List of top Questions asked in KEAM

A ball is thrown vertically upwards with an initial speed of 20 ms\(^{-1}\). The velocity (in ms\(^{-1}\)) and acceleration (in ms\(^{-2}\)) at the highest point of its motion are respectively:
The motion of a cylinder on an inclined plane is:
A long straight wire carrying a current 3 A produces a magnetic field \( B \) at a certain distance. The current that flows through the same wire will produce a magnetic field \( \frac{B}{3} \) at the same distance is:
An aqueous solution contains 20g of a non-volatile strong electrolyte \( {A}_2{B} \) (Molar mass = 60 g mol\(^{-1}\)) in 1 kg of water. If the electrolyte is 100% dissociated at this concentration, what is the boiling point of the solution? (Kb of water is 0.52 K kg mol\(^{-1}\))
What is the quantity of current required to liberate 16g of O\(_2\) (g) during electrolysis of water? (Given 1F = 96500C)

14g of cyclopropane burnt completely in excess oxygen. The number of moles of water formed is:

Strong intra-molecular hydrogen bond is present in:
A bag contains 10 green balls and 5 red balls. If two balls are selected randomly, then the probability that both are green balls, is:

The first term and the 6th term of a G.P. are 2 and \( \frac{64}{243} \) respectively. Then the sum of first 10 terms of the G.P. is:

Let \( A \) and \( B \) be two sets each containing more than one element. If \( n(A \times B) = 155 \), then \( n(A) \) is equal to:
The sum of the series \( \frac{1}{2^{10}} + \frac{1}{2^{11}} + \cdots + \frac{1}{2^{19}} \) is equal to:
For two sets \( A \) and \( B \), we have \( n(A \cup B) = 50 \), \( n(A \cap B) = 12 \), and \( n(A - B) = 15 \). Then \( n(B - A) \) is equal to:

Let \( f(x) = \log_e(x) \) and let \( g(x) = \frac{x - 2}{x^2 + 1} \). Then the domain of the composite function \( f \circ g \) is:

Phenol can be converted to salicylaldehyde by:
A reagent that can be used to reduce benzene diazonium chloride to benzene is:
If the fundamental frequency of the stretched string of length 1 m under a given tension is 3 Hz, then the fundamental frequency of the stretched string of length 0.75 m under the same tension is:

The general solution of the differential equation \( \frac{dy}{dx} = xy - 2x - 2y + 4 \) is:

The product of the total electric flux emanating from a closed surface enclosing a charge \( q \) in free space is (\( \epsilon_0 \) - electrical permittivity of free space):

Coordination compounds exhibit different types of isomerism. Some complexes are given in Column I, and the type of isomerism is given in Column II.

\[ \begin{array}{|l|l|} \hline \textbf{Column I} & \textbf{Column II} \\ \hline (a) [\text{Pt(NH}_3)_2\text{Cl}_2] & (i) \text{Ionisation isomerism} \\ \hline (b) [\text{Co(en)}_3]^{3+} & (ii) \text{Linkage isomerism} \\ \hline (c) [\text{Cr(NH}_3)_5(\text{SO}_4)]\text{Br} & (iii) \text{Optical isomerism} \\ \hline (d) [\text{Co(NH}_3)_5(\text{NO}_2)]\text{Cl}_2 & (iv) \text{Geometrical isomerism} \\ \hline \end{array} \]

Which one of the following compounds can exhibit both optical isomerism and geometrical isomerism?

An assignment of probabilities for outcomes of the sample space \( S = \{1, 2, 3, 4, 5, 6\} \) is as follows:

\[ \begin{array}{c|c c c c c c} 1 & 2 & 3 & 4 & 5 & 6 \\ \hline k & 3k & 5k & 7k & 9k & 11k \end{array} \]

If this assignment is valid, then the value of \( k \) is:

Which one of the following statement is INCORRECT?

Let \( f(x) = \frac{x^2 + 40}{7x} \), \( x \neq 0 \), \( x \in [4,5] \). The value of \( c \) in \( [4,5] \) at which \( f'(c) = -\frac{1}{7} \) is equal to:

A particle is displaced from P \( (3i + 2j - k) \) to Q \( (2i + 2j + 2k) \) by a force \( \mathbf{F} = i + j + k \). The work done on the particle (in J) is:
When a cricketer catches a ball in 30 s, the force required is 2.5 N. The force required to catch that ball in 50 s is: