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Day 295: JEE Mains Maths

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

  1. Question 1

    Matrices. Asked once: 29 Jan 2025 (same type asked 9 times) See all 9 of this type

    72
    Let S={m∈Z:Am2+Am=3I−A−6}S =\left\{ m \in Z:A^{m^{2}}+A^{m}= 3I -A^{- 6} \right\}, where A=[2−110]A =\begin{bmatrix} 2 & - 1 \\ 1 & 0 \end{bmatrix}. Then n(S)n(S) is equal to

  2. Question 2

    Application of Integrals. Asked once: 31 Jan 2024 (same type asked 9 times) See all 9 of this type

    161
    The area of the region enclosed by the parabola y=4x−x2y = 4x -x^{2} and 3y=(x−4)23y = (x - 4)^{2} is equal to

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  3. Question 3

    Three Dimensional Geometry. Asked once: 22 Jan 2026 S2 (same type asked 9 times) See all 9 of this type

    60
    Let L be the line x+12=y+13=z+36\frac{x + 1}{2}=\frac{y + 1}{3}=\frac{z + 3}{6} and let S be the set of all points (a,b,ca,b,c) on L , whose distance from the line x+12=y+13=z−90\frac{x + 1}{2}=\frac{y + 1}{3}=\frac{z - 9}{0} along the line L is 7. Then ∑(a,b,c)∈S(a+b+c)\sum_{(a,b,c) \in S}^{} (a + b + c) is equal to :

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  4. Question 4

    Three Dimensional Geometry. Asked once: 22 Jan 2025 (same type asked 9 times) See all 9 of this type

    74
    Let L1:x−13=y−1−1=z+10L_{1}:\frac{x - 1}{3}=\frac{y - 1}{- 1}=\frac{z + 1}{0} and L2:x−22=y0=z+4α,α∈RL_{2}:\frac{x - 2}{2}=\frac{y}{0}=\frac{z + 4}{\alpha},\alpha \in R, be two lines, which intersect at the point BB. If PP is the foot of perpendicular from the point A(1,1,−1)A(1,1, - 1) on L2L_{2}, then the value of 26α( PB)226\alpha(\text{ }PB)^{2} is _____\_\_\_\_\_ .

  5. Question 5

    Relations and Functions. Asked once: 4 Apr 2025 (same type asked 9 times) See all 9 of this type

    129
    Let A={−3,−2,−1,0,1,2,3}\mathbf{A = \{ - 3, - 2, - 1,0,1,2,3\}} and R be a relation on A defined by xRy if and only if 2x−y∈{0,1}\mathbf{2x - y \in \{ 0,1\}}. Let ll be the number of elements in R. Let m and n be the minimum number of elements required to be added in R to make it reflexive and symmetric relations, respectively. Then l+mnl+ mn is equal to:-

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