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Day 64: JEE Mains Maths

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

  1. Question 1

    Binomial Theorem. This type asked 3 times: 2021 Paper 5, 2021 Paper 9, 3 Apr 2025. This one: 3 Apr 2025 See all 3 of this type

    147
    Let (1+x+x2)10=a0+a1x+a2x2+….+a20x20\left( 1 + x + x^{2} \right)^{10} = a_{0} + a_{1}x + a_{2}x^{2} + \ldots. + a_{20}x^{20}. If (a1+a3+a5+…+a19)−11a2=\left( a_{1} + a_{3} + a_{5} + \ldots + a_{19} \right) - 11a_{2} = 121k121k, then k is equal to .

  2. Question 2

    Definite Integration. This type asked 3 times: 31 Jan 2023, 27 Jan 2024, 2 Apr 2025. This one: 2 Apr 2025 See all 3 of this type

    138
    4∫01(13+x2+1+x2)dx−3log⁡e(3)4\int_{0}^{1} \left( \frac{1}{\sqrt{3 +x^{2}}+\sqrt{1 +x^{2}}} \right)dx - 3\log_{e}(\sqrt{3}) is equal to:

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  3. Question 3

    Sequences and Series. This type asked 3 times: 14 Jun 2022, 22 Jan 2025, 2 Apr 2025. This one: 2 Apr 2025 See all 3 of this type

    128
    The number of terms of an A.P. is even; the sum of all the odd terms is 24 , the sum of all the even terms is 30 and the last term exceeds the first by 212\frac{21}{2}. Then the number of terms which are integers in the A.P. is :

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  4. Question 4

    Permutations and Combinations. This type asked 3 times: 5 Apr 2024, 6 Apr 2024, 29 Jan 2025. This one: 29 Jan 2025 See all 3 of this type

    135
    If all the words with or without meaning made using all the letters of the word "KANPUR" are arranged as in a dictionary, then the word at 440th 440^{\text{th~}} position in this arrangement, is :

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  5. Question 5

    Sequences and Series. This type asked 3 times: 29 Jun 2022, 29 Jul 2022, 28 Jan 2025. This one: 28 Jan 2025 See all 3 of this type

    59
    Let ⟨an⟩\left\langle a_{n} \right\rangle be a sequence such that a0=0,a1=12a_{0}= 0,a_{1}=\frac{1}{2} and 2an+2=5an+1−3an,n=0,1,2,3,……2a_{n + 2}= 5a_{n + 1}- 3a_{n},n = 0,1,2,3,\ldots\ldots Then ∑k=1100ak\sum_{k = 1}^{100} a_{k} is equal to :

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