PYQ Vault
EbooksTutor

Day 67: JEE Mains Maths

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

  1. Question 1

    Probability. This type asked 3 times: 2021 Paper 3, 5 Apr 2024, 9 Apr 2024. This one: 9 Apr 2024 See all 3 of this type

    81
    Let a,ba,b and cc denote the outcome of three independent rolls of a fair tetrahedral die, whose four faces are marked 1,2,3,41,2,3,4. If the probability that ax2+bx+c=0ax^{2}+ bx + c = 0 has all real roots is mn\frac{m}{n}, gcd(m,n)=1gcd(m,n) = 1, then m+nm + n is equal to

  2. Question 2

    Relations and Functions. This type asked 3 times: 2021 Paper 23, 30 Jan 2023, 9 Apr 2024. This one: 9 Apr 2024 See all 3 of this type

    89
    If a function ff satisfies f(m+n)=f(m)+f(n)f(m + n) = f(m) + f(n) for all m,n∈Nm,n \in N and f(1)=1f(1) = 1, then the largest natural number λ\lambda such that ∑k=12022f(λ+k)≤(2022)2\sum_{k = 1}^{2022} f(\lambda + k) \leq (2022)^{2} is equal to

  3. Question 3

    Sequences and Series. This type asked 3 times: 2021 Paper 18, 27 Jul 2022, 9 Apr 2024. This one: 9 Apr 2024 See all 3 of this type

    166
    Let a,ar,ar2a,ar,ar^{2}, ........be an infinite G.P. If ∑n=0∞arn=57\sum_{n= 0}^{\infty} ar^{n}= 57 and ∑n=0∞a3r3n=9747\sum_{n= 0}^{\infty} a^{3}r^{3n}= 9747, then a+18ra+ 18r is equal to :

    Tap an option to check your answer.

  4. Question 4

    Straight Lines. This type asked 3 times: 31 Jan 2024, 6 Apr 2024, 9 Apr 2024. This one: 9 Apr 2024 See all 3 of this type

    68
    A variable line LL passes through the point (3,5)(3,5) and intersects the positive coordinate axes at the points AA and BB. The minimum area of the triangle OABOAB, where OO is the origin, is:

    Tap an option to check your answer.

  5. Question 5

    Definite Integration. This type asked 3 times: 26 Jul 2022, 6 Apr 2024, 8 Apr 2024. This one: 8 Apr 2024 See all 3 of this type

    61
    The value of k∈Nk \in\mathbb{N} for which the integral
    In=∫01(1−xk)ndx,n∈N, satisfies 147I20=148I21I_{n}=\int_{0}^{1} \left( 1 -x^{k} \right)^{n}dx,n\in\mathbb{N}\text{, satisfies~}147I_{20}= 148I_{21}
    is:

    Tap an option to check your answer.