List of top Questions asked in KEAM- 2024

The radius of gyration of a circular disc of radius \( R \), rotating about its diameter is:
The integral \( \int \frac{dx}{1 + e^x} \) is:
An electric appliance draws 3A current from a 200 V, 50 Hz power supply. The amplitude of the supply voltage is nearly:
A coordination compound of cobalt acts as an antipericious anemia factor is:
A spherical metal shell \( A \) of radius \( R_A \) and a solid metal sphere \( B \) of radius \( R_B \) (\( R_B<R_A \)) are kept far apart and each is given charge \( +Q \). If they are connected by a thin metal wire and \( Q_A \) and \( Q_B \) are the charge on \( A \) and \( B \), respectively, then:
If the number of electron-hole pairs per cm\(^3\) of an intrinsic Si wafer at temperature 300 K is \(1.1 \times 10^{10}\) and the mobilities of electrons and holes at 300 K are 1500 and 500 cm\(^2\) per volt, second, respectively, then the conductivity of the Si wafer at this temperature (in \(\mu\)mho cm\(^{-1}\)) is nearly:
A tuning fork vibrating at 300 Hz, initially in air, is then placed in a trough of water. The ratio of the wavelength of the sound waves produced in air to that in water is (Given that the velocity of sound in water and in air at that place are 1500 m/s and 350 m/s respectively):
The oscillating magnetic field in a plane electromagnetic wave is given by \(B_y = (8 \times 10^{-6}) \sin[2 \pi \times 10^{11} t + 200 \pi x] \) tesla. Then the wavelength of the electromagnetic wave (in cm) is:

The y-intercept of the graph between the terminal voltage \(V\) with load resistance \(R\) along \(y\) and \(x\) – axis, respectively, of a cell with internal resistance \(r\), as shown, is: 

The volume of ethanol required to prepare 3 L of 0.25 M aqueous solution is (density of ethanol = 0.36 kg L\(^{-1}\), molar mass = 60 g mol\(^{-1}\)):
The value of \( K_c \) for the equilibrium reaction \[ 2 {NO}_2(g) \rightleftharpoons {N}_2{O}_4(g) \] is \(2 \times 10^{-40} \, {mol}^{-1} \, {dm}^3\) at 298 K. If the equilibrium concentration of \({NO}_2\) is \(2 \times 10^{-2}\) M, the concentration of \({N}_2{O}_4\) is:
Let \( \mathbf{u}, \mathbf{v}, \mathbf{w} \) be vectors such that \( \mathbf{u} + \mathbf{v} + \mathbf{w} = \mathbf{0} \). If \( |\mathbf{u}| = 3 \), \( |\mathbf{v}| = 4 \), and \( |\mathbf{w}| = 5 \), then \( \mathbf{u} \cdot \mathbf{v} + \mathbf{w} \cdot \mathbf{u} \) is:
The quantity of electricity required to produce 18 g of Al from molten Al\(_2\)O\(_3\) is (Atomic mass of Al = 27):
Which of the following mixture forms azeotrope?
A block of mass \( M \) is placed on the floor of a lift at the center. The acceleration required for the lift to descend so that the block exerts a force of \( \frac{Mg}{4} \) on the lift floor is:

The type of processes represented by the curves X and Y are: 

The reaction, \( 2I^- + S_2O_8^{2-} \rightarrow I_2 + 2SO_4^{2-} \), is catalysed by:

The decreasing order of stability of the following carbocations is: 
\( (i) \text{(CH}_3\text{)}_3\text{C}^+ \quad (ii) \text{(CH}_3\text{)}_2\text{C-CH}_2^+ \quad (iii) \text{CH}_3\text{CH}_2\text{-CH}_2^+ \)

The coefficient of \( x^3 \) in the binomial expansion of \( \left( \frac{1}{\sqrt{x}} - x \right)^6 \) is:
Evaluate \( \binom{10}{1} + \binom{10}{2} + \dots + \binom{10}{10} \):
The mean deviation of the numbers 3, 10, 10, 4, 7, 10 and 5 from the mean is:
A path length of 1m in air is equal to a path length of \(x\) m in a medium of refractive index 1.5. Then the value of \(x\) (in meters) is:
The displacement-time graph of a moving body is a straight line making a 45\(^{\circ}\) angle with the time axis. The body moves with:
The major products formed when one mole of \( \text{CH}_3\text{CH}_2\text{CH}(\text{CH}_3)\text{CH}_2\text{OCH}_2\text{CH}_3 \) is treated with one mole of HI are:
The reagent used for the conversion of but-2-ene to ethanol is: