\(\underline{X}\) and \(\underline{Y}\) are the two covalent molecules in which the hybridisation of the central atoms is same, but shapes are different. \(\underline{X}\) and \(\underline{Y}\) are

The ore which is concentrated by leaching

The deBroglie wavelengths of two fast moving particles \(X, Y\) are \(1 \mathrm{~nm}, 3 \mathrm{~nm}\) respectively. Mass of \(X\) is nine times the mass of \(Y\). The ratio of kinetic energies of \(\mathrm{X}, \mathrm{Y}\) is

The reagent used for converting acetylene to oxalic acid is

(i) \(\mathrm{H}_3 \mathrm{PO}_4(a q) \rightleftharpoons \mathrm{H}^{+}(a q)+\mathrm{H}_2 \mathrm{PO}_4^{-}(a q)\)
(ii) \(\mathrm{H}_2 \mathrm{PO}_4^{-}(a q) \rightleftharpoons \mathrm{H}^{+}(a q)+\mathrm{HPO}_4^{2-}(a q)\)
(iii) \(\mathrm{HPO}_4^{2-}(a q) \rightleftharpoons \mathrm{H}^{+}(a q)+\mathrm{PO}_4^{3-}(a q)\)
The equilibrium constants for the above reactions at a certain temperature are \(K_1, K_2\) and \(K_3\) respectively. The equilibrium constant for the reaction \(\mathrm{H}_3 \mathrm{PO}_4(a q) \rightleftharpoons 3 \mathrm{H}^{+}(a q)+\mathrm{PO}_4^{3-}(a q)\) in terms of \(K_1, K_2\) and \(K_3\) is

The homoleptic complex in the following is

The carbohydrate which does not react with ammonical \(\mathrm{AgNO}_3\) solution is

Two strings \(A\) and \(B\) of lengths, \(L_A=80 \mathrm{~cm}\) and \(L_B=x \mathrm{~cm}\) respectively are used separately in a sonometer. The ratio of their densities \(\left(d_A / d_B\right)\) is 0.81 . The diameter of \(B\) is one-half that of \(A\). If the strings have the same tension and fundamental frequency the value of \(x\) is :

If the subnormal at any point on the curve \(y^n=a x\) is constant then the value of \(n\) is

\(\frac{1}{81^{\mathrm{n}}}-{ }^{2 \mathrm{n}} \mathrm{C}_1 \frac{10}{81^{\mathrm{n}}}+{ }^{2 \mathrm{n}} \mathrm{C}_2 \frac{10^2}{81^{\mathrm{n}}}-\ldots+\frac{10^{2 \mathrm{n}}}{81^{\mathrm{n}}}=\)

Three charges \(4 q, Q\) and \(q\) are placed at positions \(0, \frac{l}{2}\) and \(l\) respectively along a straight line. If the resultant force on \(q\) is zero, then \(Q\) is equal to

A pair of lines \(S=\mathbf{0}\) together with the lines given by the equation \(8 x^2-14 x y+3 y^2+10 x+10 y-25=0\) form a parallelogram. If its diagonals intersect at the point \((3,2)\), then the equation \(S=0\), is

A fully charged capacitor of capacity ' \(\mathrm{C}\) ' is discharged through a small resistance wire embedded in a solid block of specific heat ' \(\mathrm{s}\) ' and mass ' \(\mathrm{m}\) ' under thermally isolated conditions. If the temperature of the block is raised by \(\Delta \mathrm{T}\), the initial potential difference across the capacitor is