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Day 36: JEE Mains Maths

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

  1. Question 1

    Sequences and Series. This type asked 4 times: 12 Apr 2023, 23 Jan 2026 S2, 2 Apr 2026 S1, 5 Apr 2026 S1. This one: 5 Apr 2026 S1 See all 4 of this type

    52
    Let the sum of the first nn terms of an A.P. be 3n2+5n3n^{2}+ 5n. Then the sum of squares of the first 10 terms of the A.P. is :

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  2. Question 2

    Straight Lines. This type asked 4 times: 2021 Paper 10, 26 Jun 2022, 28 Jan 2026 S1, 5 Apr 2026 S1. This one: 5 Apr 2026 S1 See all 4 of this type

    61
    In an equilateral triangle PQR , let the vertex P be at (3,5)(3,5) and the side QR be along the line x+y=4x+y= 4. If the orthocenter of the triangle PQRPQR is (α,β)(\alpha,\beta), then 9(α+β)9(\alpha+\beta) is equal to :

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  3. Question 3

    Three Dimensional Geometry. This type asked 4 times: 25 Jan 2023, 22 Jan 2025, 21 Jan 2026 S2, 5 Apr 2026 S1. This one: 5 Apr 2026 S1 See all 4 of this type

    63
    The square of the distance of the point P(5,6,7)P(5,6,7) from the line x−22=y−53=z−24\frac{x- 2}{2}=\frac{y- 5}{3}=\frac{z- 2}{4} is equal to :

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  4. Question 4

    Trigonometric Equations. This type asked 4 times: 2021 Paper 25, 29 Jan 2023, 27 Jan 2024, 5 Apr 2026 S1. This one: 5 Apr 2026 S1 See all 4 of this type

    62
    The sum of all the integral values of p such that the equation 3sin⁡2x+12cos⁡x−3=p,x∈R3\sin^{2}x+ 12\cos x- 3 =p,x\in R, has at least one solution, is :

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  5. Question 5

    Binomial Theorem. This type asked 4 times: 2021 Paper 2, 26 Jun 2022, 25 Jan 2023, 4 Apr 2026 S1. This one: 4 Apr 2026 S1 See all 4 of this type

    59
    Let the smallest value of k∈Nk \in\mathbb{N}, for which the coefficient of x3x^{3} in (1+x)3+(1+x)4+(1+x)5+…(1 + x)^{3}+ (1 + x)^{4}+ (1 + x)^{5}+ \ldots +(1+x)99+(1+kx)100,x≠0+ (1 +x)^{99}+ (1 +kx)^{100},x\neq 0, is (43n+1014)\left( 43n+\frac{101}{4} \right) (  100C3\ ^{100}C_{3} ) for some n∈Nn \in\mathbb{N}, be pp. Then the value of pp +n is:

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