PYQ Vault
EbooksTutor

Day 528: JEE Mains Maths

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

  1. Question 1

    Matrices. Asked once: 27 Jan 2024

    79
    Consider the matrix f(x)=[cos⁡x−sin⁡x0sin⁡xcos⁡x0001]f(x) =\begin{bmatrix} \cos x & - \sin x & 0 \\ \sin x & \cos x & 0 \\ 0 & 0 & 1 \end{bmatrix}. Given below are two statements: Statement I: f(−x)f( - x) is the inverse of the matrix f(x)f(x). Statement II: f(x)f(y)=f(x+y)f(x)f(y) = f(x + y). In the light of the above statements, choose the correct answer from the options given below

    Tap an option to check your answer.

  2. Question 2

    Permutations and Combinations. Asked once: 11 Apr 2023

    84
    In an examination, 5 students have been allotted their seats as per their roll numbers. The number of ways, in which none of the students sits on the allotted seat, is

  3. Question 3

    Probability. Asked once: 1 Feb 2023

    164
    Two dice are thrown independently. Let AA be the event that the number appeared on the 1st 1^{\text{st~}} die is less than the number appeared on the 2nd 2^{\text{nd~}} die, BB be the event that the number appeared on the 1st 1^{\text{st~}} die is even and that on the second die is odd, and CC be the event that the number appeared on the 1st 1^{\text{st~}} die is odd and that on the 2nd 2^{\text{nd~}} is even. Then:

    Tap an option to check your answer.

  4. Question 4

    Quadratic Equations. Asked once: 11 Apr 2023

    72
    The number of integral solutions xx of log⁡(x+72)(x−72x−3)2≥0\log_{\left( x +\frac{7}{2} \right)}\left( \frac{x - 7}{2x - 3} \right)^{2}\geq 0 is

    Tap an option to check your answer.

  5. Question 5

    Relations and Functions. Asked once: 27 Jan 2024

    161
    Let AA and BB be two finite sets with mm and nn elements respectively. The total number of subsets of the set AA is 56 more than the total number of subsets of BB. Then the distance of the point P(m,n)P(m,n) from the point Q(−2,−3)Q( - 2, - 3) is

    Tap an option to check your answer.