List of top Questions asked in KEAM- 2024

If \( \frac{1}{\log_2 x} + \frac{1}{\log_3 x} + \frac{1}{\log_4 x} + \frac{1}{\log_5 x} + \frac{1}{\log_6 x} = 1 \), then the value of \( x \) is
Which of the following are the conditions for a reaction spontaneous at all temperatures?
Which of the following statement is correct?
The structure of MnO\(_4^-\) ion is:
A metal rod of length 1 m at 20°C is made up of a material of coefficient of linear expansion \( 2 \times 10^{-5} \, \text{°C}^{-1} \). The temperature at which its length is increased by 1 mm is:
In a combustion reaction, heat change during the formation of 40 g of carbon dioxide from carbon and dioxygen gas is (Enthalpy of combustion of carbon = -396 kJ mol\(^1\))
When benzene diazonium fluoroborate is heated with aqueous sodium nitrite solution in the presence of copper, the product formed is:
Mass numbers of two nuclei are in the ratio 2:3. The ratio of the nuclear densities would be:
If the complex numbers \( (2 + i)x + (1 - i)y + 2i - 3 \) and \( x + (-1 + 2i)y + 1 + i \) are equal, then \( (x, y) \) is
If \( \vec{a} \) and \( \vec{b} \) are non-collinear unit vectors and \( |\vec{a} + \vec{b}|^2 = 3 \), then \( (3\vec{a} + 2\vec{b}) \cdot (3\vec{a} - \vec{b}) \) is equal to:
If the sum of distances of a point from the origin and the line \( x = 3 \) is 8, then its locus is:
If \( A = \begin{bmatrix} 3 & 7 \\ 2 & 5 \end{bmatrix} \), then \( A^2 (\text{adj} A) \) is:
The coefficient of \( x^7 \) in the expansion of \( \left( \frac{1}{x + x^2} \right)^8 \) is
If \( \frac{|z - 5i|}{|z - 5i|} = 1 \), then
Which of the following material acts as a semiconductor at 298 K?
Electric conduction in a semiconductor is due to:

In the circuit given below, the current is: 

The terminal potential difference of a cell in the open circuit is 2 V. When the cell is connected to a 10$\omega$ resistor, the terminal potential difference falls to 1.5 V. The internal resistance of the cell is:
The IUPAC name of the coordination compound Hg[Co(SCN)\(_4\)] is
The domain of the function \( f(x) = \sqrt{7 - 8x + x^2} \) is:
In an LCR circuit, at resonance, the value of the power factor is:
A steady current of 2 A is flowing through a conducting wire. The number of electrons flowing per second in it is:
On heating an aldehyde with Fehling’s reagent, a reddish-brown precipitate is obtained due to the formation of
If \( f(x) = \frac{x}{1 - x} \), \( x \neq 1 \), then the inverse of \( f \) is:
A proton and a photon have the same energy. Then the de-Broglie wavelength of proton \( \lambda_p \) and wavelength of photon \( \lambda_0 \) are related by: