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Day 610: JEE Mains Maths

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

  1. Question 1

    Matrices. Asked once: 2021 Paper 5

    66
    Let A=[i−i−ii],i=−1A=\begin{bmatrix} i & -i \\ -i & i \end{bmatrix},i=\sqrt{- 1}. Then, the system of linear equations A8[xy]=[864]A^{8}\begin{bmatrix} x \\ y \end{bmatrix}=\begin{bmatrix} 8 \\ 64 \end{bmatrix} has:

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  2. Question 2

    Sequences and Series. Asked once: 29 Jan 2023

    155
    Consider a function f:N→Rf:N \rightarrow R, satisfying f(1)+2f(2)+3f(3)+⋯+xf(x)=x(x+1)f(x);x≥2f(1) + 2f(2) + 3f(3) + \cdots + xf(x) = x(x + 1)f(x);x \geq 2 with f(1)=1f(1) = 1. Then 1f(2022)+1f(2028)\frac{1}{f(2022)}+\frac{1}{f(2028)} is equal to

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  3. Question 3

    Straight Lines. Asked once: 2021 Paper 9

    68
    The equation of one of the straight lines which passes through the point (1,3)(1,3) and makes an angle of tan⁡−1(2)\tan^{- 1}(\sqrt{2}) with the straight line, y+1=32xy + 1 = 3\sqrt{2}x is

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  4. Question 4

    Application of Derivatives. Asked once: 2021 Paper 12

    49
    The sum of all the local minimum values of the twice differentiable function f:R→Rf:R \rightarrow R defined by f(x)=x3−3x2−3f′′(2)2x+f′′(1)f(x) = x^{3} - 3x^{2} - \frac{3f''(2)}{2}x + f''(1) is :

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  5. Question 5

    Complex Numbers. Asked once: 2021 Paper 9

    71
    If the equation a∣z∣2+αˉz+αz‾‾+d=0a|z|^{2}+\overline{\bar{\alpha}z +\alpha\overline{z}}+ d = 0 represents a circle where a,d are real constants then which of the following condition is correct?

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