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Day 107: JEE Mains Maths

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

  1. Question 1

    Quadratic Equations. This type asked 2 times: 23 Jan 2025, 3 Apr 2025. This one: 3 Apr 2025 See all 2 of this type

    132
    Let the equation x(x+2)(12−k)=2x(x+ 2)(12 -k) = 2 have equal roots. Then the distance of the point (k,k2)\left( k,\frac{k}{2} \right) from the line 3x+4y+5=03x+ 4y+ 5 = 0 is.

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  2. Question 2

    Trigonometric Equations. This type asked 2 times: 2021 Paper 8, 3 Apr 2025. This one: 3 Apr 2025 See all 2 of this type

    60
    The number of solutions of the equation 2x+3tan⁡x=π,x∈[−2π,2π]−2x+ 3\tan x=\pi,x\in\left\lbrack - 2\pi,2\pi \right\rbrack- {±π2,±3π2}\left\{ \pm\frac{\pi}{2}, \pm\frac{3\pi}{2} \right\} is.

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  3. Question 3

    Determinants. This type asked 2 times: 5 Apr 2024, 29 Jan 2025. This one: 29 Jan 2025 See all 2 of this type

    70
    Let A=[aij]=[log⁡5128log⁡45log⁡58log⁡425]A =\left\lbrack a_{ij} \right\rbrack=\begin{bmatrix} \log_{5}128 & \log_{4}5 \\ \log_{5}8 & \log_{4}25 \end{bmatrix}. If AijA_{ij} is the cofactor of aij,Cij=∑k=12aikAjk,1≤ia_{ij},C_{ij}=\sum_{k = 1}^{2} a_{ik}A_{jk},1 \leq i, j≤2j \leq 2, and C=[Cij]C =\left\lbrack C_{ij} \right\rbrack, then 8∣C∣8|C| is equal to :

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  4. Question 4

    Limits and Continuity. This type asked 2 times: 2021 Paper 8, 29 Jan 2025. This one: 29 Jan 2025 See all 2 of this type

    73
    Let [t]\lbrack t\rbrack be the greatest integer less than or equal to tt. Then the least value of p∈Np \in N for which
    lim⁡x→0+(x([1x]+[2x]+…..+[px])−x2([1x2]+[22x2]+….+[92x2]))≥1\underset{x \rightarrow0^{+}}{\lim} \left( x\left( \left\lbrack \frac{1}{x} \right\rbrack+\left\lbrack \frac{2}{x} \right\rbrack+ \ldots.. +\left\lbrack \frac{p}{x} \right\rbrack \right)-x^{2}\left( \left\lbrack \frac{1}{x^{2}} \right\rbrack+\left\lbrack \frac{2^{2}}{x^{2}} \right\rbrack+ \ldots. +\left\lbrack \frac{9^{2}}{x^{2}} \right\rbrack \right) \right)\geq 1
    is equal to

  5. Question 5

    Sequences and Series. This type asked 2 times: 27 Jul 2022, 29 Jan 2025. This one: 29 Jan 2025 See all 2 of this type

    63
    Consider an A.P. of positive integers, whose sum of the first three terms is 54 and the sum of the first twenty terms lies between 1600 and 1800 . Then its 11th 11^{\text{th~}} term is :

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