A person can row a boat at \(5 km / hr\) in still water. If the speed of water current in a river is \(1 km / hr\), and it takes him \(1\) hour to row to a place and come back, how far off is the place?

If \( \vec{a}\) is a unit vector and \((\vec{x}-\vec{a}) \cdot(\vec{x}+\vec{a})=15\), then the value of \(|\vec{x}|\) is :

The Cartesian equation of the line passing through the point \((1,2,-1)\) and parallel to the line \(5 x-25=14-7 y=35 z\) is

Let \(A=\left[\begin{array}{cc}\frac{1}{3} & 2 \\ 0 & 2 x-3\end{array}\right]\) and \(B=\left[\begin{array}{cc}3 & 6 \\ 0 & -1\end{array}\right]\).
If AB = I (where I is an identity matrix of order 2), then the value of x is:

A line makes equal angles with coordinate axis. Direction cosines of the line are:

If \(f: R \rightarrow R\) be given by \(f(x)=\left(3-x^3\right)^{\frac{1}{3}}\), then (fof) (x) is:

The value of integral \(I=\int \frac{1-\sin x}{\cos ^2 x} d x\) is:

In the electrochemical series written in the increasing order of reduction potential
(A) The elements which are placed above the hydrogen in the electrochemical series are stronger oxidizing agents.
(B) The elements which are placed above the hydrogen in the electrochemical series are stronger reducing agents.
(C) The elements with the positive electrode potential values lie below the hydrogen in the electrochemical series.
(D) The activity of both the metals and non-metals in the electrochemical series decreases from top to bottom.
Choose the correct answer from the options given below:

Many features of the nuclear binding force are summarised below : Choose the correct statement.
(A) Coulomb force acting between two protons inside the nucleus is much weaker than Nuclear force between them
(B) Between proton-proton inside nucleus gravitational force is stronger than nuclear force
(C) Nuclear force between two nucleons falls rapidly to zero as their distance is more than a few femtometer
(D) Nuclear forces between proton-proton, neutron - proton and neutron-neutron is approximately same when distance between them is same.
Choose the correct answer from the options given below :

The purest form of commercial iron is

As a biocontrol agents, the ladybird and dragonflies are useful to get rid of -

Increasing order of reducing power of following hydrides would be
A. SbH 3
B. AsH3
C. NH3
D. PH3
E. BiH3
Choose the correct answer from the options given below:

Read the passage carefully and answer the questions
The osmotic pressure is one of the four colligative properties which depends on the number of particles of solute in the solution, irrespective of their nature. The osmotic pressure is equal to the product of concentration, gas constant and temperature. It is the most commonly used property for the determination of the molar mass of biomolecules. In many situations, the molecules get dissociated or
associated when they are dissolved in a solvent, thereby changing the number of molecules in the solution. As a result, an abnormal molecular mass is obtained. The extent of dissociation or association is given by van't Hoff factor (i), which is the ratio of normal molar mass to abnormal molar mass. It is related with the degree of association or ionization. The introduction of van't Hoff factor in the osmotic pressure equation modifies the equation.
What is the value of the van't Hoff factor for\(NaCl , K _2 SO _4\) and KCl,respectively?