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Day 394: JEE Mains Maths

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

  1. Question 1

    Permutations and Combinations. Asked once: 2021 Paper 24 (same type asked 8 times) See all 8 of this type

    86
    All the arrangements, with or without meaning, of the word FARMER are written excluding any word that has two RR appearing together. The arrangements are listed serially in the alphabetic order as in the English dictionary. Then the serial number of the word FARMER in this list is

  2. Question 2

    Statistics. Asked once: 2021 Paper 20 (same type asked 8 times) See all 8 of this type

    87
    Let nn be an odd natural number such that the variance of 1,2,3,4,…,n1,2,3,4,\ldots,n is 14 . Then nn is equal to

  3. Question 3

    Conic Sections. Asked once: 27 Jan 2024 (same type asked 8 times) See all 8 of this type

    75
    The length of the chord of the ellipse x225+y216=1\frac{x^{2}}{25}+\frac{y^{2}}{16}= 1, whose mid point is (1,25)\left( 1,\frac{2}{5} \right), is equal to :

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  4. Question 4

    Limits and Continuity. Asked once: 2021 Paper 3 (same type asked 8 times) See all 8 of this type

    76
    lim⁡n→∞(1+1+12+……+1nn2)n\lim_{n \rightarrow \infty} \left( 1 +\frac{1 +\frac{1}{2}+ \ldots\ldots +\frac{1}{n}}{n^{2}} \right)^{n} is equal to:

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  5. Question 5

    Quadratic Equations. Asked once: 2021 Paper 26 (same type asked 8 times) See all 8 of this type

    82
    Let α\alpha and β\beta be two real numbers such that α+β=1\alpha + \beta = 1 and αβ=−1\alpha\beta = - 1. Let Pn=(α)n+(β)n,Pn−1=11P_{n}= (\alpha)^{n}+ (\beta)^{n},P_{n - 1}= 11 and Pn+1=29P_{n + 1}= 29 for some integer n≥1n \geq 1. Then, the value of Pn2P_{n}^{2} is