List of top Questions asked in COMEDK UGET

The degree of the differential equation \[ \left( 1 + \left( \frac{dy}{dx} \right)^2 \right)^{\frac{3}{4}} = \left( \frac{d^2y}{dx^2} \right)^{\frac{1}{3}} \]

If the mean of 4, 7, 2, 8, 6 and \( k \) is 7. Then the mean deviation from the mean of these observations is

Evaluate the value of \( (1.02)^8 \) using binomial theorem up to two decimal places.

Evaluate the integral \[ \int_0^{\frac{\pi}{2}} \log \left( \frac{5 + 4 \sin x}{5 + 4 \cos x} \right) \, dx \]

If \[ \int \frac{\sin x + \cos x}{\sqrt{1 + 2 \sin x \cos x}} \, dx = \varphi(x) + C, \text{ then } \varphi(x) = \]

The area of the region bounded by the ellipse \( \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1 \) is

If \( A(\text{adj} A) = \begin{bmatrix} 5 & 0 & 0 \\ 0 & 5 & 0 \\ 0 & 0 & 5 \end{bmatrix} \), then the value of \( |A| + |\text{adj} A| \) is equal to :

The point on the line \( x + y = 4 \) that lie at a unit distance from the line \( 4x + 3y = 10 \) is

If \[ A = \begin{bmatrix} 0 & -1 & 2 1 & 0 & 3 -2 & -3 & 0 \end{bmatrix} \] then \( A + 2A^T = \)

The length of the perpendicular from the point \( P(1, -1, 2) \) to the given line \[ \frac{x + 1}{2} = \frac{y - 2}{-3} = \frac{z + 2}{4} \]

Simplified expression of \[ 1 - \frac{\sin^2 y}{1 + \cos y} + \frac{1 + \cos y}{\sin y} - \frac{\sin y}{1 - \cos y} \]

On each working day of a school there are six periods. The number of ways in which five subjects are arranged if each subject is allotted at least one period and no period remains vacant is

Differentiate \( \log_a x \) with respect to \( a^x \)

Quadrilateral PQRS is inscribed inside a rectangle of dimensions \( 10 \, \text{cm} \times 8 \, \text{cm} \). The value of \( x \), if the area of the quadrilateral is minimum, is

A bag contains \( (n + 1) \) coins. It is known that one of these coins has a head on both sides, whereas the other coins are fair. One of these coins is selected at random and tossed. If the probability that the toss results in heads is \( \frac{7}{12} \), then the value of \( n \) is :

Integrating factor of the differential equation \[ \frac{dy}{dx} + y = \frac{x^3 + y}{x} \]

If \[ \binom{n+2}{8} : \, \binom{n-2}{4} = 57 : 16, \text{ then } n \text{ is } \]

If \[ y = (\sin^{-1} x)^2 + (\cos^{-1} x)^2, \] then \[ (1 - x^2) \frac{d^2y}{dx^2} - x \frac{dy}{dx} = \]

The function \( f(x) = \left\{ \begin{array}{ll} \frac{|x|}{x} & \text{if } x \neq 0 \\ 0 & \text{if } x = 0 \end{array} \right. \) is discontinuous at

The equations \( x = a(\theta + \sin \theta) \) and \( y = a(1 - \cos \theta) \) represent the equation of a curve. If \( \theta \) changes at a constant rate \( k \), then the rate of change of the slope of the tangent to the curve at \( \theta = \frac{\pi}{3} \) is

The area of the region enclosed by the lines \( 2x + y = 10 \), \( y = 1 \), \( y = 5 \) and the y-axis is

The curve \( 4y = 3x^4 - 2x^2 \) attains

If \( A = \frac{1}{\pi} \begin{bmatrix} \sin^{-1} \frac{1}{2} & \tan^{-1} \frac{x}{\pi} \sin^{-1} \frac{x}{\pi} & \cot^{-1} \sqrt{3} \end{bmatrix} \), then \( A - B \) is:

The length of the latus rectum of a conic \( 49y^2 - 16x^2 = 784 \) is

If \( \cos A = \frac{3}{4} \), then \( 32 \sin \frac{A}{2} \sin \frac{5A}{2} = \text{?} \)