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Day 42: JEE Mains Maths

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

  1. Question 1

    Conic Sections. This type asked 4 times: 8 Apr 2024, 3 Apr 2025, 4 Apr 2025, 7 Apr 2025. This one: 7 Apr 2025 See all 4 of this type

    149
    Let the lengths of the transverse and conjugate axes of a hyperbola in standard form be 2 a and 2 b , respectively, and one focus and the corresponding directrix of this hyperbola be (−5,0)( - 5,0) and 5x+9=05x + 9 = 0, respectively. If the product of the focal distances of a point (α,25)(\alpha,2\sqrt{5}) on the hyperbola is p , then 4 p is equal to .

  2. Question 2

    Conic Sections. This type asked 4 times: 2021 Paper 21, 25 Jul 2022, 8 Apr 2024, 7 Apr 2025. This one: 7 Apr 2025 See all 4 of this type

    59
    Let C1C_{1} be the circle in the third quadrant of radius 3 , that touches both coordinate axes. Let C2C_{2} be the circle with centre (1,3)(1,3) that touches C1C_{1} externally at the point (α,β)(\alpha,\beta). If (β−α)2=mn,gcd(m,n)=1(\beta-\alpha)^{2}=\frac{m}{n},gcd(m,n) = 1, then m+nm + n is equal to :

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  3. Question 3

    Application of Integrals. This type asked 4 times: 2021 Paper 21, 11 Apr 2023, 30 Jan 2024, 4 Apr 2025. This one: 4 Apr 2025 See all 4 of this type

    134
    A line passing through the point A(−2,0)A\left( - 2,0 \right), touches the parabola P:y2=P:y^{2}= x−2x- 2 at the point BB in the first quadrant. The area, of the region bounded by the line AB , parabola P and the x -axis, is :-

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  4. Question 4

    Binomial Theorem. This type asked 4 times: 29 Jul 2022, 6 Apr 2023, 11 Apr 2023, 4 Apr 2025. This one: 4 Apr 2025 See all 4 of this type

    62
    In the expansion of (23+133)n,n∈N\left( \sqrt[3]{2}+\frac{1}{\sqrt[3]{3}} \right)^{n},n \in N, if the ratio of 15th 15^{\text{th~}} term from the beginning to the 15th 15^{\text{th~}} term from the end is 16\frac{1}{6}, then the value of  nC3\ ^{n}C_{3} is:

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  5. Question 5

    Relations and Functions. This type asked 4 times: 2021 Paper 4, 8 Apr 2024, 9 Apr 2024, 4 Apr 2025. This one: 4 Apr 2025 See all 4 of this type

    52
    Consider the sets A={(x,y)∈R×R:x2+y2=25}A =\left\{ (x,y) \in\mathbb{R}\times\mathbb{R}:x^{2}+y^{2}= 25 \right\}, B={(x,y)∈R×R:x2+9y2=144},C={(x,y)B =\left\{ (x,y) \in\mathbb{R}\times\mathbb{R}:x^{2}+ 9y^{2}= 144 \right\}\mathbf{,C = \{(x,y)}  ∈Z×Z:x2+y2≤4}\left. \ \in\mathbb{Z}\times\mathbb{Z}:x^{2}+y^{2}\leq 4 \right\}, and D=A∩BD = A \cap B. The total number of one-one functions from the set DD to the set C is:

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