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Day 5: JEE Mains Maths

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

  1. Question 1

    Three Dimensional Geometry. This type asked 11 times: 2021 Paper 10, 2021 Paper 21, 2021 Paper 26, 25 Jun 2022, 27 Jun 2022, 29 Jun 2022, 1 Feb 2023, 8 Apr 2023, 10 Apr 2023, 11 Apr 2023, 13 Apr 2023. This one: 13 Apr 2023 See all 11 of this type

    88
    Let the image of the point (53,53,83)\left( \frac{5}{3},\frac{5}{3},\frac{8}{3} \right) in the plane x−2y+z−2=0x - 2y + z - 2 = 0 be PP. If the distance of the point Q(6,−2,α),α>0Q(6, - 2,\alpha),\alpha > 0, from PP is 13 , then α\alpha is equal to

  2. Question 2

    Three Dimensional Geometry. This type asked 10 times: 2021 Paper 4, 11 Apr 2023, 30 Jan 2024, 31 Jan 2024, 29 Jan 2025, 7 Apr 2025, 24 Jan 2026 S1, 2 Apr 2026 S1, 6 Apr 2026 S1, 8 Apr 2026 S2. This one: 8 Apr 2026 S2 See all 10 of this type

    73
    Let a line L1L_{1} pass through the origin and be perpendicular to the lines L2:r→=(3+t)i^+(2t−1)j^+(2t+4)k^L_{2}:\overrightarrow{r} = (3 + t)\widehat{i} + (2t - 1)\widehat{j} + (2t + 4)\widehat{k} and L3:r→=(3+2s)i^+(3+2s)j^+(2+s)k^,tL_{3}:\overrightarrow{r} = (3 + 2s)\widehat{i} + (3 + 2s)\widehat{j} + (2 + s)\widehat{k},t, s∈Rs \in R. If (a,b,c),a∈Z(a,b,c),a \in Z, is the point on L3L_{3} at a distance of 17\sqrt{17} from the point of intersection of L1L_{1} and L2L_{2}, then (a+b+c)2(a + b + c)^{2} is equal to ____\_\_\_\_.

  3. Question 3

    Inverse Trigonometric Functions. This type asked 10 times: 2021 Paper 1, 2021 Paper 5, 2021 Paper 7, 2021 Paper 19, 27 Jun 2022, 28 Jun 2022, 30 Jan 2023, 24 Jan 2025, 4 Apr 2025, 5 Apr 2026 S1. This one: 5 Apr 2026 S1 See all 10 of this type

    74
    If π4+∑p=111tan⁡−1(2p−11+22p−1)=α\frac{\pi}{4} + \sum_{p = 1}^{11} \tan^{- 1}\left( \frac{2^{p - 1}}{1 + 2^{2p - 1}} \right) = \alpha, then tan⁡α\tan\alpha is equal to ____\_\_\_\_ .

  4. Question 4

    Quadratic Equations. This type asked 10 times: 2021 Paper 2, 2021 Paper 15, 15 Apr 2023, 30 Jan 2024, 5 Apr 2024, 8 Apr 2024, 24 Jan 2025, 7 Apr 2025, 22 Jan 2026 S1, 24 Jan 2026 S1. This one: 24 Jan 2026 S1 See all 10 of this type

    70
    The number of the real solutions of the equation : x∣x+3∣+∣x−1∣−2=0x|x + 3| + |x - 1| - 2 = 0 is

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  5. Question 5

    Vector Algebra. This type asked 10 times: 2021 Paper 17, 2021 Paper 23, 2021 Paper 25, 27 Jul 2022, 29 Jul 2022, 25 Jan 2023, 30 Jan 2023, 1 Feb 2024, 6 Apr 2024, 23 Jan 2026 S1. This one: 23 Jan 2026 S1 See all 10 of this type

    53
    Let a→=−i^+j^+2k^,b→=i^−j^−3k^,c→=a→×b→\overrightarrow{a}= -\widehat{i}+\widehat{j}+ 2\widehat{k},\overrightarrow{b}=\widehat{i}-\widehat{j}- 3\widehat{k},\overrightarrow{c}=\overrightarrow{a}\times\overrightarrow{b} and d→=c→×a→\overrightarrow{d}=\overrightarrow{c}\times\overrightarrow{a}. Then (a→−b→)⋅d→(\overrightarrow{a}-\overrightarrow{b}) \cdot\overrightarrow{d} is equal to :

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