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Day 52: JEE Mains Maths

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

  1. Question 1

    Differential Equations. Asked 3 times: 29 Jun 2022*, 28 Jul 2022*, 22 Jan 2026 S1 (* = numbers or wording changed that year) See all 3 times it was asked

    69
    Let the solution curve of the differential equation xdy−ydx=x2+y2dx,x>0,y(1)=0xdy - ydx =\sqrt{x^{2}+y^{2}}dx,x > 0,y(1) = 0, be y=y(x)y = y(x). Then y(3)y(3) is equal to

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  2. Question 2

    Binomial Theorem. Asked 3 times: 2021 Paper 18*, 24 Jan 2023*, 4 Apr 2025 (* = numbers or wording changed that year) See all 3 times it was asked

    138
    If 12⋅( 15C1)+22⋅( 15C2)+32⋅( 15C3)1^{2}\cdot\left( \ ^{15}C_{1} \right)+2^{2}\cdot\left( \ ^{15}C_{2} \right)+3^{2}\cdot\left( \ ^{15}C_{3} \right) +….+152⋅( 15C15)=+ \ldots. +15^{2}\cdot\left( \ ^{15}C_{15} \right)= 2m⋅3n⋅5k2^{m}\cdot3^{n}\cdot5^{k}, where m,n,k∈Nm,n,k \in N, then m+n+km + n + k is equal to :-

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  3. Question 3

    Vector Algebra. Asked 3 times: 2021 Paper 11*, 6 Apr 2024*, 28 Jan 2025 (* = numbers or wording changed that year) See all 3 times it was asked

    73
    Let a→=i^+j^+k^,b→=2i^+2j^+k^\overrightarrow{a}=\widehat{i}+\widehat{j}+\widehat{k},\overrightarrow{b}= 2\widehat{i}+ 2\widehat{j}+\widehat{k} and d→=a→×b→\overrightarrow{d}=\overrightarrow{a}\times\overrightarrow{b}. If c→\overrightarrow{c} is a vector such that a→⋅c→=∣c→∣,∣c→−2a→∣2=8\overrightarrow{a}\cdot\overrightarrow{c}= |\overrightarrow{c}|,|\overrightarrow{c}- 2\overrightarrow{a}|^{2}= 8 and the angle between d→\overrightarrow{d} and c→\overrightarrow{c} is π4\frac{\pi}{4}, then ∣10−3 b→⋅c→∣+∣d→×c→∣2|10 - 3\overrightarrow{\text{ }b}\cdot\overrightarrow{c}| + |\overrightarrow{d}\times\overrightarrow{c}|^{2} is equal to ….\ldots..

  4. Question 4

    Differential Equations. Asked 3 times: 2021 Paper 5, 26 Jul 2022, 24 Jan 2025 See all 3 times it was asked

    148
    Let y=y(x)y=y(x) be the solution of the differential equation 2cos⁡xdydx=sin⁡2x−4ysinx,x∈(0,π2)2\cos x\frac{dy}{dx}= \sin2x- 4ysinx,x\in\left( 0,\frac{\pi}{2} \right). If y(π3)=0y\left( \frac{\pi}{3} \right)= 0, then y′(π4)+y(π4)y^{'}\left( \frac{\pi}{4} \right)+y\left( \frac{\pi}{4} \right) is equal to _____\_\_\_\_\_ .

  5. Question 5

    Vector Algebra. Asked 3 times: 2021 Paper 1*, 28 Jun 2022*, 24 Jan 2025 (* = numbers or wording changed that year) See all 3 times it was asked

    51
    Let a→=i^+2j^+3k^,b→=3i^+j^−k^\overrightarrow{a}=\widehat{i}+ 2\widehat{j}+ 3\widehat{k},\overrightarrow{b}= 3\widehat{i}+\widehat{j}-\widehat{k} and c→\overrightarrow{c} be three vectors such that c→\overrightarrow{c} is coplanar with a→\overrightarrow{a} and b→\overrightarrow{b}. If the vector c→\overrightarrow{c} is perpendicular to b→\overrightarrow{b} and a→.c→=5\overrightarrow{a}.\overrightarrow{c}= 5, then ∣c→∣|\overrightarrow{c}| is equal to

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