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Day 595: JEE Mains Maths

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

  1. Question 1

    Matrices. Asked once: 2021 Paper 26

    86
    If the matrix A=[10002030−1]A=\begin{bmatrix} 1 & 0 & 0 \\ 0 & 2 & 0 \\ 3 & 0 & - 1 \end{bmatrix} satisfies the equation A20+αA19+βA=[100040001]A^{20}+\alpha A^{19}+\beta A=\begin{bmatrix} 1 & 0 & 0 \\ 0 & 4 & 0 \\ 0 & 0 & 1 \end{bmatrix} for some real numbers α\alpha and β\beta, then β−\beta- α\alpha is equal to

  2. Question 2

    Quadratic Equations. Asked once: 2021 Paper 9

    66
    Let α,β,γ\alpha,\beta,\gamma be the real roots of the equation, x3+ax2+bx+c=0,(a,b,c∈Rx^{3}+ ax^{2}+ bx + c = 0,(a,b,c \in R and a,b≠0)a,b \neq 0). If the system of equations (in, u,v,w) given by αu+βv+γw=0,βu+γv+αw=0;\alpha u + \beta v + \gamma w = 0,\beta u + \gamma v + \alpha w = 0; γu+αv+βw=0\gamma u + \alpha v + \beta w = 0 has non-trivial solution, then the value of a2 b\frac{a^{2}}{\text{ }b} is

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  3. Question 3

    Relations and Functions. Asked once: 2021 Paper 17

    89
    Let A={n∈N∣n2≤n+10,000},B={3k+1∣k∈N}A =\left\{ n \in N \mid n^{2}\leq n + 10,000 \right\}\mathbf{,B = \{ 3k + 1 \mid k \in N\}} and C={2k∣k∈N}C\mathbf{= \{ 2}k\mid k\in N\}, then the sum of all the elements of the set A∩(B−C)A \cap (B - C) is equal to

  4. Question 4

    Sequences and Series. Asked once: 12 Apr 2023

    87
    Let the positive numbers a1,a2,a3,a4a_{1},a_{2},a_{3},a_{4} and a5a_{5} be in a G.P. Let their mean and variance be 3110\frac{31}{10} and mn\frac{m}{n} respectively, where mm and nn are co-prime. If the mean of their reciprocals is 3140\frac{31}{40} and a3+a4+a5=14a_{3}+a_{4}+a_{5}= 14, then m+nm + n is equal to

  5. Question 5

    Straight Lines. Asked once: 29 Jun 2022

    163
    The distance of the origin from the centroid of the triangle whose two sides have the equations x−2y+1=0x - 2y + 1 = 0 and 2x−y−1=02x - y - 1 = 0 and whose orthocenter is (73,73)\left( \frac{7}{3},\frac{7}{3} \right) is:

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