Day 280: NDA Maths

5 questions (6 parts). Try each one first, then open its answer.

Question 1
Circles. Asked once: NDA 1 2020
54 $x+2=0$
Tap an option to check your answer.
Question 2 (case study, 2 parts)
Complex Numbers. Asked once: NDA 2 2024
Let $Z_1$ and $Z_2$ be any two complex numbers such that $Z_1^2+Z_2^2+Z_1 Z_2=0$ .
41 $\left|\dfrac{Z_1}{Z_2}\right|$
Tap an option to check your answer.
42 $\dfrac{1}{2}+\text{Re}\!\left(\dfrac{Z_1}{Z_2}\right)$
Tap an option to check your answer.
Question 3
Conics. Asked once: NDA 2 2022
60 $The centre of an ellipse is at (0, 0), major axis is on the y-axis. If the ellipse passes through (3, 2) and (1, 6), then what is its eccentricity?$
Tap an option to check your answer.
Question 4
Definite Integration. Asked once: NDA 2 2021
84 $\int_{0}^{\pi/2}e^{\ln(\cos x)}\,dx$
Tap an option to check your answer.
Question 5
Differential Equations. Asked once: NDA 1 2020
77 $e^{\theta\varphi}=c+4\theta\varphi$
Tap an option to check your answer.

Question 1