Three liquids of densities \(\rho _1,\rho _2\) and \(\rho _3\) (with \(\rho _1 > \rho _2 > \rho_3),\) having the same value of surface tension \(T,\) rise to the same height in three identical capillaries. The angles of contact \(\theta_1 \,,\theta_2\) and \(\theta_3\) obey  

The displacement-time graphs of two moving particles make angles of \(30^{\circ}\) and \(45^{\circ}\) with the \(x\)-axis as shown in the figure. The ratio of their respective velocity is :

Given below are two statements: one is labelled as Assertion \(A\) and the other is labelled as Reason \(R\). Assertion \(A\): The potential ( \(V\) ) at any axial point, at \(2 \mathrm{~m}\) distance ( \(r\) ) from the centre of the dipole of dipole moment vector \(\vec{P}\) of magnitude, \(4 \times 10^{-6} \mathrm{C} \mathrm{m}\), is \(\pm 9 \times 10^3 \mathrm{~V}\). (Take \(\frac{1}{4 \pi \epsilon_0}=9 \times 10^9 \mathrm{Sl}\) units) Reason \(R\): \(V= \pm \frac{2 P}{4 \pi \epsilon_0 r^2}\), where \(r\) is the distance of any axial point, situated at \(2 \mathrm{~m}\) from the centre of the dipole. In the light of the above statements, choose the correct answer from the options given below:

If the monochromatic source in Young's double slit experiment is replaced by white light, then

A \(U\) tube with both ends open to the atmosphere, is partially filled with water. Oil, which is immiscible with water, is poured into one side until it stands at a distance of \(10\,\, mm\) above the water level on the other side. Meanwhile the water rises by \(65\,\, mm\) from its original level (see diagram). The density of the oil is ......... \(kg/m^3\)

Thermodynamic processes are indicated in the following diagram.  Match the following  \(\begin{array}{|l|l|} \hline Column\,\,-\,\,1 & Column\,\,-\,\,2 \\ \hline P\,:\,Process\,\,-\,\,I & \,\,A\,\,:\,\,Adiabatic \\ \hline Q\,:\,Process\,\,-\,\,II & \,\,B\,\,:\,\,Isobaric \\ \hline R\,:\,Process\,\,-\,\,III & \,\,C\,\,:\,\,Isochoric \\ \hline S\,:\,Process\,\,-\,\,IV & \,\,D\,\,:\,\,Isothermal \\ \hline \end{array}\)  

A thin flat circular disc of radius \(4.5 \mathrm{~cm}\) is placed gently over the surface of water. If surface tension of water is \(0.07 \mathrm{~N} \mathrm{~m}^{-1}\), then the excess force required to take it away from the surface is

Which of the following salts will give highest \(pH\) in water?

Two copper vessels \(A\) and \(B\) have the same base area but of different shapes. \(A\) takes twice the volume of water as that \(B\) requires to fill upto a particular common height. Then the correct statement among the following is

For the following reactions .  . .Which of the following statements is correct ? \((A)\,\,CH_3CH_2CH_2Br + KOH  \rightarrow  CH_3CH CH_2 + KBr + H_2O\)

Match the organism with its use in biotechnology.

\((a)\) Bacillus thuringiensis	\((i)\) Cloning vector
\((b)\) Thermus aquaticus	\((ii)\) Construction of first \(rDNA\) molecule
\((c)\) Agrobacterium tumefaciens	\((iii)\) \(DNA\)polymerase
\((d)\) Salmonella typhimurium	\((iv)\) Cry proteins

Select the correct option from the following: \((a)\quad(b)\quad(c)\quad(d)\)

Which of the following is an in situ conservation method ?

The correct statement regarding \(RNA\) and \(DNA,\) respectively is