List of top Questions asked in COMEDK UGET- 2025

Given \( Z = 80x + 120y \), subject to constraints are \( x + 3y \leq 30; 3x + 4y \leq 60; x \geq 0; y \geq 0 \). \( P \) is one of the corner points of the feasible region for the given Linear Programming Problem. Then the coordinate of \( P \) is

The angle between two lines is \(45^\circ\) and slope of one line is \( \frac{1}{4} \) then which is the possible value of the slope of the other line.

If \( X = \begin{bmatrix} 1 & 0 0 & 1 \end{bmatrix} \) and \( Y = \begin{bmatrix} 0 & 1 -1 & 0 \end{bmatrix} \) and \( B = \begin{bmatrix} \cos \theta & \sin \theta -\sin \theta & \cos \theta \end{bmatrix} \), then \( B \) equals:

If the standard deviation of \( 0,1,2,3,\ldots,9 \) is \( k \), then the standard deviation of \( 10,11,12,13,\ldots,19 \) will be:

Two numbers are selected at random from integers 1 to 9. If their sum is even, what is the probability that both the numbers are odd?

The area of a triangle formed by the lines joining the vertex of the parabola \( x^2 = \lambda y \) to the ends of its latus rectum is 18 sq units then the value of \( \lambda \) is

Kiran purchased 3 pencils, 2 notebooks and one pen for INR 41. From the same shop Manasa purchased 2 pencils, one notebook and 2 pens for INR 29, while Shreya purchased 3 pencils, 2 notebooks and 2 pens for INR 44. The above situation can be represented in matrix form as \( AX = B \). Then \( \text{adj}(A) \) is equal to

Arrange the following in the increasing order of their covalent character.
\[ CaF_2;\; CaCl_2;\; CaBr_2;\; CaI_2 \]

A function \( f \) from the set of natural numbers to integers defined by \[ f(n) = \begin{cases} \frac{n-1}{2}, & \text{when } n \text{ is odd} -\frac{n}{2}, & \text{when } n \text{ is even} \end{cases} \] is

The value of \( \frac{\sin^2 20^\circ + \cos^4 20^\circ}{\sin^4 20^\circ + \cos^2 20^\circ} \) is :

Which of the following is the most stable free radical?

Identify [X] used in the given reaction.
\[ [X] \xrightarrow{\text{Cu / 573 K}} [Y] \]
\[ [Y] \xrightarrow[(ii)\ H_2O/H^+]{(i)\ CH_3MgBr} \text{Tert.butyl alcohol (major product)} \]

Two statements, one Assertion and the other Reason are given. Identify the correct option
Assertion : Primary and secondary amides on treatment with \( Br_2 \) and alcoholic \( NaOH \) yield primary and secondary amines respectively and the reaction involves stepping down the series.
Reason : The reaction occurs due to the migration of alkyl group from Carbonyl carbon atom to the Nitrogen atom with elimination of carbonyl group as the carbonate salt.

Choose the incorrect statement from the following.

The enthalpies of combustion of \( H_2 \), \( C \) (graphite) and \( C_2H_6 (g) \) are \( -286.0,\; -394.0 \) and \( -1560.0 \, kJ \, mol^{-1} \) at \( 25^\circ C \) and 1 atm pressure. The enthalpy of formation of ethane is :

Which one of the following is the product (Z) formed at the end of the given reaction:
\[ \text{Propan-1-ol} + SOCl_2 \rightarrow [X] \]
\[ [X] + HC \equiv C^-Na^+ \rightarrow [Y] \]
\[ [Y] + H_2SO_4/HgSO_4,\; 330K \rightarrow [Z] \]

Identify the Carbonyl compound which will not be formed when hydration of Alkynes is carried out with dil. \( H_2SO_4/Hg^{2+} \) at 333 K. Acetone, Butanal, Ethanal, Butanone.

Identify the type of reaction:

At 300 K the vapour pressure of an ideal solution containing 1.0 mole each of volatile liquids X and Y is 1000 mm. Keeping the temperature constant, when 2.0 moles of liquid X are added to the solution, its vapour pressure increases by 200 mm. Calculate the vapour pressure of X and Y in their pure state.

During a chemical reaction \( X \rightarrow Y \), the rates of reaction starting with initial concentrations of \( X \) as \( 4.0 \times 10^{-3} M \) and \( 2.0 \times 10^{-3} M \) are \( 4.8 \times 10^{-4} \, mol \, L^{-1}/s \) and \( 1.2 \times 10^{-4} \, mol \, L^{-1}/s \) respectively. What is the order of reaction with respect to \( X \)?

The maximum polarity and dipole moment among the following is :