List of top Mathematics Questions asked in COMEDK UGET

Let the equation of pair of lines $ y = m_1x $ and $ y = m_2x $ be written as $ (y - m_1x)(y - m_2x) = 0 $. Then, the equation of the pair of the angle bisector of the line $ 3y^2 - 5xy - 2x^2 = 0 $ is
A polygon of $ n $ sides has 105 diagonals, then $ n $ is equal to
The total number of numbers greater than 1000 but less than 4000 that can be formed using 0, 2, 3, 4 (using repetition allowed) are
There are 10 points in a plane out of which 4 points are collinear. How many straight lines can be drawn by joining any two of them?
If $ \left( \frac{3}{2} + i \frac{\sqrt{3}}{2} \right)^{50} = 3^{25}(x + iy) $, where $x$ and $y$ are real, then the ordered pair $(2x, 2y)$ is
If $i = \sqrt{-1}$ and $n$ is a positive integer, then $i^n + i^{n+1} + i^{n+2} + i^{n+3}$ is equal to
If $ z = \sqrt{3} + i $, then the argument of $ z^2 e^{-i} $ is equal to
If $ n(A) = p $ and $ n(B) = q $, then the number of relations from the set $ A $ to the set $ B $ is
If $ A = \{a, b, c\}, B = \{b, c, d\} $ and $ C = \{a, d, c\} $, then $ (A - B) \times (B \cap C) $ is equal to
If $2f(x^2) + 3f\left( \frac{1}{x^2} \right) = x^2 - 1$, for $x \in \mathbb{R} - \{0\}$, then $f(x^8)$ is equal to

The general solution of $ 2 \cos 4x + \sin^2 2x $= 0  is

The expression $ \frac{2 \tan A}{1 - \cot A} + \frac{2 \cot A}{1 - \tan A} $ can be written as

If $ \cos A = m \cos B $ and $ \cot \left( \frac{A+B}{2} \right) = \lambda \tan \left( \frac{B-A}{2} \right), $  then $ \lambda \text{ is equal to} $

In a trial, the probability of success is twice the probability of failure. In six trials, the probability of at most two failures will be
The solution of the differential equation $ \frac{dy}{dx} \tan y = \sin(x + y) + \sin(x - y) $ is
Find $ nC_{21} $, if $ nC_{10} = nC_{12} $
The general solution of $ \left( \frac{dy}{dx} \right)^2 = 1 - x^2 - y^2 + x^2y^2 $ is
The coefficient of $x^{29}$ in the expansion of $ (1 - 3x + 3x^2 - x^3)^{15} $ is}
The differential equation of all non-vertical lines in a plane is
In the expansion of $ (1 + 3x + 3x^2 + x^3)^{2n} $, the term which has the greatest binomial coefficient, is
The value of $ \frac{1}{2!} + \frac{2}{3!} + \frac{3}{4!} + ... + \frac{99}{100!} $ is equal to
The sum of $ n $ terms of the series, $ \frac{4}{3} + \frac{10}{9} + \frac{28}{27} + ... $ is
$ 2^{3n} - 7n - 1 $ is divisible by
If $ 49^n + 16^n + k $ is divisible by 64 for $ n \in \mathbb{N} $, then the least negative integral value of $ k $ is
Using mathematical induction, the numbers $ a_n $ are defined by $ a_0 = 1, a_{n+1} = 3n^2 + n + a_n, (n \geq 0) $. Then, $ a_n $ is equal to