PYQ Vault
EbooksTutor

Day 573: JEE Mains Maths

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

  1. Question 1

    Limits and Continuity. Asked once: 2021 Paper 19

    80
    lim⁡x→2(∑n=19xn(n+1)x2+2(2n+1)x+4)\lim_{x \rightarrow 2} \left( \sum_{n = 1}^{9} \frac{x}{n(n + 1)x^{2}+ 2(2n + 1)x + 4} \right) is equal to:

    Tap an option to check your answer.

  2. Question 2

    Matrices. Asked once: 28 Jul 2022

    85
    Let A=[1−12α]A =\begin{bmatrix} 1 & - 1 \\ 2 & \alpha \end{bmatrix} and B=[β110],α,β∈RB =\begin{bmatrix} \beta & 1 \\ 1 & 0 \end{bmatrix},\alpha,\beta \in R. Let α1\alpha_{1} be the value of α\alpha which satisfies (A+B)2=A2+[2222](A + B)^{2}=A^{2}+\begin{bmatrix} 2 & 2 \\ 2 & 2 \end{bmatrix} and α2\alpha_{2} be the value of α\alpha which satisfies (A+B)2=B2(A + B)^{2}=B^{2}. Then ∣α1−α2∣\left| \alpha_{1}-\alpha_{2} \right| is equal to

  3. Question 3

    Permutations and Combinations. Asked once: 2021 Paper 20

    89
    A number is called a palindrome if it reads the same backward as well as forward. For example, 285582 is a six-digit palindrome. The number of six-digit palindromes, which are divisible by 55, is

  4. Question 4

    Probability. Asked once: 2021 Paper 22

    90
    An electric instrument consists of two units. Each unit must function independently for the instrument to operate. The probability that the first unit functions is 0.9 and that of the second unit is 0.8 . The instrument is switched on and it fails to operate. If the probability that only the first unit failed and second unit is functioning is p, then 98p98p is equal to

  5. Question 5

    Quadratic Equations. Asked once: 26 Jul 2022

    84
    The number of distinct real roots of the equation x5(x3−x2−x+1)+x(3x3−4x2−2x+4)−1=0x^{5}\left( x^{3}-x^{2}- x + 1 \right)+ x\left( 3x^{3}- 4x^{2}- 2x + 4 \right)- 1 = 0 is