If the set of all a∈Ra \in R, for which the equation 2x2+(a−5)x+15=3a2x^{2}+ (a - 5)x + 15 = 3a has no real root, is the interval (α,β)(\alpha,\beta), and X={x∈Z:α<x<β}X = \{ x \in Z:\alpha < x < \beta\}, then ∑x∈Xx2\sum_{x \in X} x^{2} is equal to

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  2. Question 2

    Complex Numbers. This type asked 5 times: 2021 Paper 7, 2021 Paper 10, 26 Jul 2022, 11 Apr 2023, 28 Jan 2025. This one: 28 Jan 2025 See all 5 of this type

    68
    Let OO be the origin, the point AA be z1=3+22iz_{1}=\sqrt{3}+ 2\sqrt{2}i, the point B(z2)B\left( z_{2} \right) be such that 3∣z2∣=∣z1∣\sqrt{3}\left| z_{2} \right|=\left| z_{1} \right| and arg(z2)=arg(z1)+π6arg\left( z_{2} \right)= arg\left( z_{1} \right)+\frac{\pi}{6}. Then

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  3. Question 3

    Relations and Functions. This type asked 5 times: 2021 Paper 4, 27 Jun 2022, 24 Jan 2023, 24 Jan 2025, 28 Jan 2025. This one: 28 Jan 2025 See all 5 of this type

    54
    If f(x)=2x2x+2,x∈Rf(x) =\frac{2^{x}}{2^{x}+\sqrt{2}},x \in R, then ∑k=181f(k82)\sum_{k = 1}^{81} f\left( \frac{k}{82} \right) is equal to :

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  4. Question 4

    Differentiation. This type asked 5 times: 2021 Paper 24, 25 Jul 2022, 29 Jul 2022, 6 Apr 2023, 24 Jan 2025. This one: 24 Jan 2025 See all 5 of this type

    132
    Let [x]\lbrack x\rbrack denote the greatest integer function, and let mm and nn respectively be the numbers of the points, where the function f(x)=[x]+∣x−2∣f(x) = \lbrack x\rbrack + |x - 2|, −2<x<3- 2 < x < 3, is not continuous and not differentiable. Then m+nm + n is equal to:

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  5. Question 5

    Permutations and Combinations. This type asked 5 times: 2021 Paper 23, 29 Jan 2023, 31 Jan 2023, 1 Feb 2023, 24 Jan 2025. This one: 24 Jan 2025 See all 5 of this type

    73
    The number of 3-digit numbers, that are divisible by 2 and 3 , but not divisible by 4 and 9 , is