List of top Questions asked in KEAM

Equation of line through (0, 0, 1) and (1, 1, 0)
If \[ (a - 2)^2 + (b - 2)^2 + (c - 2)^2 = 0, \text{ then } a + b + c = \]
Equation of line through (0, 0, 1) and (1, 1, 0)
Find the range of \( f(x) = \log_e(4x^2 - 4x + 1) \)
Length of latus rectum of ellipse \[ \frac{x^2}{9} + \frac{y^2}{16} = 1 \]
Evaluate the integral: \[ \int \frac{\log(1+x)}{1+x} \, dx \]
Evaluate the integral: \[ \int_{-3}^{3} \left\lfloor x \right\rfloor \, dx \]
Variance of 240, 260, 270, 280
Evaluate the limit: \[ \lim_{x \to 2} \frac{(x^3 - 8) \sin(x - 2)}{x^2 - 4x + 4} \]
Find the \( \Delta G \) during the reaction: \[ \text{H}_2\text{O}(l) \rightleftharpoons \text{H}_2\text{O}(g) \quad \Delta S = +1 \, \text{kJ/mol} \, \text{at} \, 100^\circ C \]
The most basic oxide
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?
Coefficient of friction is the ratio of?
Electric field lines around a positive charge are directed:
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 \( a = g \).