List of top Mathematics Questions asked in COMEDK UGET

The variance of 25 observations is 8. If each observation is multiplied by 3, then the new variance of the resulting observations is

Three fair dice are thrown. What is the probability of getting a total of 15 given that they exhibit three different numbers that are in arithmetic progression?

\( -\frac{2\pi}{5} \) is the principal value of

The least value of \( a \) such that the function \( x^2 + ax + 1 \) is increasing on \([1,2]\) is

The digits of a three-digit number taken in an order are in geometric progression. If one is added to the middle digit, they form an arithmetic progression. If 594 is subtracted from the number, then a new number with the same digits in reverse order is formed. The original number is divisible by

Find the value of \( \displaystyle \lim_{h \to 0} \frac{(a+h)^2 \sin(a+h) - a^2 \sin a}{h} \)

\( 0.2 + 0.22 + 0.022 + \cdots \) up to \( n \) terms is equal to

The order of the differential equation \( \frac{d}{dz}\left[\left(\frac{dy}{dz}\right)^3\right]=0 \) is

The solution set of the system of inequalities \( 5-4x \leq -7 \) or \( 5-4x \geq 7,\ x \in R \) is

The solution of \( (x+\log y)dy+ydx=0 \) when \( y(0)=1 \) is

The domain of the function $ y = \frac{1}{\log_{10}(3 - x)} + \sqrt{x + 7} $ is:

If two positive numbers are in the ratio $ 3 + 2\sqrt{2} : 3 - 2\sqrt{2} $, then the ratio between their A.M (arithmetic mean) and G.M (geometric mean) is:

Evaluate: $ \cot^{-1} \left( -\frac{3}{\sqrt{3}} \right) - \sec^{-1} \left( -\frac{2}{\sqrt{2}} \right) - \csc^{-1}(-1) - \tan^{-1}(1) $

The equation of the circle which touches the x-axis, passes through the point (1, 1) and whose centre lies on the line $ x + y = 3 $ in the first quadrant is

The general solution of the differential equation $ x \frac{dy}{dx} = y + x \tan\left(\frac{y}{x}\right) $

The line joining two points $ A(2, 0) $ and $ B(3, 1) $ is rotated about $ A $ in an anticlockwise direction through an angle of $ 15^\circ $. If $ B $ goes to $ C $ in the new position, then the coordinates of $ C $ are:

The rate of change of the volume of a sphere with respect to its surface area $ S $ is

The value of $ \lim_{x \to 1} \frac{x^{15} - 1}{x^{10} - 1} $ is:

Let $ \alpha $ and $ \beta $ be the distinct roots of $ ax^2 + bx + c = 0 $, then $ \lim_{x \to \alpha} \frac{1 - \cos(ax^2 + bx + c)}{(x - \alpha)^2} $ is equal to:

If the straight lines $ \frac{x - 2}{1} = \frac{y - 3}{1} = \frac{z - 4}{-t} \quad \text{and} \quad \frac{x - 1}{t} = \frac{y - 4}{2} = \frac{z - 5}{1} \quad \text{are intersecting, then $ t $ can have:} $

The sum of the order and degree of the differential equation $ \left( \frac{d^5y}{dx^5} \right) + 4 \left( \frac{d^4y}{dx^4} \right) + \left( \frac{d^3y}{dx^3} \right) = x^2 - 1 $

The letters of the word "COCHIN" are permuted and all the permutations are arranged in alphabetical order as in an English dictionary. The number of words that appear before the word "COCHIN" is