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Day 43: JEE Mains Maths

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

  1. Question 1

    Three Dimensional Geometry. This type asked 4 times: 31 Jan 2024, 4 Apr 2024, 22 Jan 2025, 4 Apr 2025. This one: 4 Apr 2025 See all 4 of this type

    144
    Let A be the point of intersection of the lines L1:x−71=y−50=z−3−1L_{1}:\frac{x - 7}{1}=\frac{y - 5}{0}=\frac{z - 3}{- 1} and L2:x−13=L_{2}:\frac{x- 1}{3}= y+34=z+75\frac{y+ 3}{4}=\frac{z+ 7}{5}. Let BB and CC be the point on the lines L1L_{1} and L2L_{2} respectively such that AB=AC=15AB=AC=\sqrt{15}. Then the square of the area of the triangle ABC is :

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  2. Question 2

    Binomial Theorem. This type asked 4 times: 4 Apr 2024, 23 Jan 2025, 28 Jan 2025, 3 Apr 2025. This one: 3 Apr 2025 See all 4 of this type

    54
    The sum of all rational terms in the expansion of (2+3)8(2 +\sqrt{3})^{8} is

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  3. Question 3

    Conic Sections. This type asked 4 times: 30 Jan 2023, 27 Jan 2024, 23 Jan 2025, 3 Apr 2025. This one: 3 Apr 2025 See all 4 of this type

    143
    The shortest distance between the curves y2=8xy^{2}= 8x and x2+y2+12y+35=0x^{2}+y^{2}+ 12y+ 35 = 0 is :

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  4. Question 4

    Determinants. This type asked 4 times: 27 Jun 2022, 30 Jan 2024, 31 Jan 2024, 3 Apr 2025. This one: 3 Apr 2025 See all 4 of this type

    61
    If y(x)=∣sin⁡xcos⁡xsin⁡x+cos⁡x+1272827111∣,x∈Ry(x) =\left| \begin{matrix} \sin x & \cos x & \sin x+ \cos x+ 1 \\ 27 & 28 & 27 \\ 1 & 1 & 1 \end{matrix} \right|,x\in\mathbb{R}, then d2ydx2+y\frac{d^{2}y}{dx^{2}}+ y is equal to.

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  5. Question 5

    Definite Integration. This type asked 4 times: 10 Apr 2023, 24 Jan 2025, 28 Jan 2025, 2 Apr 2025. This one: 2 Apr 2025 See all 4 of this type

    127
    Let f:[1,∞)→[2,∞)f:\lbrack 1,\infty) \rightarrow \lbrack 2,\infty) be a differentiable function, If 10∫1xf(t)dt=5xf(x)−x5−910\int_{1}^{x} f(t)dt = 5xf(x) -x^{5}- 9 for all x≥1x \geq 1, then the value of f(3)f(3) is :

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