List of top Questions asked in COMEDK UGET

The relationship between \( a \) and \( b \) for the continuity of the function \( f(x) = \begin{cases} ax + 1, & x \leq 3 \\ bx + 3, & x \gt 3 \end{cases} \) at \( x = 3 \) is __________.
\( \int_{0}^{1} x(1 - x)^{99} \, dx = \)
Value of the determinant of a matrix \( A \) of order \( 3 \times 3 \) is 7Then the value of the determinant formed by the cofactors of matrix \( A \) is
Let \( f(x) = x\sqrt{4ax - x^2, \; a > 0 \) then \( f'(x) \) at \( x = 2a \) is:}
If \( \sin x + \sin^2 x = 1 \) then \( \cos^8 x + 2\cos^6 x + \cos^4 x \) is equal to:
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.
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
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 \( A = \begin{bmatrix} a & b \\ b & a \end{bmatrix} \) and \( (AI)^2 = \begin{bmatrix} \alpha & \beta \\ \beta & \alpha \end{bmatrix} \), where \( I \) is the identity matrix, then __________.
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
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:
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
The value of \( \frac{\sin^2 20^\circ + \cos^4 20^\circ}{\sin^4 20^\circ + \cos^2 20^\circ} \) is :
The solution for the following system of inequalities \( 3x - 7 < 5 + x \) and \( 11 - 5x \leq 1 \) on a real number line is
If \( \int \frac{\sin 2x}{(1+\sin x)(2+\sin x)} \, dx = a \log |1+\sin x| - b \log |2+\sin x| + c \), then the value of \( a \) and \( b \) is __________.
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
What are the intermediates formed during the reactions A and B ?
A. Reimer-Tiemann reaction.
B. Dehydration of alcohols in the slow rate determining step.
Which of the following is the most stable free radical?
Arrange the following in the increasing order of their covalent character.
\[ CaF_2;\; CaCl_2;\; CaBr_2;\; CaI_2 \]
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 :
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.
Choose the incorrect statement from the following.
Identify [X] used in the given reaction.
\[ [X] \xrightarrow{\text{Cu / 573 K}} [Y] \]
\[ [Y] \xrightarrow[(ii)\ H_2O/H^+]{(i)\ CH_3MgBr} \text{Tert.butyl alcohol (major product)} \]
Which one of the following is the product (Z) formed at the end of the given reaction:
\[ \text{Propan-1-ol} + SOCl_2 \rightarrow [X] \]
\[ [X] + HC \equiv C^-Na^+ \rightarrow [Y] \]
\[ [Y] + H_2SO_4/HgSO_4,\; 330K \rightarrow [Z] \]