PYQ Vault
EbooksTutor

Day 598: JEE Mains Maths

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

  1. Question 1

    Application of Derivatives. Asked once: 25 Jun 2022

    164
    If the angle made by the tangent at the point (x0,y0)\left( x_{0},y_{0} \right) on the curve x=12(t+sin⁡tcost)x = 12(t + \sin tcost), y=12(1+sin⁡t)2,0<t<π2y = 12(1 + \sin t)^{2},0 < t <\frac{\pi}{2}, with the positive xx-axis is π3\frac{\pi}{3}, then y0y_{0} is equal to

    Tap an option to check your answer.

  2. Question 2

    Complex Numbers. Asked once: 14 Jun 2022

    61
    Let A={z∈C:1≤∣z−(1+i)∣≤2}\mathbf{A = \{ z \in C:1 \leq |z - (1 + i)| \leq 2\}} and B={z∈A:∣z−(1−i)∣=1}\mathbf{B = \{ z \in A:|z - (1 - i)| = 1\}}. Then, B:B:

    Tap an option to check your answer.

  3. Question 3

    Conic Sections. Asked once: 23 Jan 2025

    148
    The focus of the parabola y2=4x+16y^{2}= 4x + 16 is the centre of the circle C of radius 5 . If the values of λ\lambda, for 3x−y=03x - y = 0 and x+λy=4x + \lambda y = 4, are λ1\lambda_{1} and λ2,λ1<λ2\lambda_{2},\lambda_{1}<\lambda_{2}, then 12λ1+29λ212\lambda_{1}+ 29\lambda_{2} is equal to _____\_\_\_\_\_ .

  4. Question 4

    Definite Integration. Asked once: 11 Apr 2023

    157
    If f:R→Rf:R \rightarrow R be a continuous function satisfying ∫0π/2f(sin⁡2x)⋅sin⁡xdx+α∫0π/4f(cos⁡2x)⋅cos⁡xdx=0\int_{0}^{\pi/2} f(\sin2x) \cdot \sin xdx + \alpha\int_{0}^{\pi/4} f(\cos2x) \cdot \cos xdx = 0, then α\alpha is equal to

    Tap an option to check your answer.

  5. Question 5

    Matrices. Asked once: 2021 Paper 19

    62
    Let A=[100011100]A =\begin{bmatrix} 1 & 0 & 0 \\ 0 & 1 & 1 \\ 1 & 0 & 0 \end{bmatrix}. Then A2025−A2020A^{2025}-A^{2020} is equal to:

    Tap an option to check your answer.