If \(x\) is real, the minimum value of \(x^2-8 x+20\) is :

The solution set of the inequality \(3 x+5 y<4\) is

The area of the region bounded by \(y=|x-5|, x=0\) and \(x=1\) is :

It is currently 9:40 AM. What will be the time in next 610 hours?

Let \(\Delta = \begin{vmatrix} 1 & \sin \theta & 1 \\ -\sin \theta & 1 & \sin \theta \\ -1 & -\sin \theta & 1 \end{vmatrix}\), then \(\Delta\) lies in the interval

Ram can row a boat in still water at the rate of 6 km/hr. He finds that it takes him twice as long to row upstream of a river as to row downstream of the same river, then the speed of the current of the river is

Integrating factor of \(\frac{dy}{dx} + y \cot x = 2x + x^2 \cot x\) (\(x \neq 0\)) is:

Which of the following is the correct equation to find the area of the shaded region, with reference to the figure given below ?

Given below are some stages of human evolution. Arrange them in correct sequence (Past to Recent)
(A) Homo habilis
(B) Homo sapiens
(C) Homo neanderthalensis
(D) Homo erectus
Choose the correct answer from the options given below:

An object of length 2.0 cm is placed at a distance of 1.5 f from a concave mirror where f is the magnitude of the focal length of the mirror. The length of the object is perpendicular to the principal axis. The length of the image will be

The angular momentum of an electron moving in the circular path of diameter D in a uniform magnetic field \( B_0 \) is:

In a series LCR circuit, \( R = 1 \text{ k}\Omega, C = 2 \text{ } \mu\text{F} \) and the voltage across R is 100 V at resonant frequency \( \omega = 200 \text{ rad/s} \). At resonant frequency, the voltage across L is:

The properties which depend on the number of solute particles irrespective of their nature relative to the total number of particles in the solution are called colligative properties. These are relative lowering of vapour pressure of the solvent, depression of freesing point of the solvent, elevation of boiling point of the solvent and osmotic pressure of the solution. All of these properties help in calculating the observed molar mass of the solute.
Determination of osmotic pressure is considered best for the determination of molecular mass of the solute.
A solution of \(12.5\) g of an unknown solute in \(170\) g of water gave a boiling point elevation of 0.63 K .
\(k_b\) for water is \(0.53 K kg mol ^{-1}\).
The molar mass of the solute is :