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Day 190: JEE Mains Maths

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

  1. Question 1

    Limits and Continuity. Asked once: 2021 Paper 7 (same type asked 3 times) See all 3 of this type

    80
    The value of lim⁡x→0+cos⁡−1(x−[x]2)⋅sin⁡−1(x−[x]2)x−x3\lim_{x\rightarrow0^{+}} \frac{\cos^{- 1}\left( x- \lbrack x\rbrack^{2} \right)\cdot\sin^{- 1}\left( x- \lbrack x\rbrack^{2} \right)}{x-x^{3}}, where [x] denotes the greatest integer ≤x\leq x is:

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  2. Question 2

    Trigonometric Equations. Asked once: 31 Jan 2024 (same type asked 3 times) See all 3 of this type

    165
    The number of solutions, of the equation esin⁡x−2e−sin⁡x=2e^{\sin x}- 2e^{- \sin x}= 2 is

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  3. Question 3

    Permutations and Combinations. Asked once: 6 Apr 2023 (same type asked 3 times) See all 3 of this type

    63
    If  2nC3: nC3=10:1\ ^{2n}C_{3}:\ ^{n}C_{3}= 10:1, then the ratio (n2+3n):(n2−3n+4)\left( n^{2}+ 3n \right):\left( n^{2}- 3n + 4 \right) is

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  4. Question 4

    Relations and Functions. Asked once: 10 Apr 2023 (same type asked 3 times) See all 3 of this type

    63
    If f(x)=(tan⁡1∘)x+log⁡e(123)xlog⁡e(1234)−(tan⁡1∘),x>0f(x) =\frac{\left( \tan1^{\circ} \right)x +\log_{e}(123)}{x\log_{e}(1234) -\left( \tan1^{\circ} \right)},x > 0, then the least value of f(f(x))+f(f(4x))f(f(x)) + f\left( f\left( \frac{4}{x} \right) \right) is

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  5. Question 5

    Complex Numbers. Asked once: 31 Jan 2023 (same type asked 3 times) See all 3 of this type

    154
    The complex number z=i−1cos⁡π3+isinπ3z =\frac{i - 1}{\cos\frac{\pi}{3}+ isin\frac{\pi}{3}} is equal to :

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