When a non-volatile solute is added to the solvent, the vapour pressure of the solvent decreases by 10 mm of Hg . The mole fraction of the solute in the solution is 0.2 . What would be the mole fraction of the solvent if decrease in vapour pressure is 20 mm of Hg ?

Trigonal bipyramidal geometry is shown by

Which of the following series correctly represents relations between the elements from \(X\) to \(Y\) ? \(X \to Y\)

A certain orbital has \(n =4\) and \(m _{ L }=-3\). The number of radial nodes in this orbital is .......... (Round off to the Nearest Integer).

\(\mathrm{A}_{(\mathrm{g})} \rightleftharpoons \mathrm{B}_{(\mathrm{g})}+\frac{\mathrm{C}}{2}(\mathrm{~g})\) The correct relationship between \(K_P, \alpha\) and equilibrium pressure \(P\) is _______.

\(19.5\) g of fluoro acetic acid (molar mass \(= 78\) g mol\(^{-1}\)) is dissolved in \(500\) g of water at \(298\) K. The depression in the freezing point of water was \(1°\)C. What is \(K_a\) of fluoro acetic acid? (For water, \(K_f = 1.86\) K kg mol\(^{-1}\)). Assume molarity and molality to have same values.

Given below are two statements: Statement \(I :\) Aniline is less basic than acetamide. Statement \(II :\) In aniline, the lone pair of electrons on nitrogen atom is delocalised over benzene ring due to resonance and hence less available to a proton. Choose the most appropriate option:

The quantities \(\quad x=\frac{1}{\sqrt{\mu_{0} \epsilon_{0}}}, y=\frac{E}{B}\) and \(z=\frac{l}{C R}\) are defined where \(C-\) capacitance \(R-\)Resistance, \(l-\)length, \(E-\)Electric field, \(B-\)magnetic field and \(\varepsilon_{0}, \mu_{0},\) -free space permittivity and permeability respectively. Then....

The correct statements from the following are : \((A)\) The decreasing order of atomic radii of group \(13\) elements is \(\mathrm{Tl}>\mathrm{In}>\mathrm{Ga}>\mathrm{Al}>\mathrm{B}\). \((B)\) Down the group \(13\) electronegativity decreases from top to bottom. \((C)\) \(\mathrm{Al}\) dissolves in dil. \(\mathrm{HCl}\) and liberate \(\mathrm{H}_2\) but conc. \(\mathrm{HNO}_3\) renders Al passive by forming a protective oxide layer on the surface. \((D)\) All elements of group \(13\) exhibits highly stable +1 oxidation state. \((E)\) Hybridisation of \(\mathrm{Al}\) in \(\left[\mathrm{Al}\left(\mathrm{H}_2 \mathrm{O}\right)_6\right]^{3+}\) ion is \(\mathrm{sp}^3 \mathrm{~d}^2\). Choose the correct answer from the options given below:

Let a line L passing through the point P(1, 1, 1) be perpendicular to the lines \(\frac{x-4}{4}=\frac{y-1}{1}=\frac{z-1}{1}\) and \(\frac{ x -17}{1}=\frac{ y -71}{1}=\frac{ z }{0}\). Let the line L intersect the yz-plane at the point Q. Another line parallel to L and passing through the point S(1,0, –1) intersects the yz-plane at the point R. Then the square of the area of the parallelogram PQRS is equal to ___ .

Let \(A = \{2, 3, 4, 5, 6\}\). Let R be a relation on the set \(A \times A\) given by \((x, y) R (z, w)\) if and only if \(x\) divides \(z\) and \(y \leq w\). Then the number of elements in R is _______.

If electric field intensity of a uniform plane electro magnetic wave is given as \(E =-301.6 \sin ( kz -\omega t ) \hat{a}_{ x }+452.4 \sin ( kz -\omega t )\) \(\hat{a}_{y} \frac{V}{m}\) Then, magnetic intensity \(H\) of this wave in \(Am ^{-1}\) will be [Given: Speed of light in vacuum \(c =3 \times 10^{8} ms ^{-1}\), permeability of vacuum \(\mu_{0}=4 \pi \times 10^{-7} NA ^{-2}\) ]

Two parallel long current carrying wire separated by a distance \(2 \mathrm{r}\) are shown in the figure. The ratio of magnetic field at \(\mathrm{A}\) to the magnetic field produced at \(C\) is \(\frac{x}{7}\). The value of \(x\) is _______.