List of top Questions asked in COMEDK UGET

Evaluate the integral \[ \int_0^2 x^2 + 2x - 3 \, dx \]
Bag A contains 3 white and 2 red balls. Bag B contains only 1 white ball. A fair coin is tosse(D) If head appears then 1 ball is drawn at random from bag A and put into bag (B) However if tail appears then 2 balls are drawn at random from bag A and put into bag (B) Now one ball is drawn at random from bag (B) Given that the drawn ball from B is white, the probability that head appeared on the coin is
In a 12 storey house, 10 people enter a lift cabin. It is known that they will leave the lift in pre-decided groups of 2, 3, and 5 people at different storeys. The number of ways they can do so if the lift does not stop up to the second storey is
The minimum value of \( Z = 3x + 5y \), given subject to the constraints \( x + y \geq 2 \), \( x + 3y \geq 3 \), \( x, y \geq 0 \), is:
\[ \lim_{x \to 0} \frac{a^x - b^x}{x} \text{ is equal to:} \]
The coordinates of the vertices of the triangle are \( A(-2, 3, 6) \), \( B(-4, 4, 9) \), and \( C(0, 5, 8) \). The direction cosines of the median \( BE \) are:
How many factors of \( 2^5 \times 3^6 \times 5^2 \) are perfect squares?
The general solution of the differential equation \[ (1 + y^2) \, dx = ( \tan^{-1} y - x ) \, dy \] is:
The function \( f(x) = \frac{x}{2} + \frac{2}{x} \) has a local minimum at:
If the direction ratios of two lines are given by \( 3lm - 4ln + mn = 0 \) and \( l + 2m + 3n = 0 \), then the angle between the lines is:
Which of the following is a singleton set?
If the conjugate of \( (x + iy)(1 - 2i) \) be \( 1 + i \), then:
If the length of the major axis of an ellipse is 3 times the length of the minor axis, then its eccentricity is:
A die is thrown twice and the sum of numbers appearing is observed to be 8. What is the conditional probability that the number 5 has appeared at least once?
The particular solution of \( e^{\frac{dy}{dx}} = 2x + 1 \) given that \( y = 1 \) when \( x = 0 \) is:
If \( A = \left( \begin{matrix} 1 & 2 \\ 0 & 1 \end{matrix} \right), \, P = \left( \begin{matrix} \cos \theta & \sin \theta \\ -\sin \theta & \cos \theta \end{matrix} \right), \, Q = P^T A P \), then \( PQ^{2014} \) is:
\( A \) and \( B \) are invertible matrices of the same order such that \( (AB)^{-1}= 8 \), if \( |A| = 2 \), then \( |B| \) is:
The centre of the circle passing through \( (0, 0) \) and \( (1, 0) \) and touching the circle \( x^2 + y^2 = 9 \) is:

Pick out the incorrect statement(s) from the following.

1.  Glucose exists in two different crystalline forms, \( \alpha \)-D-glucose and \( \beta \)-D-glucose.
2.  \( \alpha \)-D-glucose and \( \beta \)-D-glucose are anomers.
3.  \( \alpha \)-D-glucose and \( \beta \)-D-glucose are enantiomers.
4.  Cellulose is a straight chain polysaccharide made of only \( \beta \)-D-glucose units.
5.  Starch is a mixture of amylase and amylopectin, both contain unbranched chain of \(\alpha\)-D-glucose units.

Which of the following is incorrect?

Rank the following compounds in order of increasing basicity.

Ammoniacal silver nitrate forms a white precipitate easily with
Consider the following equilibrium, $$ 2 \text{NO}(g) \rightleftharpoons \text{N}_2 (g) + \text{O}_2 (g); K_1 = 2.4 \times 10^{20} $$ $$ \text{NO}(g) + \frac{1}{2} \text{Br}_2 (g) \rightleftharpoons \text{NOBr}(g); K_2 = 1.4 $$ Calculate $ K_C $ for the reaction, $$ \frac{1}{2} \text{N}_2 (g) + \frac{1}{2} \text{O}_2 (g) + \frac{1}{2} \text{Br}_2 (g) \rightleftharpoons \text{NOBr}(g) $$
Which of the following is incorrect regarding Henry's law?
t-butyl chloride preferably undergo hydrolysis by