\(20\, mL\) of \(0.1\, M\, H_2SO_4\) is added to \(30\, mL\) of \(0.2\, M\, NH_4OH\) solution. The \(pH\) of the resultant mixture is [\(pk_b\) of \(NH_4OH = 4.7\)]

Among the statements \((a)-(d)\), the incorrect ones are \((a)\) Octahedral \(Co(III)\) complexes with strong field ligands have very high magnetic moments \((b)\) When \(\Delta_{0}< P\), the \(d-\)electron configuration of \(Co(III)\) in an octahedral complex is \(t_{\text {eg }}^{4} e_{g}^{2}\) \((c)\) Wavelength of light absorbed by \(\left[\mathrm{Co}(\mathrm{en})_{3}\right]^{3+}\) is lower than that of \(\left[\mathrm{CoF}_{6}\right]^{3-}\) \((d)\) If the \(\Delta_{0}\) for an octahedral complex of \(\mathrm{Co}(\mathrm{III})\) is \(18,000 \;\mathrm{cm}^{-1},\) the \(\Delta_{\mathrm{t}}\) for its tetrahedral complex with the same ligand will be \(16,000\;\mathrm{cm}^{-1}\)

If the principal quantam number \(n=6,\) the correct sequence of filling of electron will be

Cerium \((IV)\) has a noble gas configuration. Which of the following is correct statement about it?

Consider the following reaction : The product \('P'\) gives positive ceric ammonium nitrate test. This is because of the presence of which of these \(-OH\) group(s)\(?\)

The correct order of acid character of the following compounds is :

The first and second ionisation enthalpies of a metal are \(496\) and \(4560 \;\mathrm{kJ} \mathrm{mol}^{-1},\) respectively. How many moles of \(\mathrm{HCl}\) and \(\mathrm{H}_{2} \mathrm{SO}_{4}\) respectively, will be needed to react completely with \(1\) mole of the metal hydroxide?

What will be the effect on the root mean square velocity of oxygen molecules if the temperature is doubled and oxygen molecule dissociates into atomic oxygen?

Some \(\mathrm{CO}_2\) gas was kept in a sealed container at a pressure of 1 atm and at 273 K . This entire amount of \(\mathrm{CO}_2\) gas was later passed through an aqueous solution of \(\mathrm{Ca}(\mathrm{OH})_2\). The excess unreacted \(\mathrm{Ca}(\mathrm{OH})_2\) was later neutralized with 0.1 M of 40 mL HCl . If the volume of the sealed container of \(\mathrm{CO}_2\) was \(x\), then \(x\) is ________ \(\mathrm{cm}^3\) (nearest integer).
[Given : The entire amount of \(\mathrm{CO}_2(\mathrm{~g})\) reacted with exactly half the initial amount of \(\mathrm{Ca}(\mathrm{OH})_2\) present in the aqueous solution.]

Let the equation of two sides of a triangle be \(3x\,-\,2y\,+\,6\,=\,0\) and \(4x\,+\,5y\,-\,20\,=\,0.\) If the orthocentre of this triangle is at \((1, 1),\) then the equation of its third side is

Let P be the parabola, whose focus is \((-2,1)\) and directrix is \(2 x+y+2=0\). Then the sum of the ordinates of the points on P , whose abscissa is -2 , is

' X ' is the number of acidic oxides among \(\mathrm{VO}_2\), \(\mathrm{V}_2 \mathrm{O}_3, \mathrm{CrO}_3, \mathrm{~V}_2 \mathrm{O}_5\) and \(\mathrm{Mn}_2 \mathrm{O}_7\). The primary valency of cobalt in \(\left[\mathrm{Co}\left(\mathrm{H}_2 \mathrm{NCH}_2 \mathrm{CH}_2 \mathrm{NH}_2\right)_3\right]_2\left(\mathrm{SO}_4\right)_3\) is Y. The value of \(\mathrm{X}+\mathrm{Y}\) is _______.

\(KMnO _4\) is titrated with ferrous ammonium sulphate hexahydrate in presence of dilute \(H _2 SO _4\). Number of water molecules produced for \(2\) molecules of \(KMnO _4\) is \(..........\).