List of top Questions asked in KEAM

In which of the following \( K_c = K_p \)? a) \( \text{PCl}_5(g) \rightleftharpoons \text{PCl}_3(g) + \text{Cl}_2(g) \) b) \( \text{H}_2(g) + \text{I}_2(g) \rightleftharpoons 2\text{HI}(g) \)
Given the following concentrations and rates, which one corresponds to the rate law for the reaction? \[ [A] = 0.10 \quad [D] = 0.2 \quad \text{Rate} = 0.2 \] \[ [A] = 0.2 \quad [D] = 0.2 \quad \text{Rate} = 0.4 \] \[ [A] = 0.10 \quad [D] = 0.1 \quad \text{Rate} = 0.05 \]
Friedel Craft's reaction is an example of:
Which of the following is an ambidentate ligand? a) \( \text{C}_2 \text{O}_4^{2-} \) b) \( \text{CN}^- \) c) \( \text{NH}_3 \)
Pressure of pure benzene is 0.75. When 0.2g of a non-volatile solute is added to 39g of benzene, pressure changes to 0.745. The molar mass of solute is?
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?
If \( n \) cells of emf \( E \) and internal resistance \( r \) are connected in parallel, what is the equivalent emf and internal resistance of the combination?
A guitar string is vibrating in the third harmonic. The number of nodes and antinodes present are:
A rod of length 0.5 m moves with a velocity of 3 m/s in a perpendicular magnetic field of strength 2 T. Find the emf induced across its ends.
The center of mass of a rod of length \( l \) is at a distance ______ from one end of the rod.
What is the potential energy of an object of mass \( m \) placed on the surface of the Earth? (Mass of Earth = \( M \), radius of Earth = \( R \))
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 \( a = g \).
Find the center of the ellipse given by the equation \[ 4x^2 + 24x + 9y^2 - 18y + 9 = 0 \]
When a rotating disc suddenly shrinks in radius, what happens to the angular velocity \( \omega \)?
Evaluate the following integral: \[ \int_{-\frac{\pi}{2}}^{\frac{\pi}{2}} \left( x^4 + x^3 + x \right) \cos x \, dx \]
Find the minimum of the function \[ f(x) = |x+2| \]
Given the following probabilities: \[ P(A) = 0.7, P(B) = 0.5, P(A \cup B) = 0.9, \quad \text{find} \quad P(A/B) \]
If $ a_n = 2^{n-1} $, where $ n = 1, 2, 3, ... $, then find $ \sum_{n=1}^{20} a_n $.
Solve for $ \alpha $ if: $ \cos^{-1}(2 \sin \alpha) = \frac{47}{12} $
If a box has 8 red balls, 12 white balls, 17 black balls. If two balls are taken one by one without replacement, then the probability of taking one red ball and one black ball is
Evaluate the integral: $ \int e^{-x} \cdot e^{3x} \, dx $
Given that $ x = \frac{\sin^2 \theta}{\tan \theta - \sec \theta}, \quad y = \frac{\sec \theta + \tan \theta}{\sec^2 \theta}, \quad \text{find} \, \frac{y}{x} $
What is the de Broglie wavelength of the particle having kinetic energy of $ 2E $?
Write the product of the reaction: $ \text{CH}_3 \text{CH}_2 \text{CH}_2 \text{O} \text{Na} + \text{C}_6 \text{H}_5 \text{Br} \to ? $
Evaluate the integral: $ \int \frac{1}{x(x^4 + 1)} \, dx $