List of top Questions asked in COMEDK UGET

The mean energy per molecule for a diatomic gas is
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
If $ A $, $ B $, and $ C $ are mutually exclusive and exhaustive events of a random experiment such that $ P(B) = \frac{3}{2} P(A) $ and $ P(C) = \frac{1}{2} P(B) $, then $ P(A \cup C) $ equals to
Three vertices are chosen randomly from the nine vertices of a regular 9-sided polygon. The probability that they form the vertices of an isosceles triangle, is

If a number $ n $ is chosen at random from the set $\{11, 12, 13, ..., 30\}\,$ then, the probability that $ n $ is neither divisible by 3 nor divisible by 5, is

A five-digit number is formed by using the digits 1, 2, 3, 4, 5 with no repetition. The probability that the numbers 1 and 5 are always together, is
If two lines $ L_1 : \frac{x-1}{2} = \frac{y+1}{3} = \frac{z-1}{4} $ and $ L_2 : \frac{x-3}{1} = \frac{y-k}{2} = z $ intersect at a point, then $ 2k $ is equal to

The lines $ \frac{x-1}{2} = \frac{y-4}{4} = \frac{z-2}{3} \quad \text{and} \quad \frac{1-x}{1} = \frac{y-2}{5} = \frac{3-z}{a} \quad \text{are perpendicular to each other, then} \ a \ \text{equals to} $

The integral $ \int_{-\frac{\pi}{2}}^{\frac{\pi}{2}} \sin^2 x \, dx \text{ is equal to} $
The integral $ \int \frac{4x^2}{\sqrt{1-16x^2}} \, dx \text{ is equal to} $