List of top Questions asked in KEAM

Let \( f(x) = x - \lfloor x \rfloor \), where \( \lfloor \cdot \rfloor \) denotes the greatest integer function and \( x \in (-1, 2) \). The number of points at which the function is not continuous is:
The equation of the line passing through the point \( (1, 2) \) and perpendicular to the line \( x + y + 1 = 0 \) is:
In an incompressible liquid flow, mass conservation leads to:
An electric appliance draws 3A current from a 200 V, 50 Hz power supply. The amplitude of the supply voltage is nearly:
The decreasing order of first ionization enthalpy of the following elements is:
The period of \( 2 \sin 4x \cos 4x \) is:
If \( \sin \theta = \frac{b}{a} \), then \( \frac{\sqrt{a+b}} {\sqrt{a-b}} + \frac{\sqrt{a-b}} {\sqrt{a+b}} \) is equal to:
One mole of an alkene on ozonolysis gives a mixture of one mole pentan-3-one and one mole methanal. The alkene is:
The displacement-time graph of a moving body is a straight line making a 45\(^{\circ}\) angle with the time axis. The body moves with:
The domain of the function \( f(x) = \frac{\sin^{-1} \left( x-3 \right)}{\sqrt{9 - x^2}} \) is:
If \( \frac{\sec^2 15^\circ - 1}{\sec^2 15^\circ} \) equals:
For a smoothly running analog clock, the angular velocity of its second hand in rad s\(^{-1}\) is:
If the acceleration due to gravity on the surface of a planet is 2.5 times that on Earth and radius, 10 times that of the Earth, then the ratio of the escape velocity on the surface of a planet to that on Earth is:
If the determinant of the matrix \( \begin{bmatrix} |x| & 1 & 2 \\ 4 & 1 & x \\ 1 & -1 & 3 \end{bmatrix} \) equals -10, then the values of \( x \) are:
If A and B are two sets, such that A has 20 elements, \( A \cup B \) has 32 elements, and \( A \cap B \) has 10 elements, the number of elements in the set B is:
The value of \( \tan \left[ \tan^{-1} \left( \frac{3}{4} \right) + \tan^{-1} \left( \frac{2}{3} \right) \right] \) is:
Let \( A = (a_{ij}) \) be a square matrix of order 3 and let \( M_{ij} \) be the minors of \( a_{ij} \). If \( M_{11} = -40, M_{12} = -10, M_{13} = 35 \), and \( a_{11} = 1, a_{12} = 3, a_{13} = -2 \), then the value of \( |A| \) is equal to:
If the points \( (2, -3), (\lambda, -1) \) and \( (0, 4) \) are collinear, then the value of \( \lambda \) is equal to:
If \( _nP_r = 480 \) and \( _nC_r = 20 \), then the value of \( r \) is equal to:
The coefficient of \( x^3 \) in the binomial expansion of \( \left( \frac{1}{\sqrt{x}} - x \right)^6 \) is:
The constant term in the expansion of \( \left( x^3 + \frac{1}{x^2} \right)^{10} \) is:
The INCORRECT statement is:
The wavelength of the de Broglie wave (in meter) associated with a particle of mass \(m\) moving with \(\frac{1}{10}\) of the velocity of light is (h = Planck's constant, c = velocity of light):

If 

then the value of \( x - y \) is:

The coefficient of linear expansion of aluminum is \( 2.5 \times 10^{-5} \, {K}^{-1} \). Its coefficient of volume expansion in \( {K}^{-1} \) is: