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Day 468: JEE Mains Maths

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

  1. Question 1

    Limits and Continuity. Asked once: 29 Jan 2025

    65
    The value of lim⁡n→∞(∑K=1nk3+6k2+11k+5(k+3)!)\lim_{n \rightarrow \infty} \left( \sum_{K = 1}^{n} \frac{k^{3}+ 6k^{2}+ 11k + 5}{(k + 3)!} \right) is:

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  2. Question 2

    Matrices. Asked once: 22 Jan 2026 S2

    59
    If X=[xyz]X =\begin{bmatrix} x \\ y \\ z \end{bmatrix} is a solution of the system of equations AX=BAX = B, where adj A=[422−5051−23]A =\begin{bmatrix} 4 & 2 & 2 \\ - 5 & 0 & 5 \\ 1 & - 2 & 3 \end{bmatrix} and B=[402]B =\begin{bmatrix} 4 \\ 0 \\ 2 \end{bmatrix}, then ∣x+y+z∣|x + y + z| is equal to :

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  3. Question 3

    Permutations and Combinations. Asked once: 3 Apr 2025

    74
    If the number of seven-digit numbers, such that the sum of their digits is even, is m⋅n⋅10nm \cdot n \cdot 10^{n}; m,n∈{1,2,3,…,9}m,n \in \{ 1,2,3,\ldots,9\}, then m+nm + n is equal to

  4. Question 4

    Probability. Asked once: 4 Apr 2025

    55
    The probability, of forming a 12 persons committee from 4 engineers, 2 doctors and 10 professors containing at least 3 engineers and at least 1 doctor, is:

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  5. Question 5

    Quadratic Equations. Asked once: 24 Jan 2026 S2

    68
    The smallest positive integral value of a , for which all the roots of x4−ax2+9=0x^{4}-ax^{2}+ 9 = 0 are real and distinct, is equal to

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