List of top Mathematics Questions asked in COMEDK UGET

Consider an infinite geometric series with first term $ a $ and common ratio $ r $. If the sum of infinite geometric series is 4 and the second term is $ \frac{3}{4} $, then:

The mean of five observations is 4 and their variance is 5.2. If three of these observations are 1, 2, and 6, then the other two observations are:

The area of the region enclosed by the curve $ \left\{ (x, y) : 4x^2 + 25y^2 = 100 \right\} $ is:

The value of the integral $ \int_{1/3}^1 \frac{(x - x^3)^{\frac{1}{3}}}{x^4} \, dx $ is:

While shuffling a pack of cards, 3 cards were accidentally dropped, then find the probability that the missing cards belong to different suits?

The area of the triangle whose vertices are $ (-2, a) $, $ (2, -6) $, and $ (5, 4) $ is 35 square units. Then the value of $ a $ is:

If $3A + 4B^{t} = \left( \begin{array}{cc} 7 & -10 \\ 0 & 6 \end{array} \right) $ and $ 2B - 3A^{t} = \left( \begin{array}{cc} -1 & 18 \\ 4 & -6 \\ -5 & -7 \end{array} \right) $, then find $ (5B)^{t}$:

Let $ X $ and $ Y $ be the set of all positive divisors of 400 and 1000 respectively (including 1 and the number). Then $ n(X \cap Y) $ is equal to

If \[ \cos \alpha = k \cos \beta \] then \[ \cot \left( \frac{\alpha + \beta}{2} \right) \] is equal to

If $P(B) = \frac{3}{5}$, $P(A/B) = \frac{1}{2}$, and $P(A \cup B) = \frac{4}{5}$, then $P(A \cup B)' + P(A')$ is :

$\int x^x(1 + \log x) \, dx$, $\text{ is equal to:}$

The range of $ x $ which satisfy the inequality \[ -5 \leq \frac{2 - 3x}{4} \leq 9 \] is

Let $ x $ be the arithmetic mean and $ y, z $ be the two geometric means between any two positive numbers, then \[ \frac{y^3 + z^3}{x y z} = \text{----------} \]

Evaluate the integral \[ \int \frac{\cos 4x + 1}{\cot x - \tan x} \, dx \]

If $ \vec{a} $ and $ \vec{b} $ are unit vectors, then the angle between $ \vec{a} $ and $ \vec{b} $ for which $ \vec{a} - \vec{b} = 0 $

The probability distribution of a discrete random variable $ X $ is given as \[ \begin{array}{|c|c|c|c|c|c|} \hline X & 1 & 2 & 4 & 2A & 3A & 5A \\ \hline P(X) & \frac{1}{2} & \frac{1}{5} & \frac{3}{25} & K & \frac{1}{25} & \frac{1}{25} \\ \hline \end{array} \] Then the value of $ A $ if $ E(X) = 2.94 $ is

18 Points are indicated on the perimeter of a triangle ABC as shown below. If three points are chosen then probability that it will form a triangle is

What can be said regarding a line if its slope is negative?

The value of \[ \sin^{-1} \left[ \cos \left( \frac{39\pi}{5} \right) \right] \] is

If the volume of a sphere is increasing at a constant rate, then the rate at which its radius is increasing is

The altitude of a cone is 20 cm and its semi vertical angle is 30°. If the semi vertical angle is increasing at the rate of 2° per second, then the radius of the base is increasing at the rate of

If the position vector of a point A is $ \vec{A} = \vec{a} + 2\vec{b} $ and $ \vec{a} $ divides $ AB $ in the ratio 2 : 3, then the position vector of B is