The diagonal elements of a skew symmetric matrix are all

Two charged particles, placed at a distance d apart in vacuum, exert a force F on each other. Now, each of the charges is doubled. To keep the force unchanged, the distance between the charges should be changed to :

The foot of the perpendicular drawn from the point \((1,6,3)\) to the line \(\frac{x}{1}=\frac{y-1}{2}=\frac{z-2}{3}\) is :

The area (in sq. units) of the region bounded by the curve \(y=x^5\), the \(x\)-axis and the ordinates \(x=-1\) and \(x=1\) is equal to:

The value of \(2 y-3 x\), if \(2\left[\begin{array}{cc}x & 5 \\ 7 & y-3\end{array}\right]+\left[\begin{array}{cc}3 & -4 \\ 1 & 2\end{array}\right]=\left[\begin{array}{cc}7 & 6 \\ 15 & 14\end{array}\right]\) is :

Match List-l with List-ll

List-I	List-II
(A) The measurable characteristic of a population is called	(I) sample
(B) The measurable characteristics of a sample is called	(II) Alternative hypothesis
(C) A smaller group of a population selected to represent a population is caller	(III) Parameter
(D) The assumption made opposite to the null hypothesis is called	(IV) statistic

Choose the correct answer from the options given below:

If A is a matrix of order \(m \times n\) and B is a matrix such that \(A B^T\) and \(B^T A\) are both well-defined matrices, then order of matrix B is

Answer the question on basis of passage given below :
Lyophobic sols like those of metals (Au, Ag, etc) are unstable and are easily precipitated by addition of electrolytes. However, it is observed that the addition of certain lyophilic colloids like gums, soaps, gelatine, etc. to lyophobic colloids (like a metal sol) render lyophobic colloids difficult to coagulate by the addition of electrolytes. The process is known as 'protection' and the lyophilic colloids are termed as Protective colloids. It is believed that the protective action of the lyophilic colloids is due to the covering up of the particles of the lyophobic colloid by those of the lyophilic colloid.
Evidently, smaller the gold number of a protective colloid, the greater is its protective action.
Which of the following has the highest flocculating power for a positive sol?

Arrange the following solutions according to their increasing boiling points.
A. \(0.1 M Glucose\)
B. \(0.1 M NaCl\)
C. \(0.1 M K _4\left[ Fe ( CN )_6\right]\)
D. \(0.1 M MgCl _2\)
E. \(0.1 M AlCl _3\)
Choose the correct answer from the options given below:

Calculate the molality of KI if the density of 20% (mass/mass) aqueous solution of KI is 1.202 g mL^-1.
(Molar mass of KI is 166 g mol^-1)

The half life of a radioactive substance is 10 days. How many days will it take to disintegrate 3/4 of its initial value ?

\(\int \frac{d x}{e^x+e^{-x}}\) is equal to

Arrange the following complexes in increasing order of conductivity of their solution:
(A) \(\left[ Co \left( NH _3\right)_3 Cl _3\right]\)
(B) \(\left[ Co \left( NH _3\right)_4 Cl _2\right] Cl\)
(C) \(\left[ Co \left( NH _3\right)_6\right] Cl _3\)
(D) \(\left[ Co \left( NH _3\right)_5 Cl \right] Cl _2\)
Choose the correct answer from the options given below: