List of top Mathematics Questions asked in COMEDK UGET

In a 12 storey house, 10 people enter a lift cabin. It is known that they will leave the lift in pre-decided groups of 2, 3, and 5 people at different storeys. The number of ways they can do so if the lift does not stop up to the second storey is

Evaluate the integral \[ \int_0^2 x^2 + 2x - 3 \, dx \]

Evaluate the integral \[ \int \sqrt{\csc x - 1} \, dx = \]

The scalar components of a unit vector which is perpendicular to each of the vectors \( \hat{i} + 2\hat{j} - \hat{k} \) and \( 3\hat{i} - \hat{j} + 2\hat{k} \) are:

A candidate is required to answer 7 questions out of 12 questions which are divided into two groups, each containing 6 questions. He is not permitted to attempt more than 5 questions from either group. The number of ways in which he can choose the 7 questions is:

How many factors of \( 2^5 \times 3^6 \times 5^2 \) are perfect squares?

\[ \lim_{x \to 0} \frac{a^x - b^x}{x} \text{ is equal to:} \]

The minimum value of \( Z = 3x + 5y \), given subject to the constraints \( x + y \geq 2 \), \( x + 3y \geq 3 \), \( x, y \geq 0 \), is:

The general solution of the differential equation \[ (1 + y^2) \, dx = ( \tan^{-1} y - x ) \, dy \] is:

The coordinates of the vertices of the triangle are \( A(-2, 3, 6) \), \( B(-4, 4, 9) \), and \( C(0, 5, 8) \). The direction cosines of the median \( BE \) are:

The function \( f(x) = \frac{x}{2} + \frac{2}{x} \) has a local minimum at:

If the direction ratios of two lines are given by \( 3lm - 4ln + mn = 0 \) and \( l + 2m + 3n = 0 \), then the angle between the lines is:

Which of the following is a singleton set?

If the length of the major axis of an ellipse is 3 times the length of the minor axis, then its eccentricity is:

If the conjugate of \( (x + iy)(1 - 2i) \) be \( 1 + i \), then:

If \( A = \left( \begin{matrix} 1 & 2 \\ 0 & 1 \end{matrix} \right), \, P = \left( \begin{matrix} \cos \theta & \sin \theta \\ -\sin \theta & \cos \theta \end{matrix} \right), \, Q = P^T A P \), then \( PQ^{2014} \) is:

The particular solution of \( e^{\frac{dy}{dx}} = 2x + 1 \) given that \( y = 1 \) when \( x = 0 \) is:

\( A \) and \( B \) are invertible matrices of the same order such that \( (AB)^{-1}= 8 \), if \( |A| = 2 \), then \( |B| \) is:

The centre of the circle passing through \( (0, 0) \) and \( (1, 0) \) and touching the circle \( x^2 + y^2 = 9 \) is:

S $ \equiv x^2 + y^2 - 2x - 4y - 4 = 0 $ and $ S' \equiv x^2 + y^2 - 4x - 2y - 16 = 0 $ are two circles. The point $ (-2, -1) $ lies