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Day 509: JEE Mains Maths

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

  1. Question 1

    Binomial Theorem. Asked once: 13 Apr 2023

    81
    Let α\alpha be the constant term in the binomial expansion of (x−6x32)n,n≤15\left( \sqrt{x}-\frac{6}{x^{\frac{3}{2}}} \right)^{n},n \leq 15. If the sum of the coefficients of the remaining terms in the expansion is 649 and the coefficient of x−nx^{- n} is λα\lambda\alpha, then λ\lambda is equal to

  2. Question 2

    Complex Numbers. Asked once: 6 Apr 2024

    84
    Let x1,x2,x3,x4x_{1},x_{2},x_{3},x_{4} be the solution of the equation 4x4+8x3−17x2−12x+9=04x^{4}+ 8x^{3}- 17x^{2}- 12x + 9 = 0 and (4+x12)(4+x22)(4+x32)(4+x42)=12516 m\left( 4 +x_{1}^{2} \right)\left( 4 +x_{2}^{2} \right)\left( 4 +x_{3}^{2} \right)\left( 4 +x_{4}^{2} \right)=\frac{125}{16}\text{ }m. Then the value of mm is

  3. Question 3

    Conic Sections. Asked once: 28 Jan 2026 S2

    62
    Let the circle x2+y2=4x^{2}+y^{2}= 4 intersect xx-axis at the points A(a,0),a>0A(a,0),a > 0 and B(b,0)B(b,0). Let P(2cos⁡α,2sin⁡α),0<α<π2P(2\cos\alpha, 2\sin\alpha), 0 <\alpha<\frac{\pi}{2} and Q(2cos⁡β,2sin⁡β)Q(2\cos\beta,2\sin\beta) be two points such that (α−β)=π2(\alpha-\beta) =\frac{\pi}{2}. Then the point of intersection of AQ and BP lies on :

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  4. Question 4

    Definite Integration. Asked once: 21 Jan 2026 S2

    71
    Let [ • ] denote the greatest integer function and f(x)=lim⁡n→∞1n3∑k=1n[k23x]f(x) = \lim_{n \rightarrow \infty} \frac{1}{n^{3}}\sum_{k = 1}^{n} \left\lbrack \frac{k^{2}}{3^{x}} \right\rbrack. Then 12∑j=1∞f(j)12\sum_{j = 1}^{\infty} f(j) is equal to ____\_\_\_\_ .

  5. Question 5

    Determinants. Asked once: 2021 Paper 25

    69
    The value of ∣(a+1)(a+2)a+21(a+2)(a+3)a+31(a+3)(a+4)a+41∣\left| \begin{matrix} (a+ 1)(a+ 2) & a+ 2 & 1 \\ (a+ 2)(a+ 3) & a+ 3 & 1 \\ (a+ 3)(a+ 4) & a+ 4 & 1 \end{matrix} \right| is

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