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Day 156: JEE Mains Maths

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

  1. Question 1

    Differential Equations. Asked once: 28 Jul 2022 (same type asked 5 times) See all 5 of this type

    162
    The differential equation of the family of circles passing through the points (0,2)(0,2) and (0,−2)(0, - 2) is

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  2. Question 2

    Complex Numbers. Asked once: 14 Jun 2022 (same type asked 5 times) See all 5 of this type

    171
    Let S={z∈C:∣z−3∣≤1\mathbf{S = \{ z \in C:|z - 3| \leq 1} and z(4+3i)+zˉ(4−3i)≤24}z(4 + 3i) +\bar{z}(4 - 3i) \leq 24\}. If α+iβ\alpha + i\beta is the point in SS which is closest to 4i4i, then 25(α+β)25(\alpha + \beta) is equal to

  3. Question 3

    Vector Algebra. Asked once: 29 Jul 2022 (same type asked 5 times) See all 5 of this type

    179
    Let a→\overrightarrow{a} and b→\overrightarrow{b} be two vectors such that ∣a→+b→∣2=∣a→∣2+2∣b→∣2,a→⋅b→=3|\overrightarrow{a}+\overrightarrow{b}|^{2}= |\overrightarrow{a}|^{2}+ 2|\overrightarrow{b}|^{2},\overrightarrow{a}\cdot\overrightarrow{b}= 3 and ∣a→×b→∣2=75|\overrightarrow{a}\times\overrightarrow{b}|^{2}= 75. Then ∣a→∣2|\overrightarrow{a}|^{2} is equal to

  4. Question 4

    Three Dimensional Geometry. Asked once: 30 Jan 2023 (same type asked 5 times) See all 5 of this type

    165
    If a plane passes through the points (−1,k,0),(2,k,−1),(1,1,2)( - 1,k,0),(2,k, - 1),(1,1,2) and is parallel to the line x−11=\frac{x - 1}{1}= 2y+12=z+1−1\frac{2y + 1}{2}=\frac{z + 1}{- 1}, then the value of k2+1(k−1)(k−2)\frac{k^{2}+ 1}{(k - 1)(k - 2)} is

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  5. Question 5

    Differential Equations. Asked once: 25 Jan 2023 (same type asked 5 times) See all 5 of this type

    80
    Let y=y(x)y = y(x) be the solution curve of the differential equation dydx=yx(1+xy2(1+log⁡ex)),x>0,y(1)=3\frac{dy}{dx}=\frac{y}{x}\left( 1 + xy^{2}\left( 1 +\log_{e}x \right) \right),x > 0,y(1) = 3. Then y2(x)9\frac{y^{2}(x)}{9} is equal to :

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