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Day 115: JEE Mains Maths

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

  1. Question 1

    Determinants. This type asked 2 times: 2021 Paper 5, 29 Jan 2024. This one: 29 Jan 2024 See all 2 of this type

    151
    Let A=[2126211332]A =\begin{bmatrix} 2 & 1 & 2 \\ 6 & 2 & 11 \\ 3 & 3 & 2 \end{bmatrix} and P=[120502715]P =\begin{bmatrix} 1 & 2 & 0 \\ 5 & 0 & 2 \\ 7 & 1 & 5 \end{bmatrix}. The sum of the prime factors of ∣P−1AP−2I∣\left| P^{- 1}AP - 2I \right| is equal to

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  2. Question 2

    Differentiation. This type asked 2 times: 25 Jan 2023, 29 Jan 2024. This one: 29 Jan 2024 See all 2 of this type

    167
    Let y=log⁡e(1−x21+x2),−1<x<1y =\log_{e}\left( \frac{1 -x^{2}}{1 +x^{2}} \right), - 1 < x < 1. Then at x=12x =\frac{1}{2}, the value of 225(y′−y′′)225\left( y^{'}-y^{''} \right) is equal to

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  3. Question 3

    Sequences and Series. This type asked 2 times: 31 Jan 2023, 29 Jan 2024. This one: 29 Jan 2024 See all 2 of this type

    62
    In an A.P., the sixth terms a6=2a_{6}= 2. If the a1a4a5a_{1}a_{4}a_{5} is the greatest, then the common difference of the A.P., is equal to

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  4. Question 4

    Straight Lines. This type asked 2 times: 2021 Paper 18, 29 Jan 2024. This one: 29 Jan 2024 See all 2 of this type

    67
    In a △ABC\bigtriangleup ABC, suppose y=xy = x is the equation of the bisector of the angle BB and the equation of the side ACAC is 2x−y=22x - y = 2. If 2AB=BC2AB = BC and the point AA and B are respectively (4,6)(4,6) and (α,β)(\alpha,\beta), then α+2β\alpha + 2\beta is equal to

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  5. Question 5

    Indefinite Integration. This type asked 2 times: 2021 Paper 6, 27 Jan 2024. This one: 27 Jan 2024 See all 2 of this type

    164
    The integral ∫(x8−x2)dx(x12+3x6+1)tan⁡−1(x3+1x3)\int\frac{\left( x^{8}-x^{2} \right)dx}{\left( x^{12}+ 3x^{6}+ 1 \right)\tan^{- 1}\left( x^{3}+\frac{1}{x^{3}} \right)} is equal to :

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