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Day 399: JEE Mains Maths

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

  1. Question 1

    Definite Integration. Asked once: 2021 Paper 19 (same type asked 11 times) See all 11 of this type

    78
    The value of ∫−π2π2(1+sin⁡2x1+πsin⁡x)dx\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}} \left( \frac{1 +\sin^{2}x}{1 +\pi^{\sin x}} \right)dx is

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  2. Question 2

    Limits and Continuity. Asked once: 29 Jul 2022 (same type asked 11 times) See all 11 of this type

    65
    If lim⁡x→0αex+βe−x+γsin⁡xxsin⁡2x=23\lim_{x\rightarrow 0} \frac{\alpha e^{x}+\beta e^{-x}+\gamma \sin x}{x\sin^{2}x}=\frac{2}{3}, where α,β,γ∈R\alpha,\beta,\gamma\in R, then which of the following is NOT correct?

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  3. Question 3

    Binomial Theorem. Asked once: 2021 Paper 4 (same type asked 11 times) See all 11 of this type

    84
    If the remainder when xx is divided by 4 is 3 , then the remainder when (2020+x)2022(2020 +x)^{2022} is divided by 8 is

  4. Question 4

    Three Dimensional Geometry. Asked once: 2021 Paper 26 (same type asked 11 times) See all 11 of this type

    78
    If the mirror image of the point (1,3,5)(1,3,5) with respect to the plane 4x−5y+2z=84x- 5y+ 2z= 8 is (α,β,γ)(\alpha,\beta,\gamma), then 5(α+β+γ)5(\alpha+\beta+\gamma) equals:

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  5. Question 5

    Three Dimensional Geometry. Asked once: 30 Jan 2024 (same type asked 10 times) See all 10 of this type

    163
    Let L1:r→=(i^−j^+2k^)+λ(i^−j^+2k^),λ∈RL_{1}:\overrightarrow{r}= (\widehat{i}-\widehat{j}+ 2\widehat{k}) + \lambda(\widehat{i}-\widehat{j}+ 2\widehat{k}),\lambda \in R L2:r→=(j^−k^)+μ(3i^+j^+pk^),μ∈RL_{2}:\overrightarrow{r}= (\widehat{j}-\widehat{k}) + \mu(3\widehat{i}+\widehat{j}+ p\widehat{k}),\mu \in R and L3:r→=δ(li^+mj^+nk^)δ∈RL_{3}:\overrightarrow{r}= \delta(\mathcal{l}\widehat{i}+ m\widehat{j}+ n\widehat{k})\delta \in R Be three lines such that L1L_{1} is perpendicular to L2L_{2} and L3L_{3} is perpendicular to both L1L_{1} and L2L_{2}. Then the point which lies on L3L_{3} is

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