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Day 447: JEE Mains Maths

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

  1. Question 1

    Binomial Theorem. Asked once: 5 Apr 2026 S1

    73
    If the sum of the coefficients of x7x^{7} and x14x^{14} in the expansion of (1x3−x4)n,x≠0\left( \frac{1}{x^{3}} - x^{4} \right)^{n},x \neq 0, is zero, then the value of nn is ____\_\_\_\_.

  2. Question 2

    Complex Numbers. Asked once: 4 Apr 2026 S1

    53
    Let z be a complex number such that ∣z+2∣=∣z−2∣|z + 2| = |z - 2| and arg(z+3z−i)=π4arg\left( \frac{z+ 3}{z-i} \right)=\frac{\pi}{4}. Then ∣z∣2|z|^{2} is equal to :

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  3. Question 3

    Conic Sections. Asked once: 6 Apr 2026 S2

    73
    Let the line x−y=4x - y = 4 intersect the circle C:(x−4)2+(y+3)2=9C:(x - 4)^{2} + (y + 3)^{2} = 9 at the points Q and R . If P(α,β)P(\alpha,\beta) is a point on C such that PQ=PRPQ = PR, then (6α+8β)2(6\alpha + 8\beta)^{2} is equal to ____\_\_\_\_ .

  4. Question 4

    Definite Integration. Asked once: 6 Apr 2026 S2

    70
    The value of the integral ∫−11(x3+∣x∣+1x2+2∣x∣+1)dx\int_{- 1}^{1} \left( \frac{x^{3}+ |x| + 1}{x^{2}+ 2|x| + 1} \right)dx is equal to

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  5. Question 5

    Determinants. Asked once: 3 Apr 2025

    146
    Let I be the identity matrix of order 3×33 \times 3 and for the matrix A=A = [λ234567−12],∣A∣=−1\begin{bmatrix} \lambda & 2 & 3 \\ 4 & 5 & 6 \\ 7 & - 1 & 2 \end{bmatrix},|A| = - 1. Let B be the inverse of the matrix adj(A adj(A2))adj\left( A\ adj\left( A^{2} \right) \right). Then ∣λB+I∣|\lambda B + I| is equal to.