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Day 31: JEE Mains Maths

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

  1. Question 1

    Differential Equations. This type asked 5 times: 2021 Paper 9, 2021 Paper 21, 2021 Paper 25, 28 Jul 2022, 5 Apr 2024. This one: 5 Apr 2024 See all 5 of this type

    152
    The differential equation of the family of circles passing the origin and having center at the line y=xy = x is:

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  2. Question 2

    Complex Numbers. This type asked 5 times: 2021 Paper 17, 2021 Paper 26, 14 Jun 2022, 29 Jun 2022, 1 Feb 2024. This one: 1 Feb 2024 See all 5 of this type

    87
    Let P={z∈C:∣z+2−3i∣≤1}\mathbf{P = \{ z \in C:|z + 2 - 3i| \leq 1\}} and Q={z∈C:z(1+i)+z‾(1−i)≤−8}\mathbf{Q = \{ z \in C:z(1 + i) +}\overline{z}(1 - i) \leq - 8\}. Let in P∩Q,∣z−3+2i∣P \cap Q,|z - 3 + 2i| be maximum and minimum at z1z_{1} and z2z_{2} respectively. If ∣z1∣2+2∣z2∣2=α+β2\left| z_{1} \right|^{2}+ 2\left| z_{2} \right|^{2}= \alpha + \beta\sqrt{2}, where α,β\alpha,\beta are integers, then α+β\alpha + \beta equals

  3. Question 3

    Vector Algebra. This type asked 5 times: 2021 Paper 15, 25 Jun 2022, 29 Jul 2022, 31 Jan 2023, 30 Jan 2024. This one: 30 Jan 2024 See all 5 of this type

    154
    Let a→=i^+αj^+βk^,α,β∈R\overrightarrow{a}=\widehat{i}+\alpha\widehat{j}+\beta\widehat{k},\alpha,\beta\in R. Let a vector b→\overrightarrow{b} be such that the angle between a→\overrightarrow{a} and b→\overrightarrow{b} is π4\frac{\pi}{4} and ∣b→∣2=6|\overrightarrow{b}|^{2}= 6, If a→⋅b→=32\overrightarrow{a}\cdot\overrightarrow{b}= 3\sqrt{2}, then the value of (α2+β2)∣a→×b→∣2\left( \alpha^{2}+\beta^{2} \right)|\overrightarrow{a}\times\overrightarrow{b}|^{2} is equal to

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  4. Question 4

    Three Dimensional Geometry. This type asked 5 times: 2021 Paper 10, 25 Jun 2022, 28 Jul 2022, 30 Jan 2023, 13 Apr 2023. This one: 13 Apr 2023 See all 5 of this type

    153
    The plane, passing through the points (0,−1,2)(0, - 1,2) and (−1,2,1)( - 1,2,1) and parallel to the line passing through (5, 1,−7)1, - 7) and (1,−1,−1)(1, - 1, - 1), also passes through the point.

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  5. Question 5

    Differential Equations. This type asked 5 times: 2021 Paper 4, 2021 Paper 10, 2021 Paper 26, 25 Jan 2023, 12 Apr 2023. This one: 12 Apr 2023 See all 5 of this type

    69
    Let y=y(x),y>0y = y(x),y > 0, be a solution curve of the differential equation (1+x2)dy=y(x−y)dx\left( 1 +x^{2} \right)dy = y(x - y)dx. If y(0)=1y(0) = 1 and y(22)=βy(2\sqrt{2}) = \beta, then

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