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Day 57: JEE Mains Maths

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

  1. Question 1

    Permutations and Combinations. This type asked 3 times: 6 Apr 2024, 7 Apr 2025, 2 Apr 2026 S2. This one: 2 Apr 2026 S2 See all 3 of this type

    57
    Let pnp_{n} denote the total number of triangles formed by joining the vertices of an n -side regular polygon. If pn+1−pn=66p_{n+ 1}-p_{n}= 66, then the sum of all distinct prime divisors of n is :

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  2. Question 2

    Probability. This type asked 3 times: 2021 Paper 11, 25 Jul 2022, 2 Apr 2026 S1. This one: 2 Apr 2026 S1 See all 3 of this type

    73
    Let a,b,c∈{1,2,3,4}a,b,c \in \{ 1,2,3,4\}. If the probability, that ax2+22bx+c>0{ax}^{2} + 2\sqrt{2}bx + c > 0 for all x∈Rx \in R, is mn\frac{m}{n}, gcd(m,n)=1gcd(m,n) = 1, then m+nm + n is equal to ____\_\_\_\_ .

  3. Question 3

    Application of Integrals. This type asked 3 times: 27 Jun 2022, 25 Jan 2023, 28 Jan 2026 S2. This one: 28 Jan 2026 S2 See all 3 of this type

    61
    Let P1:y=4x2P_{1}:y= 4x^{2} and P2:y=x2+27P_{2}:y=x^{2}+ 27 be two parabolas. If the area of the bounded region enclosed between P1P_{1} and P2P_{2} is six times the area of the bounded region enclosed between the line y=αx,α>0y =\alpha x,\alpha> 0 and P1P_{1}, then α\alpha is equal to :

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  4. Question 4

    Sequences and Series. This type asked 3 times: 25 Jun 2022, 28 Jul 2022, 28 Jan 2026 S2. This one: 28 Jan 2026 S2 See all 3 of this type

    70
    6326+10.1325+10.2324+10.22323+…+10.2243\frac{6}{3^{26}}+\frac{10.1}{3^{25}}+\frac{10.2}{3^{24}}+\frac{10.2^{2}}{3^{23}}+ \ldots +\frac{10.2^{24}}{3} is equal to

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  5. Question 5

    Probability. This type asked 3 times: 31 Jan 2023, 1 Feb 2024, 28 Jan 2026 S1. This one: 28 Jan 2026 S1 See all 3 of this type

    59
    A bag contains 10 balls out of which k are red and (10−k)(10 - k) are black, where 0≤k≤100 \leq k \leq 10. If three balls are drawn at random without replacement and all of them are found to be black, then the probability that the bag contains 1 red and 9 black balls is :

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