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Day 206: JEE Mains Maths

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

  1. Question 1

    Quadratic Equations. Asked once: 23 Jan 2025 (same type asked 2 times) See all 2 of this type

    75
    If the equation a(b−c)x2+b(c−a)x+c(a−b)=0a(b-c)x^{2}+b(c-a)x+c(a-b)=0 has equal roots, where a+c=15a+c=15 and b=365b=\frac{36}{5}, then a2+c2a^{2}+c^{2} is equal to

  2. Question 2

    Trigonometric Equations. Asked once: 2021 Paper 8 (same type asked 2 times) See all 2 of this type

    68
    The number of solutions of the equation x+2tan⁡x=π2x+ 2\tan x=\frac{\pi}{2} in the interval [0,2π]\lbrack 0,2\pi\rbrack is :

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  3. Question 3

    Determinants. Asked once: 5 Apr 2024 (same type asked 2 times) See all 2 of this type

    168
    Let αβ≠0\alpha\beta \neq 0 and A=[βα3ααβ−βα2α]A =\begin{bmatrix} \beta & \alpha & 3 \\ \alpha & \alpha & \beta \\ - \beta & \alpha & 2\alpha \end{bmatrix}. If B=[3α−93α−α7−2α−2α5−2β]B =\begin{bmatrix} 3\alpha & - 9 & 3\alpha \\ - \alpha & 7 & - 2\alpha \\ - 2\alpha & 5 & - 2\beta \end{bmatrix} is the matrix of cofactors of the elements of AA, then det(AB)det(AB) is equal to :

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  4. Question 4

    Limits and Continuity. Asked once: 2021 Paper 8 (same type asked 2 times) See all 2 of this type

    65
    The value of lim⁡n→∞[r]+[2r]+…..+[nr]n2\lim_{n\rightarrow \infty} \frac{\lbrack r\rbrack + \lbrack 2r\rbrack + \ldots.. + \lbrack nr\rbrack}{n^{2}}, where rr is non-zero real number and [r] denotes the greatest integer less than or equal to rr, is equal to :

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  5. Question 5

    Sequences and Series. Asked once: 27 Jul 2022 (same type asked 2 times) See all 2 of this type

    66
    Suppose a1,a2,…,an,…a_{1},a_{2},\ldots,a_{n},\ldots be an arithmetic progression of natural numbers. If the ratio of the sum of the first five terms to the sum of first nine terms of the progression is 5:175:17 and 110<a15<110 <a_{15}< 120 , then the sum of the first ten terms of the progression is equal to -

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