List of top Questions asked in KEAM

Evaluate the integral: \[ \int \frac{2x^2 + 4x + 3}{x^2 + x + 1} \, dx \]
Evaluate the following statement: \[ f(x) = \sin(|x|) - |x| \text{ is not differentiable at } x = \underline{\hspace{2cm}} \]
Methyl fluoride is prepared by heating methyl bromide in the presence of AgF. This reaction is known as
Highest limiting conductance at 298 K is:
Evaluate the integral: \[ \int \frac{\sin(2x)}{\sin(x)} \, dx \]
Energy dissipated per unit time by a wire of resistance \(2R\) connected to a 2V battery.
If $ \tan\left( \alpha - \frac{\pi}{12} \right) = \frac{1}{\sqrt{3}} $, find $ \alpha $.
Minimum wavelength of Brackett series corresponds to transition from $ n_1 $ to $ n_2 $, where $ n_1 $ and $ n_2 $ are respectively...
If maximum height and range are equal in projectile motion, then $ \tan \theta = ... $:

The following data were obtained for the reaction: \[ 2NO(g) + O_2(g) \rightarrow 2N_2O(g) \] at different concentrations: 

 The rate law of this reaction is:

When C6H5CHO reacts with the mixture of HNO3 and H2SO4 at 273-283K, it gives

Match the following: 

What is the color of the complex \([Ni(en)_3]^{2+}\) in water?

Benzene diazonium chloride on treatment with reagent 'X' gives iodobenzene. The reagent ‘X’ is

The order of acidity of the following compounds is:
 (i) o-Nitrophenol 
(ii) Phenol 
(iii) o-Cresol 
(iv) Ethanol

An ideal Carnot engine has an efficiency of 40 %. The ratio of the temperature of the sink to that of the source is
If a particle is moving with a momentum of (2 × 1010) h kg·m/s, then the de Broglie wavelength associated with it (in angstrom) is (where h is Planck's constant)
The angular momentum of the electron revolving in the 2nd orbit is
In the nuclear process, 1122Na → 1022Ne + e+ + νe, then X is
In a semiconductor crystal, the total number of electrons in the outer shell is 4N . At absolute zero, the number of energy states of valence and conduction band are respectively
If an electron moves with a velocity \( v \) in a magnetic field \( B \), the magnetic force on the electron is maximum when the angle between \( v \) and \( B \) is
The eye defect astigmatism can be corrected by using a
If the frequency of an electromagnetic wave is 2 MHz, then the time period of oscillation of the accelerated charge is
The intensity of a polarized light can be controlled by a second polarizer from
The flux linked with a coil at any instant is given by \( \Phi = 5t^2 - 25t - 150 \) (in SI units). The emf induced in the coil at \( t = 2 \) s is