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Day 459: JEE Mains Maths

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

  1. Question 1

    Probability. Asked once: 22 Jan 2026 S1

    54
    Two distinct numbers a and b are selected at random from 1,2,3,……,501,2,3,\ldots\ldots,50. The probability, that their product ab is divisible by 3 , is

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  2. Question 2

    Quadratic Equations. Asked once: 28 Jan 2026 S2

    57
    Let the arithmetic mean of 1a\frac{1}{a} and 1b\frac{1}{b} be 516,a>2\frac{5}{16},a> 2. If α\alpha is such that a,4,α, ba,4,\alpha,\text{ }b are in A.P., then the equation αx2−ax+2(α−2b)=0\alpha x^{2}-ax+ 2(\alpha- 2b) = 0 has :

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  3. Question 3

    Relations and Functions. Asked once: 2 Apr 2025

    62
    Let A be the set of all functions f:Z→Zf:Z \rightarrow Z and R be a relation on A such that R={(f,g):f(0)=g(1)\mathbf{R = \{(f,g):}f(0) = g(1) and f(1)=g(0)}f(1) = g(0)\}. Then R is:

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  4. Question 4

    Sequences and Series. Asked once: 4 Apr 2026 S2

    57
    Let α=14+18+116+…∞\alpha=\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+ \ldots\infty and β=13+19+127+…∞\beta=\frac{1}{3}+\frac{1}{9}+\frac{1}{27}+ \ldots\infty. Then the value of (0.2)log⁡5(α)+(0.04)log⁡5(β)(0.2)^{\log_{\sqrt{5}}(\alpha)}+ (0.04)^{\log_{5}(\beta)} is equal to :

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  5. Question 5

    Statistics. Asked once: 27 Jan 2024

    74
    Let a1,a2,….a10a_{1},a_{2},\ldots.a_{10} be 10 observations such that ∑k=110ak=50\sum_{k = 1}^{10} a_{k}= 50 and ∑∀k<jak⋅aj=1100\sum_{\forall k < j} a_{k}\cdot a_{j}= 1100. Then the standard deviation of a1,a2,..,a10a_{1},a_{2},..,a_{10} is equal to:

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