PYQ Vault
EbooksTutor

Day 560: JEE Mains Maths

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

  1. Question 1

    Limits and Continuity. Asked once: 27 Jun 2022

    175
    Let [t]\lbrack t\rbrack denote the greatest integer ≤t\leq t and {t}\mathbf{\{ t\}} denote the fractional part of tt. Then integral value of α\alpha for which the left hand limit of the function f(x)=[1+x]+α2[x]+{x}+[x]−12[x]+{x}f(x) = \lbrack 1 + x\rbrack +\frac{\alpha^{\mathbf{2\lbrack x\rbrack + \{ x\}}}+ \lbrack x\rbrack - 1}{\mathbf{2\lbrack x\rbrack + \{ x\}}} at x=0x = 0 is equal to α−43\alpha -\frac{4}{3} is

  2. Question 2

    Matrices. Asked once: 24 Jan 2023

    71
    If AA and BB are two non-zero n×nn \times n matrics such that A2+B=A2BA^{2}+ B =A^{2}B, then

    Tap an option to check your answer.

  3. Question 3

    Permutations and Combinations. Asked once: 29 Jun 2022

    90
    Let b1b2b3b4b_{1}b_{2}b_{3}b_{4} be a 4-element permutation with bi∈b_{i}\in {1,2,3,…,100}\{ 1,2,3,\ldots,100\} for 1≤i≤41 \leq i \leq 4 and bi≠bjb_{i}\neq b_{j} for i≠ji \neq j, such that either b1, b2, b3b_{1},{\text{ }b}_{2},{\text{ }b}_{3} are consecutive integers or b2,b3,b4b_{2},b_{3},b_{4} are consecutive integers. Then the number of such permutations b1b2b3b4b_{1}b_{2}b_{3}b_{4} is equal to

  4. Question 4

    Probability. Asked once: 27 Jun 2022

    76
    Five numbers x1,x2,x3,x4,x5x_{1},x_{2},x_{3},x_{4},x_{5} are randomly selected from the numbers 1,2,3,…,181,2,3,\ldots,18 and are arranged in the increasing order (x1<x2<x3<x4<x5)\left( x_{1}<x_{2}<x_{3}<x_{4}<x_{5} \right). The probability that x2=7x_{2}= 7 and x4=11x_{4}= 11 is:

    Tap an option to check your answer.

  5. Question 5

    Quadratic Equations. Asked once: 24 Jan 2023

    72
    The equation x2−4x+[x]+3=x[x]x^{2}- 4x + \lbrack x\rbrack + 3 = x\lbrack x\rbrack, where [x]\lbrack x\rbrack denotes the greatest integer function, has :

    Tap an option to check your answer.