The correct electronic configuration of the element \(\mathrm{Au}\) is

Which of the following has more \(\mathrm{pK}_{\mathrm{a}}\) value?

If for a hypothetical reaction, \(E_a=0\) at \(273 \mathrm{~K}\), then find the ratio of the rate constants at \(383 \mathrm{~K}\) and \(273 \mathrm{~K}\).

If a gas contains only three molecules that move with velocities of \(100,200,500 \mathrm{~ms}^{-1}\). What is the rms velocity of that gas in \(\mathrm{ms}^{-1}\) ?

Statement I: Boron does not exhibit allotropy
Statement II: Boron is extremely hard and black coloured solid

\(\mathrm{K}_{\mathrm{c}}\) for the following reaction is 99.0
\(\mathrm{A}_2(\mathrm{~g}) \stackrel{\mathrm{T}(\mathrm{~K})}{\rightleftharpoons} \mathrm{B}_2(\mathrm{~g})\)
In a one litre flask, 2 moles of \(\mathrm{A}_2\) was heated to \(\mathrm{T}(\mathrm{K})\) and the above equilibrium is reached. The concentrations at equilibrium of \(\mathrm{A}_2\) and \(\mathrm{B}_2\) are \(\mathrm{C}_1\left(\mathrm{~A}_2\right)\) and \(\mathrm{C}_2\left(\mathrm{~B}_2\right)\) respectively. Now, one mole of \(\mathrm{A}_2\) was added to flask and heated to \(\mathrm{T}(\mathrm{K})\) to establish the equilibrium again. The concentrations of \(\mathrm{A}_2\) and \(\mathrm{B}_2\) are \(\mathrm{C}_3\left(\mathrm{~A}_2\right)\) and \(\mathrm{C}_4\left(\mathrm{~B}_2\right)\) respectively. What is the value of \(\mathrm{C}_3\left(\mathrm{~A}_2\right)\) in \(\mathrm{mol}^{-1}\) ?

Which one among the following has the "S-O-S" bonding?

A sphere of mass \(4 \mathrm{~kg}\) is attached to one end of a steel wire of length \(1 \mathrm{~m}\) and radius \(1 \mathrm{~mm}\). It is whirled in a vertical circle with an angular velocity \(10 \mathrm{rad} \mathrm{s}^{-1}\). If the sphere is at the lowest point of its path, the elongation in the wire is ____
\(\left(\mathrm{g}=10 \mathrm{~ms}^{-2}, \mathrm{Y}_{\text {steel }}=20 \times 10^{10} \mathrm{Nm}^{-2}\right)\)

\(\int \frac{1+x+\sqrt{x+x^2}}{\sqrt{x}+\sqrt{1+x}} d x\) is equal to

A ball \(A\) of mass \(m\) moving along positive \(x\)-direction with kinetic energy \(K\) and momentum \(p\) undergoes elastic head on collision with a stationary ball \(B\) of mass \(M\) after collision the ball \(A\) moves along negative \(x\)-direction with kinetic energy \(\frac{K}{9}\), final momentum of \(B\) is

If the standard deviation of the numbers 2,3 , \(2 x\) and 11 is 3.5. Find the possible values of \(x\).

If \(x=\frac{2.5}{(2 !) 3}+\frac{2.5 .7}{(3 !) 3^2}+\frac{2.5 .7 .9}{(4 !) 3^3}+\ldots\) then \(x^2+8 x+8=\)

A circle \(S \equiv x^2+y^2-16=0\) intersects another circle \(S^{\prime}=0\) of radius 5 units such that their common chord is of maximum length. If the slope of that chord is \(\frac{3}{4}\), then the centre of such a circle \(S^{\prime}=0\) is