PYQ Vault
EbooksTutor

Day 524: JEE Mains Maths

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

  1. Question 1

    Permutations and Combinations. Asked once: 12 Apr 2023

    82
    Let the digits a,b,ca,b,c be in A.P. Nine-digit numbers are to be formed using each of these three digits thrice such that three consecutive digits are in A.P. at least once. How many such numbers can be formed?

  2. Question 2

    Probability. Asked once: 6 Apr 2023

    151
    Three dice are rolled. If the probability of getting different numbers on the three dice is pq\frac{p}{q}, where pp and qq are co-prime, then q−pq - p is equal to

    Tap an option to check your answer.

  3. Question 3

    Quadratic Equations. Asked once: 30 Jan 2024

    88
    Let α,β∈N\alpha,\beta \in N be roots of equation x2−70x+λ=0x^{2}- 70x + \lambda = 0, where λ2,λ3∉N\frac{\lambda}{2},\frac{\lambda}{3}\notin N. If λ\lambda assumes the minimum possible value, then (α−1+β−1)(λ+35)∣α−β∣\frac{(\sqrt{\alpha - 1}+\sqrt{\beta - 1})(\lambda + 35)}{|\alpha - \beta|} is equal to:

  4. Question 4

    Relations and Functions. Asked once: 27 Jan 2024

    70
    Let S={1,2,3,…,10}\mathbf{S = \{ 1,2,3,\ldots,10\}}. Suppose MM is the set of all the subsets of SS, then the relation R={(A,B):A∩B≠ϕ;A,B∈M}\mathbf{R = \{(A,B):A \cap B \neq \phi;A,B \in M\}} is:

    Tap an option to check your answer.

  5. Question 5

    Sequences and Series. Asked once: 28 Jan 2025

    61
    Let TrT_{r} be the rth r^{\text{th~}} term of an A.P. If for some mm, Tm=125, T25=120T_{m}=\frac{1}{25},{\text{ }T}_{25}=\frac{1}{20} and 20∑r=125 Tr=1320\sum_{r = 1}^{25} {\text{ }T}_{r}= 13, then 5 m∑r=m2 m Tr5\text{ }m\sum_{r = m}^{2\text{ }m} {\text{ }T}_{r} is equal to :

    Tap an option to check your answer.