A swimmer's speed in still water is \(6 km / hr\). He swims between two points in a river and returns back to the starting point. He took 24 minutes more to cover the distance

The area of triangle with vertices \(P, Q, R\) is given by (where \(\overrightarrow{A B}=\) position vector of point \(B-\) position vector of point \(A\) )

The probability distribution of a random variable \(X\) is given below :

x	0	1	2	3
\(P ( x )\)	\(\frac{k}{3}\)	\(\frac{k}{2}\)	\(\frac{k}{4}\)	\(\frac{k}{7}\)

Then the value of \(k\) is

\(P, Q, R\) and \(S\) are four wires of resistances \(3,3,3\) and \(4 \Omega\) respectively. They are connected to form the four arms of a wheatstone bridge circuit. The resistance with which S must be shunted in order that the bridge may be balanced is

The greatest integer function \(f(x)=\lfloor x\rfloor\) is differentiable for all values of

A boat covers 32 km upstream and 36 km downstream in 7 hours.
Also, it covers 40 km upstream and 48 km downstream in 9 hours.
The speed of the boat in still water is :

If a line makes angles \(\frac{2 \pi}{3}\) and \(\frac{\pi}{3}\) with positive direction of \(x\)-axis and \(y\)-axis respectively,
then the acute angle made by the line with positive \(z\)-axis is:

If there are 4 states, represented as L, M, N, O where L is located near the equator, and others are located at 80°N, 71°N, 41°N, respectively. Which one of the following will have least number of bird species?

Which of the following statements are correct for dilute solutions?
(A) The elevation in boiling point is directly proportional to the molality of the solution.
(B) The elevation in boiling point is inversely proportional to the molality of the solution.
(C) The depression in freezing point is directly proportional to the molality of the solution.
(D) The depression in freezing point is inversely proportional to the molality of the solution.
Choose the correct answer from the options given below:

Read the passage carefully. Attempt the questions.
An overwhelming majority (99 per cent) of animals and nearly all plants cannot maintain a constant internal environment. Their body temperature changes with the ambient temperature. In aquatic animals, the osmotic concentration of the body fluids change with that of the ambient air and water osmotic concentration. These animals and plants are simply conformers. Considering the benefits of a constant internal environment to the organism, we must ask why these conformers had not evolved to become regulators. Recall the human analogy we used above; much as they like, how many people can really afford an air conditioner? Many simply 'sweat it out' and resign themselves to suboptimal performance in hot summer months. Very small animals are rarely found in polar regions. During the course of evolution, the costs and benefits of maintainin a constant internal environment are taken into consideration. Some species have evolved the ability to regulate, but only over a limited range of environmental conditions, beyond which they simply conform.
If the stressful external conditions are localised or remain only for a short duration, the organism has five other alternatives for survival.
Identify the animal which is NOT a conformer.

How many C \(\text{mol}^{-1}\) are required to convert 1 mol of \(\text{MnO}_4^-\) to \(\text{Mn}^{2+}\)?
[1F = 96500 C]

The correct order for increasing the boiling point of hydrides (given below) of group 15 is:
(A) \(NH _3\)
(B) \(PH _3\)
(C) \(AsH _3\)
(D) \(SbH _3\)
(E) \(BiH _3\)
Choose the correct answer from the options given below :

The unit vector in the direction of sum of vectors \(\vec{a}=2 \hat{i}-\hat{j}+\hat{k}\) and \(\vec{b}=2 \hat{j}+\hat{k}\) is: