List of top Questions asked in COMEDK UGET

The approximate value of $ f(5.001) $, $\text{where} $ $f(x) = x^3 - 7x^2 + 10 $

Let $ f(x) = a + \left( (x - 4) \right)^4 / 9 $, $\text{ then minima of } $ f(x) $\text{ is} $

The circle $x^2 + y^2 + 3x - y + 2 = 0$ cuts an intercept on X-axis of length

The points of intersection of circles $ (x + 1)^2 + y^2 = 4 \quad \text{and} \quad (x - 1)^2 + y^2 = 9 \quad \text{are} \quad (a, \pm b), \quad \text{then} \quad (a, b) \quad \text{equals to} $

The value of $ \lim_{x \to 0} \frac{e^{ax} - e^{bx}}{2x} \text{ is equal to} $

The slope of the tangent to the curve, $ y = x^2 - xy $ at $ (1, \frac{1}{2}) $ is

The value of $a^{\log_b c} - c^{\log_b a}$, where $a, b, c>0$ but $a, b, c \neq 1$, is

An air bubble in water ($ \mu = \frac{4}{3} $) is shown in the figure. The apparent depth of the image of the bubble in a plane mirror viewed by the observer is.

If the sum of 12th and 22nd terms of an AP is 100, then the sum of the first 33 terms of an AP is

In the expansion of (1 - 3x + 3x² - x³)²ⁿ, the middle term is

The chemical formula of Lucas reagent is

There are two identical containers $C_1$ and $C_2$ containing identical gases. Gas in $C_1$ is reduced to half of its original volume adiabatically, while the gas in container $C_2$ is also reduced to half of its initial volume isothermally. Find the ratio of final pressure in these containers. $\gamma$ be the adiabatic constant)

During the phenomenon of resonance

Shade the feasible region for the inequalities
$ 6x + 4y \leq 120 $, $ 3x + 10y \leq 180 $, $ x, y \geq 0 $ in a rough figure.

A source of sound emits sound waves at frequency $ f_0 $. It is moving towards an observer with fixed speed $ v_s $ ($ v_s < v $, where $ v $ is the speed of sound in air). If the observers were to move towards the source with speed $ v_0 $, one of the following two graphs (A and B) will give the correct variation of the frequency $ f $ heard by the observer as $ v_0 $ changes.

A plane glass mirror of thickness 3 cm of material of $ \mu = \frac{3}{2} $ is silvered on the black surface. When a point object is placed 9 cm from the front surface of the mirror, then the position of the brightest image from the front surface is:

An ideal gas is taken through the cycle $ A \to B \to C \to A $, as shown in the figure. If the net heat supplied to the gas in the cycle is 5 J, the work done by the gas in the process $ C \to A $ is

A series L-C-R circuit is connected to an AC source of 220V and 50 Hz shown in figure. If the readings of the three voltmeters $ V_1, V_2, $ and $ V_3 $ are 65V, 415V, and 204V respectively, the value of inductance and capacitance will be

The displacement $ x $ of a particle in a straight line motion is given by $ x = 1 - t - t^2 $. The correct representation of the motion is

Which of the following diagram represents the variation of the electric field with distance $ r $ from the centre of a uniformly charged non-conducting sphere of radius $ R $?

From the following $ p-V $ diagram, an ideal gas undergoing a change of state from A to B. Four different processes I, II, III, and IV as shown in the figure may lead to the same change of state.

A regular hexagon of side $ m $, which is a wire of length 24 m, is coiled on that hexagon. If current in hexagon is $ I $, then the magnetic moment is

Which of the following gate gives the similar output as the output of the circuit diagram shown in the figure?

Ultraviolet light of wavelength 99 nm falls on a metal plate of work function 1.0 eV. If the mass of the electron is $ 9.1 \times 10^{-31} $ kg, the wavelength of the fastest photoelectron emitted is:

In Young's double slit experiment, the fringe width is found to be 0.4 mm. If the whole apparatus is immersed in a liquid of refractive index $ \frac{4}{3} $ without changing the geometrical arrangement, the new fringe width will be: