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Day 464: JEE Mains Maths

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

  1. Question 1

    Quadratic Equations. Asked once: 28 Jan 2026 S1

    58
    Let S={x3+ax2+bx+c:a,b,c∈NS=\left\{ x^{3}+ax^{2}+bx+c:a,b,c\in N \right. and a,b,c≤20}a,b,c\leq 20\} be a set of polynomials. Then the number of polynomials in S , which are divisible by x2+2x^{2}+ 2, is

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  2. Question 2

    Relations and Functions. Asked once: 2 Apr 2025

    129
    Let A={1,2,3,…,100}\mathbf{A = \{ 1,2,3,\ldots,100\}} and R be a relation on A such that R={(a,b):a=2b+1}R = \{(a,b):a = 2b + 1\}. Let (a1,a2)\left( a_{1},a_{2} \right), (a2,a3),(a3,a4),…,(ak,ak+1)\left( a_{2},a_{3} \right),\left( a_{3},a_{4} \right),\ldots,\left( a_{k},a_{k+ 1} \right) be a sequence of kk elements of R such that the second entry of an ordered pair is equal to the first entry of the next ordered pair. Then the largest integer k , for which such a sequence exists, is equal to :

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  3. Question 3

    Sequences and Series. Asked once: 4 Apr 2026 S1

    57
    The first term of an A.P. of 30 non-negative terms is 103\frac{10}{3}. If the sum of this A.P. is the cube of its last term, then its common difference is :

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  4. Question 4

    Statistics. Asked once: 10 Apr 2023

    88
    If the mean of the frequency distribution is 28, then its variance is

  5. Question 5

    Straight Lines. Asked once: 23 Jan 2026 S1

    54
    A rectangle is formed by the lines x=0,y=0x = 0,y = 0, x=3x = 3 and y=4y = 4. Let the line L be perpendicular to 3x+y+6=03x + y + 6 = 0 and divide the area of the rectangle into two equal parts. Then the distance of the point (12,−5)\left( \frac{1}{2}, - 5 \right) from the line L is equal to :

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