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Day 196: JEE Mains Maths

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

  1. Question 1

    Three Dimensional Geometry. Asked once: 2021 Paper 4 (same type asked 3 times) See all 3 of this type

    61
    A plane passes through the points A(1,2,3),B(2,3,1)A(1,2,3),B(2,3,1) and C(2,4,2)C(2,4,2). If OO is the origin and PP is (2,−1,1)(2, - 1,1), then the projection of OP→\overrightarrow{OP} on this plane is of length:

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  2. Question 2

    Differential Equations. Asked once: 2021 Paper 23 (same type asked 3 times) See all 3 of this type

    70
    If dydx=2xy+2y⋅2x2x+2x+ylog⁡e2,y(0)=0\frac{dy}{dx}=\frac{2^{x}y+2^{y}\cdot2^{x}}{2^{x}+2^{x+y}\log_{e}2},y(0) = 0, then for y=1y= 1, the value of xx lies in the interval:

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  3. Question 3

    Limits and Continuity. Asked once: 2021 Paper 24 (same type asked 3 times) See all 3 of this type

    82
    Let f(x)=x6+2x4+x3+2x+3,x∈Rf(x) =x^{6}+ 2x^{4}+x^{3}+ 2x+ 3,x\in R. Then the natural number nn for which lim⁡x→1xnf(1)−f(x)x−1=44\lim_{x\rightarrow 1} \frac{x^{n}f(1) -f(x)}{x- 1}= 44 is

  4. Question 4

    Conic Sections. Asked once: 22 Jan 2026 S1 (same type asked 2 times) See all 2 of this type

    67
    If the chord joining the points P1(x1,y1)P_{1}\left( x_{1},y_{1} \right) and P2(x2P_{2}\left( x_{2} \right., y2y_{2} ) on the parabola y2=12xy^{2}= 12x subtends a right angle at the vertex of the parabola, then x1x2−y1y2x_{1}x_{2}-y_{1}y_{2} is equal to

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  5. Question 5

    Relations and Functions. Asked once: 28 Jan 2025 (same type asked 2 times) See all 2 of this type

    145
    Let f:R−{0}→(−∞,1)f\mathbf{:R - \{ 0\} \rightarrow ( - \infty,1)} be a polynomial of degree 2 , satisfying f(x)f(1x)=f(x)+f(1x)f(x)f\left( \frac{1}{x} \right)=f(x) +f\left( \frac{1}{x} \right). If f( K)=−2 Kf(\text{ }K) = - 2\text{ }K, then the sum of squares of all possible values of K is :

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