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Day 70: JEE Mains Maths

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

  1. Question 1

    Limits and Continuity. This type asked 3 times: 2021 Paper 6, 2021 Paper 7, 1 Feb 2024. This one: 1 Feb 2024 See all 3 of this type

    85
    Let {x}\{ x\} denote the fractional part of xx and f(x)=cos⁡−1(1−{x}2)sin⁡−1(1−{x}){x}−{x}3,x≠0f(x) =\frac{\cos^{- 1}\left( 1 - \{ x\}^{2} \right)\sin^{- 1}\left( 1 - \{ x\} \right)}{\{ x\} - \{ x\}^{3}},x\neq 0. If LL and RR respectively denotes the left hand limit and the right hand limit of f(x)f(x) at x=0x= 0, then 32π2(L2+R2)\frac{32}{\pi^{2}}\left( L^{2}+R^{2} \right) is equal to

  2. Question 2

    Trigonometric Equations. This type asked 3 times: 29 Jul 2022, 31 Jan 2024, 1 Feb 2024. This one: 1 Feb 2024 See all 3 of this type

    153
    The number of solutions of the equation 4sin⁡2x−44\sin^{2}x - 4 cos⁡3x+9−4cos⁡x=0;x∈[−2π,2π]\cos^{3}x + 9 - 4\cos x = 0;x \in \lbrack - 2\pi,2\pi\rbrack is:

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  3. Question 3

    Permutations and Combinations. This type asked 3 times: 31 Jan 2023, 6 Apr 2023, 31 Jan 2024. This one: 31 Jan 2024 See all 3 of this type

    167
    If for some m,n; 6Cm+2( 6Cm+1)+ 6Cm+2> 8C3m,n;\ ^{6}C_{m}+ 2\left( \ ^{6}C_{m + 1} \right)+\ ^{6}C_{m + 2}>\ ^{8}C_{3} and  n−1P3: nP4=1:8\ ^{n- 1}P_{3}:\ ^{n}P_{4}= 1:8, then  nPm+1+ n+1Cm\ ^{n}P_{m+ 1}+\ ^{n+ 1}C_{m} is equal to

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  4. Question 4

    Relations and Functions. This type asked 3 times: 2021 Paper 12, 10 Apr 2023, 31 Jan 2024. This one: 31 Jan 2024 See all 3 of this type

    66
    If f(x)=4x+36x−4,x≠23f(x) =\frac{4x + 3}{6x - 4},x \neq\frac{2}{3} and (fof) (x)=g(x)(x) = g(x), where g:R−{23}→R−{23}g:\mathbb{R}-\left\{ \frac{2}{3} \right\}\rightarrow\mathbb{R}-\left\{ \frac{2}{3} \right\}, then (gogog) (4)(4) is equal to

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  5. Question 5

    Complex Numbers. This type asked 3 times: 30 Jan 2023, 31 Jan 2023, 29 Jan 2024. This one: 29 Jan 2024 See all 3 of this type

    156
    Let rr and θ\theta respectively be the modulus and amplitude of the complex number z=2−i(2tan⁡5π8)z = 2 - i\left( 2\tan\frac{5\pi}{8} \right), then (r,θ)(r,\theta) is equal to

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