At \(27^{\circ} \mathrm{C}, 100 \mathrm{~mL}\) of 0.5 M HCl is mixed with 100 mL of 0.4 M NaOH solution. To this resultant solution, 800 mL of distilled water is added. What is the pH of final solution?

The pair of molecules/ions with same geometry but central atoms in them are in different states of hybridization is

Identify the correct statements from the folluwing (A) At 298 K, the potential of hydrogen electrode placed in a solution of \(\mathrm{pH}=10\), is -0.59 V (B) The limiting molar conductivity of \(\mathrm{Ca}^{2+}\) and \(\mathrm{Cl}^{-}\)is 119 and \(76 \mathrm{~S} \mathrm{~cm}^2 \mathrm{~mol}^{-1}\) respectively. The limiting molar conductivity of \(\mathrm{CaCl}_2\) is \(195 \mathrm{~S} \mathrm{~cm}^2 \mathrm{~mol}^{-\frac{1}{2}}\) (C) The correct relationship between \(\mathrm{K}_{\mathrm{c}}\) and \(\mathrm{E}_{\text {cell }}^0\) is \(\mathrm{E}_{\mathrm{ccll}}^{-}=\frac{2.303 \mathrm{RT}}{\mathrm{nF}} \log \mathrm{~K}_{\mathrm{c}}\)

The correct order of ionic radii for the given species is

Match the following:

The correct answer is

The most acidic among the following compounds is

Assertion (A) \(\mathrm{Mg}^{2+}\) and \(\mathrm{Al}^{3+}\) are isoelectronic but the magnitude of ionic radius of \(\mathrm{Al}^{3+}\) is less than that in \(\mathrm{Mg}^{2+}\). Reason \((R)\) The effective nuclear charge on the outermost electrons in \(\mathrm{Al}^{3+}\) is greater than that in \(\mathrm{Mg}^{2+}\). The correct option among the following is

If \(p\) and \(q\) are two distinct real values of \(\lambda\) for which the system of equations
\(\begin{aligned}
(\lambda-1) x+(3 \lambda+1) y+2 \lambda z & =0 \\
(\lambda-1) x+(4 \lambda-2) y+(\lambda+3) z & =0 \\
2 x+(3 \lambda+1) y+3(\lambda-1) z & =0
\end{aligned}\)
has non-zero solution, then \(p^2+q^2-p q=\)

Which of the following reaction represents Deacon's method?

The van der Waals' equation for a gas is \[ \left(P+\frac{a}{V^2}\right)(V-b)=n R T \] where \(P, V, R, T\) and \(n\) represent the pressure, volume, universal gas constant, absolute temperature and number of moles of a gas, respectively. \(a\) and \(b\) are constants. The ratio \(\frac{b}{a}\) will have the following dimensional formula.

If \(y=\frac{e^{\sin x}+\sin \mathrm{h}^3 x}{\cosh x-\tan x}\), then \(\mathrm{y}^{\prime}(0)=\)

Choose correct statement (A) The position of centre of mass of a system is dependent on the choice of coordinate system. (B) Newton's second law of motion is applicable to the centre of mass of the system. (C) Internal forces can not change the state of centre of mass. (D) Internal forces can change the state of centre of mass.

Consider an ideal gas at pressure \(p\), volume \(V\) and temperature \(T\). The mean free path for molecules of the gas is \(L\). If the radius of gas molecules, as well as pressure, volume and temperature of the gas are doubled, then the mean free path will be