List of top Mathematics Questions asked in COMEDK UGET

If A, B, and C are three mutually exclusive and exhaustive events such that \( P(A) = 2P(B) = 3P(C) \). What is \( P(B) \)?
If 2 and 3 are intercepts of a line \( L = 0 \), then the distance of \( L \equiv 0 \) from the origin is
Evaluate $\left[i^{22} + \left(\dfrac{1}{i}\right)^{25}\right]^3$
\( (2^{3n} - 1) \) is divisible by
If \( S = \frac{2^2 - 1}{2} + \frac{3^2 - 2}{6} + \frac{4^2 - 3}{12} + \ldots\) \text{ upto 10 terms, then S is equal to}
\( \sum_{n=1}^{m} n \cdot n! \) is equal to
The first and fifth terms of an A.P. are -14 and 2 respectively and the sum of its $n$ terms is 40. The value of $n$ is
If the probability for A to fail in an examination is 0.2 and that for B is 0.3, then the probability that either A or B fail is.
If \( \theta \) be the angle between the vectors \( a = 2\hat{i} + 2\hat{j} - \hat{k} \) and \( b = 6\hat{i} - 3\hat{j} + 2\hat{k} \), then
The probability of choosing randomly a number \( c \) from the set \( \{1, 2, 3, \dots, 9\} \) such that the quadratic equation \( x^2 + 4x + c = 0 \) has real roots, is
If \( x, y \) and \( z \) are non-zero real numbers and \( a = x\hat{i} + 2\hat{j}, b = y\hat{j} + 3\hat{k} \) and \( c = x\hat{i} + y\hat{j} + z\hat{k} \) are such that \( a \times b = z\hat{i} - 3\hat{j} + \hat{k} \), then \( [abc] \) is equal to
If \( p = \hat{i} + \hat{j}, q = 4\hat{k} - \hat{j} \) and \( r = \hat{i} + \hat{k} \), then the unit vector in the direction of \( 3p + q - 2r \) is
The line \( \frac{x-3}{4} = \frac{y-4}{5} = \frac{z-5}{6} \) is parallel to the plane.
The angle between the lines \( \frac{x+4}{3} = \frac{y-1}{5} = \frac{z+3}{4} \) and \( \frac{x+1}{1} = \frac{y-4}{1} = \frac{z-5}{2} \)
The point of intersection of the lines \( \frac{x - 1}{1} = \frac{y - 1}{2} = \frac{z - 2}{3} \) and \( \frac{x - 5}{2} = \frac{y - 2}{1} = \frac{z - 5}{2} \)
If \( ^nC_3 = 220 \), then \( n = \ ? \)
There are 12 points in a plane out of which 3 points are collinear. How many straight lines can be drawn by joining any two of them?
A regular polygon of \( n \) sides has 170 diagonals. Then \( n \) is equal to:
Evaluate the integral \( \int_{-\frac{\pi}{2}}^{\frac{\pi}{2}} \cos x \, dx \)
Three vertices are chosen randomly from the seven vertices of a regular 7-sided polygon. The probability that they form the vertices of an isosceles triangle is.
Five persons A, B, C, D and E are in queue at a shop. The probability that A and B are always together is.
The circle \( x^2 + y^2 + 4x - 7y + 12 = 0 \) cuts an intercept on the Y-axis of length
If two circles \( (x - 1)^2 + (y - 3)^2 = r^2 \) and \( x^2 + y^2 - 8x + 2y + 8 = 0 \) are given, then
If the tangent to the curve \( xy + ax + by = 0 \) at \( (1, 1) \) is inclined at an angle \( \tan^{-1}{2} \) with the X-axis, then
The value of \( 3\log_5{5} - 5\log_4{3} \) is