List of top Mathematics Questions asked in COMEDK UGET

The shortest distance between the lines $\frac{ x - 3}{3} = \frac{y-8}{-1}= \frac{z - 3}{1} $ and $\frac{ x + 3}{-3} = \frac{y +7}{2}= \frac{z - 6}{4} $ is

The angle between the curves $y^2 = 4ax$ and $ay = 2x^2$ is

The area in square units bounded by the normal at $(1, 2)$ to the parabola $y^2 = 4x, x$-axis and the curve is given by

A ladder $5\,m$ long is leaning against a wall. The bottom of the ladder is pulled along the ground away from the wall, at the rate of $2m/sec$. The speed at which its height on the wall decreases when the foot of the ladder is $4\, m$ away from the wall is

$\tan\left(\cos^{-1}\left( \frac{1}{5\sqrt{2}}\right)-\sin^{-1}\left(\frac{4}{\sqrt{17}}\right)\right)$ is

The differential equation of the family of parabolas $y^2 = 4ax$, where $a$ is parameter, is

The value of $c$ in Lagrange's theorem for the function $f(x) = \log (\sin \, x)$ in the interval $\left[ \frac{\pi}{6} , \frac{5 \pi}{6} \right]$ is

If a class of $175$ students the following data shows the number of students opting one or more subjects. Mathematics $100$, Physics $70$, Chemistry $40$, Mathematics and Physics $30$, Mathematics and Chemistry $28$, Physics and Chemistry $23$, Mathematics, Physics and Chemistry $18$. The number of students who have opted Mathematics alone is

The maximum area in square units of an isosceles triangle inscribed in an ellipse $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$ with its vertex at one end of the major axis is

If $\tan(x + y) = 33$ and $x = \tan^{-1} \, 3,$ then $y$ is

The direction ratios of the line which is perpendicular to the lines $\frac{ x - 7}{2} = \frac{y +17}{-3}= \frac{z - 6}{1} $ and $\frac{ x + 5}{1} = \frac{y +3}{2}= \frac{z - 4}{-2} $ are

If a set $A$ has $4$ elements, then the total number of proper subsets of set $A$, is

A line making angles $45^\circ$. and $60^\circ$ with the positive directions of the axis of $x$ and $y$, makes with the positive direction of $z$-axis, an angle of

A bag contains $3$ white, $4$ black, $2$ red balls. If $2$ balls are drawn at random, then the probability that both the balls are white, is

The medians $AD$ and $BE$ of a triangle with vertices $A(0, b), B(0, 0) $ & $C(a, 0)$ are perpendicular to each other, if

A straight line meets the coordinates axes at $A$ and $B$, so that the centroid of the triangle $OAB\, is \, (1, 2)$. Then the equation of the line $AB$ is