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Day 605: JEE Mains Maths

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

  1. Question 1

    Definite Integration. Asked once: 1 Feb 2023

    180
    If ∫0π5cos⁡x(1+cos⁡xcos⁡3x+cos⁡2x+cos⁡3xcos⁡3x)1+5cos⁡xdx=kπ16\int_{0}^{\pi}\frac{5^{\cos x}\left( 1 + \cos x\cos3x +\cos^{2}x +\cos^{3}x\cos3x \right)}{1 +5^{\cos x}}dx=\frac{k\pi}{16}, then kk is equal to

  2. Question 2

    Matrices. Asked once: 2021 Paper 9

    78
    Let A+2B=[1206−33−531]A + 2B =\begin{bmatrix} 1 & 2 & 0 \\ 6 & - 3 & 3 \\ - 5 & 3 & 1 \end{bmatrix} and 2A−B=[2−152−16012]2A - B =\begin{bmatrix} 2 & - 1 & 5 \\ 2 & - 1 & 6 \\ 0 & 1 & 2 \end{bmatrix}. If Tr(A)Tr(A) denotes the sum of all diagonal elements of the matrix A, then Tr(A)−Tr(B)Tr(A) - Tr(B) has value equal to

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  3. Question 3

    Relations and Functions. Asked once: 2021 Paper 7

    61
    The inverse of y=5log⁡xy =5^{\log x} is :

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  4. Question 4

    Sequences and Series. Asked once: 31 Jan 2023

    76
    If the sum and product of four positive consecutive terms of a G.P., are 126 and 1296, respectively, then the sum of common ratios of all such GPs is

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  5. Question 5

    Straight Lines. Asked once: 2021 Paper 20

    63
    Let AA be a fixed point (0,6)(0,6) and BB be a moving point (2t,0)(2t, 0). Let MM be the mid-point of ABAB and the perpendicular bisector of ABAB meets the yy-axis at CC. The locus of the mid-point PP of MCMC is :

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