List of top Questions asked in COMEDK UGET

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:

If the vectors \(\vec a=2\hat i+3\hat j-\hat k\) and \(\vec b=\hat i-2\hat j+4\hat k\), then \(\vec a\cdot\vec b\) is:

A company is migrating its database, and two software engineers, Ishaan and Kavya, take turns running a data-sync script that has a constant success rate of \(\dfrac38\) per attempt. If Ishaan initiates the first attempt and they persist until the migration is successful, what is the probability that Kavya is the one who initiates the successful sync?

Let the population of a species of birds surviving at a time \(t\) be governed by the differential equation \[ \frac{dp}{dt}-p=-100 \] If \(p(0)=50\), then \(p(-\ln2)\) is equal to:

\[ \int(\sin^6x+\cos^6x+3\sin^2x\cos^2x)\,dx= \]

If the two ends of the major axis of an ellipse are \((5,0)\) and \((-5,0)\) and one focus lies on the line \(3x-5y-9=0\), then its equation is:

If \[ \lim_{x\to0}\left(\frac{p\sin2x+1-\cos2x}{x+\tan x}\right)=1, \] then the value of $p$ is: