Subject Experts Solutions for Chapter: Solved Paper 2018 (I), Exercise 1: PAPER I : Mathematics

What is the angle between the straight lines $\left(m^2-mn\right)y=\left(mn+n^2\right)x+n^3$ and $\left(mn+m^2\right)y=\left(mn-n^2\right)x+m^3,$ where $m>n?$

What is the equation of the straight line cutting-off an intercept $2$ from the negative direction of $Y$-axis and inclined at $30°$ with the positive direction of $X$-axis?

What is the equation of the line passing through the point of intersection of the lines $x+2y-3=0$ and $2x-y+5=0$ and parallel to the line $y-x+10=0 ?$

What is the equation of the ellipse whose vertices are $(\pm 5,0)$ and foci are at $(\pm 4,0)?$

What is the equation of the straight line passing through the point $\left(2,3\right)$ and making an intercept on the positive $Y$-axis equal to twice its intercept on the positive $X$-axis?

Let the coordinates of the points $A,B,C$ be $(1,8,4),(0,-11,4)$ and $(2,-3,1)$ respectively. What are the coordinates of the point $D$ which is the foot of the perpendicular from $A$ on $BC?$

What is the equation of the plane passing through the points $(-2,6,-6),(-3,10,-9)$ and $(-5,0,-6)?$

A sphere of constant radius $r$ through the origin intersects the coordinate axes in $A, B$ and $C.$ What is the locus of the centroid of the $\Delta ABC$?