List of top Mathematics Questions asked in COMEDK UGET

The expression \[ \frac{\tan\left(x-\frac{\pi}{2}\right)\cos\left(\frac{3\pi}{2}+x\right)-\sin^2\left(\frac{7\pi}{2}-x\right)} {\cos\left(x-\frac{\pi}{2}\right)\tan\left(\frac{3\pi}{2}+x\right)} \] simplifies to:

The function \[ x+y=\tan^{-1}y \] is the solution of which of the following differential equations?

The absolute maximum and minimum values of the function \[ f(x)=\sin x+\sqrt3\cos x,\quad x\in[0,\pi] \] are:

Let point \( Q \) be the image of point \( P(2,-1) \) in the line \[ 3x+5=4y. \] Find the area of the circle that has the segment \( PQ \) as the diameter.

Every term of a geometric progression is positive, and every term is the sum of the two preceding terms. Then the common ratio of the geometric progression is:

Cards are numbered from \(12\) to \(51\). Two cards are drawn one after the other without replacement. Find the probability that one card is a multiple of \(6\) and the other card is a multiple of \(8\).

Let \( A \) be a square matrix of order \(3\times3\). If \( |A|=-4 \), then the value of \[ \left|\frac{A^{-1}}{-2}\right| \] is:

Let \( A \) and \( B \) be two subsets of \( \{1,2,3,_____,44,45\} \) such that \[ A = \{x : x \text{ is divisible by } 3 \text{ and } 4\} \] \[ B = \{x : x \text{ is a perfect square number}\} \] Then \( n(B-A) \) equals

The foci of a hyperbola are the same as those of the ellipse \[ 9x^2+16y^2=144 \] If the length of the transverse axis of the hyperbola is $2\cos\alpha$, then its equation is:

\[ \int \frac{dx}{x\sqrt{x^2+4}}= \]

If the inverse of a matrix exists, then the matrix is called:

If \[ A= \begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix} \] then $A$ is:

If the matrix \[ A= \begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix} \] then the value of $|A|$ is:

If $A$ is a skew-symmetric matrix of order $3$, then $|A|$ is:

If the system of equations \[ x+y+z=6 \] \[ x+2y+3z=14 \] \[ 2x+y+z=7 \] has solution $(x,y,z)$, then the value of $x+y+z$ is:

If \[ \begin{vmatrix} 1 & 1 & 1 \\ a & b & c \\ a^2 & b^2 & c^2 \end{vmatrix}=0 \] then:

If $\dfrac{dy}{dx}=y\tan x$, then the solution of the differential equation is:

The order and degree of the differential equation \[ \left(\frac{d^2y}{dx^2}\right)^3+\left(\frac{dy}{dx}\right)^2+y=0 \] are respectively:

If the tangent at any point $(x,y)$ of a curve intercepts equal lengths on the coordinate axes, then the differential equation of the curve is:

If $y=e^{mx}\sin(nx)$, then the value of \[ \frac{d^2y}{dx^2}-2m\frac{dy}{dx}+(m^2+n^2)y \] is:

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

If $\log y=\log(\sin x)-x^2$, then \[ \frac{d^2y}{dx^2}+4x\frac{dy}{dx}+4x^2y= \]

An open hemispherical storage tank has radius $13$ m. Oil flows into the tank such that the depth $h$ of oil in the tank changes at the rate of $3$ m/hr. When $h=1$ m, the rate of change of the area of the top surface of the oil is:

If the equation of the tangent to the parabola $y^2=4ax$ at the point $(at^2,2at)$ is perpendicular to the line $x+y=1$, then the value of $t$ is:

If the mean and variance of the numbers $2, 4, 6, 8, 10$ are $\mu$ and $\sigma^2$ respectively, then the value of $\mu + \sigma^2$ is: