List of top Questions asked in KEAM

If an ideal engine needs to transmit a torque of 200 Nm to maintain a rotor at a uniform angular speed of 300 rads\(^{-1}\), then the power required for the engine is:
If an ideal gas, in an insulated vessel, is allowed to expand into another similar evacuated vessel through a valve then:
The total energy of a gas mixture of one mole of oxygen and 3 moles of argon at a temperature \( T \) by neglecting vibrational modes is:
Two spheres A and B having respective charges 6 C and 12 C placed at a distance \( d \) repel each other by a force \( F \). The charge given to sphere A to reverse the force as \( -F \) is:
The de Broglie wavelength associated with the electrons accelerated by a potential of 81 V is lying in the region of electromagnetic waves:
Let \[ f(x) = |\sin x| + |\cos x|, \quad x \in \mathbb{R}. \] The period of \( f(x) \) is:
In a Carnot engine, the temperature of the sink is 350 K. If the efficiency of the engine is 50%, the temperature of the source should be:
cos \( A \cos 2A \) is equal to:
The integral

\[ \int \frac{dx}{x^8 \left( 1 + x^7 \right)^{2/3}} \] is equal to:
The expression
\[ \frac{1 + \cos\left(\frac{\pi}{5}\right) + i \sin\left(\frac{\pi}{5}\right)}{1 + \cos\left(\frac{\pi}{5}\right) - i \sin\left(\frac{\pi}{5}\right)} \] is equal to:
The integral \( \int \tan^5 x \sec^2 x \, dx \) is equal to:
The integral

\[ \int \frac{\sec x}{(\sec x + \tan x)^2} \, dx \] is:
Find the value of \[ \sin \left( 2 \sin^{-1} \left( \frac{1}{2} \right) \right). \] The answer is:
If a ray of light passes through a medium, its frequency and wavelength are \( 4 \times 10^{14} \) Hz and 450 nm respectively. Then the refractive index of the medium is:
The sum of the oxidation numbers of all the carbon and oxygen atoms in carbonate ion is:
The centre of the circle \( (x-3)(x+1)+(y-1)(y+3)=0 \) is:

The value of \[ \int_{-\frac{\pi}{2}}^{\frac{\pi}{2}} \frac{\cos^2 x}{1 + 2^{-x}} \, dx \] is equal to:

During the formation of p - n junction:
If \( \overrightarrow{a} = \alpha \hat{i} + \beta \hat{j} \) and \( \overrightarrow{b} = \alpha \hat{i} - \beta \hat{j} \) are perpendicular, where \( \alpha \neq \beta \), then \( \alpha + \beta \) is equal to:
Three dice are thrown simultaneously. The probability that all the three outcomes are the same number, is:
If \( E_c \) and \( E_v \) represent the energy of the conduction band and valence band, \( E_D \) represent the donor energy level, and the band gap in a n-type semiconductor, then the true relation among them is:
If \[ \sin^{-1} x + \sin^{-1} y + \sin^{-1} z = \frac{3\pi}{2}, \] then \( x + y + z = \):
The dimensional formula of the gravitational constant is \( M^a L^b T^c \), the values of \( a \), \( b \), and \( c \) are respectively:
The value of \( \int_{-4}^{-2} \left[ (x+3)^3 + 2 + (x+3)\cos(x+3) \right] \, dx \) is equal to:
If \( f(x) = \frac{|x|}{1 + |x|}, \, x \in \mathbb{R} \), then \( f'(-2) \) is equal to: