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Day 324: JEE Mains Maths

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

  1. Question 1

    Conic Sections. Asked once: 2021 Paper 21 (same type asked 4 times) See all 4 of this type

    87
    Two circles each of radius 5 units touch each other at the point (1,2)(1,2). If the equation of their common tangent is 4x+3y=104x + 3y = 10, and C1(α,β)C_{1}(\alpha,\beta) and C2(γ,δ)C_{2}(\gamma,\delta), C1≠C2C_{1}\neq C_{2} are their centres, then ∣(α+β)(γ+δ)∣|(\alpha + \beta)(\gamma + \delta)| is equal to

  2. Question 2

    Application of Integrals. Asked once: 2021 Paper 21 (same type asked 4 times) See all 4 of this type

    76
    The area of the region bounded by the parabola (y−2)2=(x−1)(y- 2)^{2}= (x- 1), the tangent to it at the point whose ordinate is 3 and the xx-axis is:

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  3. Question 3

    Relations and Functions. Asked once: 2021 Paper 4 (same type asked 4 times) See all 4 of this type

    66
    Let xx denote the total number of one-one functions from a set AA with 3 elements to a set BB with 5 elements and yy denote the total number of one-one functions from the set AA to the set A×BA\times B. Then:

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  4. Question 4

    Binomial Theorem. Asked once: 4 Apr 2024 (same type asked 4 times) See all 4 of this type

    70
    The sum of all rational terms in the expansion of (215+513)15\left( 2^{\frac{1}{5}}+5^{\frac{1}{3}} \right)^{15} is equal to:

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  5. Question 5

    Determinants. Asked once: 27 Jun 2022 (same type asked 4 times) See all 4 of this type

    152
    Let f(x)=∣a−10axa−1ax2axa∣,a∈Rf(x) =\left| \begin{matrix} a & - 1 & 0 \\ ax & a & - 1 \\ ax^{2} & ax & a \end{matrix} \right|,a\in R. Then the sum of the squares of all the values of a for which 2f′(10)−f′(5)+100=02f^{'}(10) -f^{'}(5) + 100 = 0 is:

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