List of top Questions asked in COMEDK UGET

If $ y = \sqrt{\sin x + y} $, then find $ \frac{dy}{dx} $ at $ x = 0, y = 1 $.

If $ f(x) = \begin{cases} x, & 0 \leq x \leq 1 \\ 2x - 1, & x > 1 \end{cases} $, then:

Let A and B be two events such that $ P(A/B) = \frac{1}{2}, \quad P(B/A) = \frac{1}{3}, \quad \text{and} \quad P(A \cap B) = \frac{1}{6} $ Then, which one of the following is not true?
If $ \hat{i} + \hat{j} - \hat{k} $ and $ 2\hat{i} - 3\hat{j} + \hat{k} $ are adjacent sides of a parallelogram, then length of its diagonal is
If $ \frac{\cos x}{\cos(x - 2y)} = \lambda \quad \text{then} \quad \tan(x - y) \tan y = $
If $ y = f(x), \, p = \frac{dy}{dx}, \, q = \frac{d^2 y}{dx^2}, \text{ then } \frac{d^2 x}{dy^2} \text{ is equal to } $
The line joining two points $ A(2, 0) $ and $ B(3, 1) $ is rotated about $ A $ in an anticlockwise direction through an angle of $ 15^\circ $. If $ B $ goes to $ C $ in the new position, then the coordinates of $ C $ are:
The value of the integral $ \int_{1/3}^1 \frac{(x - x^3)^{\frac{1}{3}}}{x^4} \, dx $ is:
The mean of five observations is 4 and their variance is 5.2. If three of these observations are 1, 2, and 6, then the other two observations are:
The area of the region enclosed by the curve $ \left\{ (x, y) : 4x^2 + 25y^2 = 100 \right\} $ is:
Consider an infinite geometric series with first term $ a $ and common ratio $ r $. If the sum of infinite geometric series is 4 and the second term is $ \frac{3}{4} $, then:

If $3A + 4B^{t} = \left( \begin{array}{cc} 7 & -10 \\ 0 & 6 \end{array} \right) $ and $ 2B - 3A^{t} = \left( \begin{array}{cc} -1 & 18 \\ 4 & -6 \\ -5 & -7 \end{array} \right) $, then find $ (5B)^{t}$:
 

The area of the triangle whose vertices are $ (-2, a) $, $ (2, -6) $, and $ (5, 4) $ is 35 square units. Then the value of $ a $ is:
While shuffling a pack of cards, 3 cards were accidentally dropped, then find the probability that the missing cards belong to different suits?
The rate of change of the volume of a sphere with respect to its surface area $ S $ is
A polygon of $ n $ sides has 105 diagonals, then $ n $ is equal to
When $ 10^{19} $ electrons are removed from a neutral metal plate, the electric charge on it is
In an electrical circuit $ R, L, C $ and AC voltage source are all connected in series. When $ L $ is removed from the circuit, the phase difference between the voltage and the current in the circuit is $ \frac{\pi}{3} $. If instead $ C $ is removed from the circuit, the phase difference is again $ \frac{\pi}{3} $. The power factor of the circuit is
A string vibrates with a frequency of 200 Hz. When its length is doubled and tension is altered, it begins to vibrate with a frequency of 300 Hz. The ratio of the new tension to the original tension is
Two cells with the same emf $ E $ and different internal resistances $ r_1 $ and $ r_2 $ are connected in series to an external resistance $ R $. If the potential difference across the first cell is zero then the value of $ R $ is
The speeds of air-flow on the upper and lower surfaces of a wing of an aeroplane are $ v_1 $ and $ v_2 $, respectively. If $ A $ is the cross-sectional area of the wing and $ \rho $ is the density of air, then the upward lift is

A square wire of each side $ l $ carries a current $ I $. The magnetic field at the mid-point of the square

Two slabs are of the thicknesses $ d_1 $ and $ d_2 $. Their thermal conductivities are $ K_1 $ and $ K_2 $, respectively. They are in series. The free ends of the combination of these two slabs are kept at temperatures $ \theta_1 $ and $ \theta_2 $. Assume $ \theta_1>\theta_2 $. The temperature $ \theta $ of their common junction is
A galvanometer having a resistance of $ 8 \, \Omega $ is shunted by a wire of resistance $ 2 \, \Omega $. If the total current is 1 A, the part of it passing through the shunt will be
A ball is projected horizontally with a velocity of $ 5 \, \text{m/s} $ from the top of a building 19.6 m high. How long will the ball take to hit the ground?