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Day 593: JEE Mains Maths

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

  1. Question 1

    Matrices. Asked once: 14 Jun 2022

    172
    Let S={(−1a0 b);a,b∈{1,2,3,…100}}S=\left\{ \begin{pmatrix} - 1 & a \\ 0 & \text{ }b \end{pmatrix}\mathbf{;a,b \in \{ 1,2,3,\ldots 100\}} \right\} and let Tn={A∈S:An(n+1)=I}T_{n}=\left\{ A\in S:A^{n(n+ 1)}=I \right\}. Then the number of elements in ⋂n=1100 Tn\bigcap_{n = 1}^{100} {\text{ }T}_{n} is

  2. Question 2

    Quadratic Equations. Asked once: 2021 Paper 20

    78
    If x2+9y2−4x+3=0,x,y∈Rx^{2}+ 9y^{2}- 4x+ 3 = 0,x,y\in\mathbb{R}, then xx and yy respectively lie in the intervals:

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  3. Question 3

    Relations and Functions. Asked once: 2021 Paper 17

    64
    Let f:R→Rf:R \rightarrow R be defined as f(x+y)+f(x−y)=2f(x)f(y),f(12)=−1f(x+y) +f(x-y) = 2f(x)f(y),f\left( \frac{1}{2} \right)= - 1. Then, the value of ∑k=1201sin⁡(k)sin⁡(k+f(k))\sum_{k = 1}^{20} \frac{1}{\sin(k)\sin(k + f(k))} is equal to:

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  4. Question 4

    Sequences and Series. Asked once: 13 Apr 2023

    78
    Let s1, s2, s3,…..,s10s_{1},{\text{ }s}_{2},{\text{ }s}_{3},\ldots..,s_{10} respectively be the sum to 12 terms of 10 A.P.s whose first terms are 1, 2, 3, ...., 10 and the common differences are 1,3,5,….,191,3,5,\ldots.,19 respectively. Then ∑i=110 si\sum_{i = 1}^{10} {\text{ }s}_{i} is equal to

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  5. Question 5

    Straight Lines. Asked once: 25 Jul 2022

    160
    Let the point P(α,β)P(\alpha,\beta) be at a unit distance from each of the two lines L1:3x−4y+12=0L_{1}:3x - 4y + 12 = 0, and L2:8x+6y+11=0L_{2}:8x + 6y + 11 = 0. If PP lies below L1L_{1} and above L2L_{2}, then 100(α+β)100(\alpha + \beta) is equal to

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