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Day 130: JEE Mains Maths

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

  1. Question 1

    Limits and Continuity. Asked once: 4 Apr 2025 (same type asked 11 times) See all 11 of this type

    57
    If lim⁡x→1+(x−1)(6+λcos⁡(x−1))+μsin⁡(1−x)(x−1)3=−1\lim_{x\rightarrow1^{+}} \frac{(x- 1)(6 +\lambda \cos(x- 1)) +\mu \sin(1 -x)}{(x- 1)^{3}}= - 1, where λ,μ∈R\lambda,\mu\in\mathbb{R}, then λ+μ\lambda+\mu is equal to.

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  2. Question 2

    Binomial Theorem. Asked once: 9 Apr 2024 (same type asked 11 times) See all 11 of this type

    85
    The remainder when 4282024428^{2024} is divided by 21 is

  3. Question 3

    Three Dimensional Geometry. Asked once: 11 Apr 2023 (same type asked 11 times) See all 11 of this type

    77
    Let (α,β,γ)(\alpha,\beta,\gamma) be the image of the point P(2,3,5)P(2,3,5) in the plane 2x+y−3z=62x + y - 3z = 6. Then α+β+γ\alpha + \beta + \gamma is equal to

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  4. Question 4

    Three Dimensional Geometry. Asked once: 6 Apr 2026 S1 (same type asked 10 times) See all 10 of this type

    66
    Let a line L be perpendicular to both the lines L1:x+13=y+35=z+57L_{1}:\frac{x + 1}{3}=\frac{y + 3}{5}=\frac{z + 5}{7} and L2:x−21=y−44=z−67L_{2}:\frac{x - 2}{1}=\frac{y - 4}{4}=\frac{z - 6}{7}. If θ\theta is the acute angle between the lines L and L3:x−872=y−471=z2L_{3}:\frac{x -\frac{8}{7}}{2}=\frac{y -\frac{4}{7}}{1}=\frac{z}{2}, then tan⁡θ\tan\theta is equal to:

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  5. Question 5

    Inverse Trigonometric Functions. Asked once: 4 Apr 2025 (same type asked 10 times) See all 10 of this type

    128
    The sum of the infinite series cot⁡−1(74)+cot⁡−1(194)+cot⁡−1(394)+cot⁡−1(674)+…\cot^{- 1}\left( \frac{7}{4} \right)+\cot^{- 1}\left( \frac{19}{4} \right)+\cot^{- 1}\left( \frac{39}{4} \right)+\cot^{- 1}\left( \frac{67}{4} \right)+ \ldots. is :

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