The fragrance of flowers is due to the presence of some steam volatile organic compounds called essential oils. These are generally insoluble in water at room temperature but are miscible with water vapour in vapour phase. \(A\) suitable method for the extraction of these oils from the flowers is _______.

The maximum number of orbitals which can be identified with \(\mathrm{n}=4\) and \(\mathrm{m}_l=0\) is _______.

A solid \(XY\) kept in an evacuated sealed container undergoes decomposition to form a mixture of gases \(X\) and \(Y\) at temperature \(T\). The equilibrium pressure is \(10\, bar\) in the vessel. \(K_p\) for this reaction is

Lead storage battery contains \(38\,\%\) by weight solution of \(H _2 SO _4\). The van't Hoff factor is \(2.67\) at this concentration. The temperature in Kelvin at which the solution in the battery will freeze is \(..........\) (Nearest integer).Given \(K _{ f }=1.8\,K\, kg\, mol^{-1}\)

Consider an elementary reaction
\(\mathrm{A}(\mathrm{g})+\mathrm{B}(\mathrm{g}) \rightarrow \mathrm{C}(\mathrm{g})+\mathrm{D}(\mathrm{g})\)
If the volume of reaction mixture is suddenly reduced to \(\frac{1}{3}\) of its initial volume, the reaction rate will become ' \(x\) ' times of the original reaction rate. The value of \(x\) is :

In which pairs, the first ion is more stable than the second?

Match List \(I\) with List \(II\) \(1-\) Bromopropane is reacted with reagents in List \(I\) to give product in List \(II\)

List\(I-\)  Reagent	List\(II-\)Product
\(A\) \(KOH (\text { alc) }\)	\(I\) Nitrile
\(B\) \(KCN \text { (alc) }\)	\(II\) Ester
\(C\) \(AgNO _2\)	\(III\) Alkene
\(D\) \(H _3 CCOOAg\)	\(IV\) Nitroalkane

A uniform cylinder of mass \(M\) and radius \(R\) is to be pulled over a step of height \(a (a < R\)) by applying a force \(F\) at its centre \('O'\) perpendicular to the plane through the axes of the cylinder on the edge of the step ( see figure). The minimum value of \(F\) required is 

Let \(\mathrm{A}(4,-2), \mathrm{B}(1,1)\) and \(\mathrm{C}(9,-3)\) be the vertices of a triangle \(A B C\). Then the maximum area of the parallelogram AFDE , formed with vertices \(\mathrm{D}, \mathrm{E}\) and F on the sides \(\mathrm{BC}, \mathrm{CA}\) and AB of the triangle ABC respectively, is ______ .

Let the plane \(2 x+3 y+z+20=0\) be rotated through a right angle about its line of intersection with the plane \(x-3 y+5 z=8\). If the mirror image of the point \(\left(2,-\frac{1}{2}, 2\right)\) in the rotated plane is \(B ( a , b , c )\), then

An ideal gas undergoes a cyclic transformation starting from the point \(\mathrm{A}\) and coming back to the same point by tracing the path \(\mathrm{A} \rightarrow \mathrm{B} \rightarrow \mathrm{C} \rightarrow \mathrm{A}\) as shown in the diagram. The total work done in the process is _______ \(J\).

For two non-zero complex number \(z_1\) and \(z_2\), if \(\operatorname{Re}\left(z_1 z_2\right)=0\) and \(\operatorname{Re}\left(z_1+z_2\right)=0\), then which of the following are possible ? \((A)\) \(\operatorname{Im}\left(z_1\right) > 0\) and \(\operatorname{Im}\left(z_2\right) > 0\) \((B)\) \(\operatorname{Im}\left(z_1\right) < 0\) and \(\operatorname{Im}\left(z_2\right) > 0\) \((C)\) \(\operatorname{Im}\left(z_1\right) > 0\) and \(\operatorname{Im}\left(z_2\right) < 0\) \((D)\) \(\operatorname{Im}\left( z _1\right) < 0\) and \(\operatorname{Im}\left( z _2\right) < 0\) Choose the correct answer from the options given below :

Consider three boxes, each containing \(10\) balls labelled \(1, 2, ….., 10\). Suppose one ball is randomly drawn from each of the boxes. Denote by \(n_i\), the label of the ball drawn from the \(i^{th}\) box, \((i = 1, 2, 3)\). Then, the number of ways in which the balls can be chosen such that \(n_1 < n_2 < n_3\) is: