List of top Questions asked in COMEDK UGET

Which of the following two molecular species are Diamagnetic in nature?

Match the names of reactions given in Column I with the appropriate reactions given in Column II

Based on Valence Bond Theory, match the complexes listed in Column I with the number of unpaired electrons on the central metal ion, given in Column II.

What is the wave number (Units cm$^{-1}$) of the longest wavelength transition in the Balmer series of the Hydrogen spectrum? $ Z = 1 $ for $ H $
Identify the correct statement regarding corrosion of iron rod left exposed to atmosphere.

Identify the final product formed when Benzamide undergoes the following reactions:

For a given reaction, $ X(g) + Y(g) \to Z(g) $, the order of reaction with respect to $ X $ and $ Y $ are $ m $ and $ n $ respectively. If the concentration of $ X $ is tripled and that of $ Y $ is decreased to one third, what is the ratio between the new rate to the original rate of the reaction?

Identify the end-product $ [D] $ formed when solution salicylate undergoes the following series of reactions.

Given are 4 statements related to the chemical properties of Glucose. Identify the two incorrect statements from the following.
What is the nature of the function $ f(x) = x^3 - 3x^2 + 4x $ on real numbers?
Evaluate: $ \cos^{-1} \left( \cos \frac{35\pi}{18} \right) - \sin^{-1} \left( \sin \frac{35\pi}{18} \right) $
The maximum value of $ P = 500x + 400y $ for the given constraints $ x + y \leq 200, \quad x \geq 20, \quad y \geq 4x, \quad y \geq 0 $
What is the probability of a randomly chosen 2-digit number being divisible by 3?
If $ \frac{dy}{dx} = y + 3 \quad \text{and} \quad y(0) = 2, \quad \text{then} \quad y(\log 2) \text{ is equal to:} $
If $ y = \sin^{-1} \left( \frac{5x + 12\sqrt{1 - x^2}}{13} \right) $ then $ \frac{dy}{dx} $ equals
The area bounded by the curve $ y = \cos x $, $ x = 0 $, and $ x = \pi $ is
If $ I_n = \int_0^\pi \tan^n x \, dx $, for $ n \geq 2 $, then $ I_n + I_{n-2} = $
If $ (1 - 4i)^3 = a + ib $, then the value of $ a $ and $ b $ is
Two finite sets have $ m $ and $ n $ number of elements respectively. The total number of subsets of the first set is 112 more than the total number of subsets of the second set. Then the values of $ m $ and $ n $ are respectively.
The integral $ \int e^x \left[ \frac{x^2 + 1}{(x+1)^2} \right] \, dx $
Value of $ \cos 105^\circ $
Find the value of 'b' such that the scalar product of the vector $ \hat{i} + \hat{j} + \hat{k} $ with the unit vector parallel to the sum of the vectors $ 2\hat{i} + 4\hat{j} - 5\hat{k} $ and $ b\hat{i} + 2\hat{j} + 3\hat{k} $ is unity.
The general solution of the differential equation $ (1 + \tan y)(dx - dy) + 2x \, dx \, dy = 0 $
The co-ordinate of the foot of the perpendicular from $ P(1, 8, 4) $ on the line joining $ R(0, -1, 3) $ and $ Q(2, -3, -1) $ is
If a real number $ a $ is such that $ \int_0^a x \, dx \leq a + 4 $, then what is the range of $ a $?