List of top Questions asked in KEAM- 2024

A particle having mass 2000 times that of an electron travels with a velocity thrice that of the electron. The ratio of the de Broglie wavelength of the particle to that of the electron is
The process by which the electrons can come out of the metal in a spark plug is:
The energy required to excite the hydrogen atom from its first excited state to second excited state is:
In gamma emission, the nucleus emits
If the initial decay rate of a radioactive sample is \( R_0 \), then the decay rate after a half-life time \( T_{1/2} \) is
If the conductivity of the material lies in the range \(10^2 - 10^8 \, \Omega^{-1}m^{-1}\), then it is a
The thickness of the depletion layer on either side of the p-n junction is of the order of
The angle between \( \vec{A} \times \vec{B} \) and \( \vec{B} \times \vec{A} \) is:
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:
All real gases behave like an ideal gas at:
The radiations used in LASIK eye surgery are:
An external voltage \( V \) is supplied to a semiconductor diode having built-in potential \( V_0 \). The effective barrier height under forward bias 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:
Phenol can be converted to salicylaldehyde by:

For \(1 \leq x<\infty\), let \(f(x) = \sin^{-1}\left(\frac{1}{x}\right) + \cos^{-1}\left(\frac{1}{x}\right)\). Then \(f'(x) =\)

A reagent that can be used to reduce benzene diazonium chloride to benzene is:

\[ \int_0^{\frac{\pi}{4}} (\tan^3 x + \tan^5 x) \, dx \]

Let \( I = \int_{-\frac{\pi}{4}}^{\frac{\pi}{4}} \frac{\tan^2 x}{1+5^x} \, dx \). Then:

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

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

\[ \cos^{-1} \left( \cos \left( \frac{-7\pi}{9} \right) \right) = \]

\[ \int \left( \frac{\log_e t}{1+t} + \frac{\log_e t}{t(1+t)} \right) dt \]

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