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Day 75: JEE Mains Maths

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

  1. Question 1

    Application of Derivatives. This type asked 3 times: 2021 Paper 1, 2021 Paper 4, 28 Jul 2022. This one: 28 Jul 2022 See all 3 of this type

    77
    If the minimum value of f(x)=5x22+αx5,x>0f(x) =\frac{5x^{2}}{2}+\frac{\alpha}{x^{5}},x > 0, is 14, then the value of α\alpha is equal to:

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  2. Question 2

    Application of Derivatives. This type asked 3 times: 2021 Paper 2, 2021 Paper 4, 26 Jul 2022. This one: 26 Jul 2022 See all 3 of this type

    155
    Let PP and QQ be any points on the curves ( x−x - 1)2+(y+1)2=11)^{2}+ (y + 1)^{2}= 1 and y=x2y =x^{2}, respectively. The distance between PP and QQ is minimum for some value of the abscissa of PP in the interval

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  3. Question 3

    Inverse Trigonometric Functions. This type asked 3 times: 2021 Paper 20, 2021 Paper 25, 26 Jul 2022. This one: 26 Jul 2022 See all 3 of this type

    166
    If 0<x<120 < x <\frac{1}{\sqrt{2}} and sin⁡−1xα=cos⁡−1xβ\frac{\sin^{- 1}x}{\alpha}=\frac{\cos^{- 1}x}{\beta}, then a value of sin⁡(2παα+β)\sin\left( \frac{2\pi\alpha}{\alpha+\beta} \right) is

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  4. Question 4

    Three Dimensional Geometry. This type asked 3 times: 2021 Paper 19, 26 Jun 2022, 26 Jul 2022. This one: 26 Jul 2022 See all 3 of this type

    172
    The largest value of aa, for which the perpendicular distance of the plane containing the lines r→=(i^+j^)+λ(i^+aj^−k^)\overrightarrow{r}= (\widehat{i}+\widehat{j}) + \lambda(\widehat{i}+ a\widehat{j}-\widehat{k}) and r→=(i^+j^)+μ(−i^+j^−ak^)\overrightarrow{r}= (\widehat{i}+\widehat{j}) + \mu( -\widehat{i}+\widehat{j}- a\widehat{k}) from the point (2,1,4)(2,1,4) is 3\sqrt{3}, is

  5. Question 5

    Matrices. This type asked 3 times: 2021 Paper 14, 28 Jun 2022, 25 Jul 2022. This one: 25 Jul 2022 See all 3 of this type

    81
    Let A=[2−1−110−11−10]A =\begin{bmatrix} 2 & - 1 & - 1 \\ 1 & 0 & - 1 \\ 1 & - 1 & 0 \end{bmatrix} and B=A−IB = A - I. If ω=3i−12\omega =\frac{\sqrt{3}i - 1}{2}, then the number of elements in the set {n∈{1,2,…,100}:An+(ωB)n=A+B}\left\{ \mathbf{n \in \{ 1,2,\ldots,100\}:}A^{n}+ (\omega B)^{n}= A + B \right\} is equal to