List of top Questions asked in KEAM

The temperature of the source and sink of a heat engine are 127°C and 27°C respectively. By how much should the temperature of the source be increased so as to double the efficiency?
A first-order reaction is 75 percent completed in 6000s. What is the half-life?
Evaluate the following integral: \[ \int_{-\frac{\pi}{2}}^{\frac{\pi}{2}} \left( x^4 + x^3 + x \right) \cos x \, dx \]
Evaluate the integral: \[ \int \frac{\sin(2x)}{\sin(x)} \, dx \]
If \[ \frac{x}{4} + \frac{x}{3} < 13, \text{ then } x \in \]
Find the integral: \[ \int \left( \sin^{-1} \sqrt{x} + \cos^{-1} \sqrt{x} \right) \, dx \]
Find the limit: \[ \lim_{x \to 0} \frac{\sin[x]}{[x]}, \text{ where } [x] \text{ represents greatest integer function} \]
Find the limit: \[ \lim_{x \to 0} \frac{\sin(\pi \sin^2 x)}{x^2} \]

Find the mean deviation of the following data: 

A guitar string is vibrating in the third harmonic. The number of nodes and antinodes present are:
Equation of line through (0, 0, 1) and (1, 1, 0)
Evaluate the following integral: \[ \int e^x \left[\frac{1}{1+x(1+x)^2}\right] dx \]
Water flows through a pipe with velocity \( V_1 = 3 \, \text{m/s} \) where the area of the pipe is \( A_1 \). What is the velocity \( V_2 \), where the diameter of the pipe is half of that at area \( A_1 \)?
Find the minimum of the function \[ f(x) = |x+2| \]
Find the \( \Delta G \) during the reaction: \[ \text{H}_2\text{O}(l) \rightleftharpoons \text{H}_2\text{O}(g) \quad \Delta S = +1 \, \text{kJ/mol} \, \text{at} \, 100^\circ C \]
Coefficient of friction is the ratio of?
A block is tied to a string of length 98 cm and is rotated in a horizontal circle. Find the angular velocity if the centripetal acceleration \( a = g \).
According to Huygen's principle, secondary wavelets move:
\( E^\circ_{\text{Cell}} = 1.1 \, \text{V}. \, \text{Find} \, E_{\text{Cell}} \, \text{for the reaction:} \, \text{Zn} + \text{Cu}^{2+} \, (0.1M) \rightleftharpoons \text{Zn}^{2+} \, (0.001M) + \text{Cu} \)
Alkali metal with highest first ionization enthalpy is:
In which of the following \( K_c = K_p \)? a) \( \text{PCl}_5(g) \rightleftharpoons \text{PCl}_3(g) + \text{Cl}_2(g) \) b) \( \text{H}_2(g) + \text{I}_2(g) \rightleftharpoons 2\text{HI}(g) \)
When a rotating disc suddenly shrinks in radius, what happens to the angular velocity \( \omega \)?
If \[ (a - 2)^2 + (b - 2)^2 + (c - 2)^2 = 0, \text{ then } a + b + c = \]
Name of the reaction in which benzoyl chloride is converted to benzaldehyde is
Given that \( \mathbf{a} \times (2\hat{i} + 3\hat{j} + 4\hat{k}) = (2\hat{i} + 3\hat{j} + 4\hat{k}) \times \mathbf{b} \), \( |\mathbf{a} + \mathbf{b}| = \sqrt{29} \), \( \mathbf{a} \cdot \mathbf{b} = ? \)