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Day 169: JEE Mains Maths

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

  1. Question 1

    Matrices. Asked once: 8 Apr 2023 (same type asked 4 times) See all 4 of this type

    65
    Let P=[3212−1232],A=[1101]P =\begin{bmatrix} \frac{\sqrt{3}}{2} & \frac{1}{2} \\ -\frac{1}{2} & \frac{\sqrt{3}}{2} \end{bmatrix},A =\begin{bmatrix} 1 & 1 \\ 0 & 1 \end{bmatrix} And Q=PQPTQ =PQP^{T}. If  PTQ2007P=[abcd]\ P^{T}Q^{2007}P =\begin{bmatrix} a & b \\ c & d \end{bmatrix}, then 2a+b−3c−4d2a + b - 3c - 4d equal to

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  2. Question 2

    Permutations and Combinations. Asked once: 2021 Paper 13 (same type asked 4 times) See all 4 of this type

    48
    Find the number of numbers >10000> 10000 that can be formed with the digits 0, 2, 4, 6, 8, if repetition is not allowed.

  3. Question 3

    Conic Sections. Asked once: 25 Jan 2023 (same type asked 4 times) See all 4 of this type

    61
    Let the points of intersection of the line ax+by=0 (a≠b)ax+by=0\ (a\neq b) and the circle x2+y2−2x=0x^{2}+y^{2}-2x=0 be A(α,0)A(\alpha,0) and B(1,β)B(1,\beta). The image of the circle with ABAB as a diameter in the line x+y+2=0x+y+2=0 is:

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  4. Question 4

    Application of Integrals. Asked once: 29 Jan 2024 (same type asked 4 times) See all 4 of this type

    88
    The area (in sq. units) of the part of circle x2+y2=169x^{2}+y^{2}= 169 which is below the line 5x−y=135x-y= 13 is πα2β−652+αβsin⁡−1(1213)\frac{\pi\alpha}{2\beta}-\frac{65}{2}+\frac{\alpha}{\beta}\sin^{- 1}\left( \frac{12}{13} \right) where α,β\alpha,\beta are coprime numbers. Then α+β\alpha+\beta is equal to

  5. Question 5

    Application of Integrals. Asked once: 6 Apr 2024 (same type asked 4 times) See all 4 of this type

    168
    If the area of the region {(x,y):ax2≤y≤1x,1≤x≤2,0<a<1}\left\{ (x,y):\frac{a}{x^{2}}\leq y \leq\frac{1}{x},1 \leq x \leq 2,0 < a < 1 \right\} is (log⁡e2)−17\left( \log_{e}2 \right)-\frac{1}{7} then the value of 7a−37a - 3 is equal to:

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