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Day 588: JEE Mains Maths

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

  1. Question 1

    Matrices. Asked once: 25 Jun 2022

    171
    Let A=(2−21−1)A =\begin{pmatrix} 2 & - 2 \\ 1 & - 1 \end{pmatrix} and B=(−12−12)B =\begin{pmatrix} - 1 & 2 \\ - 1 & 2 \end{pmatrix}. Then the number of elements in the set {(n,m):n,m∈{1,2,……,10}\left\{ (n,m):n,m\mathbf{\in \{ 1,2,\ldots\ldots,10\}} \right. and  nAn+mBm=I}\left. \ nA^{n}+mB^{m}=I \right\} is

  2. Question 2

    Permutations and Combinations. Asked once: 2021 Paper 9

    81
    The number of times the digit 3 will be written when listing the integers from 1 to 1000 is

  3. Question 3

    Probability. Asked once: 2021 Paper 8

    67
    Let a computer program generate only the digits 0 and 1 to form a string of binary numbers with probability of occurrence of 0 at even places be 12\frac{1}{2} and probability of occurrence of 0 at the odd place be 13\frac{1}{3}. Then the probability that ' 10 ' is followed by ' 01 ' is equal to:

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  4. Question 4

    Quadratic Equations. Asked once: 2021 Paper 24

    74
    The numbers of pairs (a,b)(a,b) of real numbers, such that whenever α\alpha is a root of the equation x2+ax+b=0x^{2}+ ax + b = 0, α2−2\alpha^{2}- 2 is also a root of this equation, is:

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  5. Question 5

    Relations and Functions. Asked once: 2021 Paper 25

    79
    Let R={(P,Q)∣P and Q are at the same distance from the origin}R=\{(P,Q)\mid P \text{ and } Q \text{ are at the same distance from the origin}\} be a relation, then the equivalence class of (1,−1)(1,-1) is the set:

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