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Day 263: JEE Mains Maths

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

  1. Question 1

    Conic Sections. Asked once: 27 Jul 2022 (same type asked 4 times) See all 4 of this type

    84
    An ellipse E:x2a2+y2b2=1E:\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}= 1 passes through the vertices of the hyperbola H:x249−y264=−1H:\frac{x^{2}}{49}-\frac{y^{2}}{64}= - 1. Let the major and minor axes of the ellipse E coincide with the transverse and conjugate axes of the hyperbola HH. Let the product of the eccentricities of EE and HH be 12\frac{1}{2}. If ll is the length of the latus rectum of the ellipse EE, then the value of 113l113l is equal to

  2. Question 2

    Conic Sections. Asked once: 3 Apr 2025 (same type asked 4 times) See all 4 of this type

    72
    Let the product of the focal distances of the point P(4,23)P(4,2\sqrt{3}) on the hyperbola H:x2a2−y2 b2=1H:\frac{x^{2}}{a^{2}} - \frac{y^{2}}{{\text{ }b}^{2}} = 1 be 32.Let the length of the conjugate axis of H be p and the length of its latus rectum be qq. Then p2+q2p^{2} + q^{2} is equal to ......

  3. Question 3

    Conic Sections. Asked once: 25 Jul 2022 (same type asked 4 times) See all 4 of this type

    178
    If the circles x2+y2+6x+8y+16=0x^{2}+y^{2}+ 6x + 8y + 16 = 0 and x2+y2+2(3−3)x+2(4−6)yx^{2}+y^{2}+ 2(3 -\sqrt{3})x + 2(4 -\sqrt{6})y =k+63+86,k>0= k + 6\sqrt{3}+ 8\sqrt{6},k > 0, touch internally at the point P(α,β)P(\alpha,\beta), then (α+3)2+(β+6)2(\alpha +\sqrt{3})^{2}+ (\beta +\sqrt{6})^{2} is equal to

  4. Question 4

    Application of Integrals. Asked once: 11 Apr 2023 (same type asked 4 times) See all 4 of this type

    180
    If AA is the area in the first quadrant enclosed by the curve C:2x2−y+1=0C:2x^{2}- y + 1 = 0, the tangent to CC at the point (1,3)(1,3) and the line x+y=1x + y = 1, then the value of 60 A60\text{ }A is

  5. Question 5

    Relations and Functions. Asked once: 8 Apr 2024 (same type asked 4 times) See all 4 of this type

    74
    Let [t] be the greatest integer less than or equal to t. Let A be the set of all prime factors of 2310 and f:A→Zf:A \rightarrow Z be the function f(x)=[log⁡2(x2+[x35])]f(x) =\left\lbrack \log_{2}\left( x^{2}+\left\lbrack \frac{x^{3}}{5} \right\rbrack \right) \right\rbrack. The number of one-to-one functions from AA to the range of ff is:

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