For a first order reaction, the ratio between the time taken to complete \(\frac{3}{4}\) th of the reaction and time taken to complete half of the reaction is

The correct order of decomposition temperature of \(\mathrm{MgCO}_3\) \((\mathrm{X}) . \mathrm{BaCO}_3(\mathrm{Y}), \mathrm{CaCO}_3(\mathrm{Z})\) is

Which one of the following methods is used to prepare carbon monoxide on commercial scale?

Example of a biodegradable polymer pair is

Identify the correct statements from the following :
I. \(\mathrm{Ga}_2 \mathrm{O}_3\) is an amphoteric oxide.
II. The dimer of aluminium chloride has three \(\mathrm{Al}-\mathrm{Cl}-\mathrm{Al}\) bridge bonds.
III. Boron is very hard refractory solid of high melting temperature.

With increasing Principal Quantum number, the energy difference between adjacent energy levels in H-atom

Identify the reactions in which dichromate acts as an oxidising reagent.
I. \(\mathrm{Cr}_2 \mathrm{O}_7^{2-}+6 \mathrm{Fe}^{2+}+14 \mathrm{H}^{+} \longrightarrow 2 \mathrm{Cr}^{3+}+6 \mathrm{Fe}^{3+}+7 \mathrm{H}_2 \mathrm{O}\)
II. \(\mathrm{Cr}_2 \mathrm{O}_7^{2-}+2 \mathrm{OH}^{-} \longrightarrow 2 \mathrm{CrO}_4^{2-}+\mathrm{H}_2 \mathrm{O}\)
III. \(\mathrm{Cr}_2 \mathrm{O}_7^{2-}+6 \mathrm{I}^{-}+14 \mathrm{H}^{+} \longrightarrow 2 \mathrm{Cr}^{3+}+3 \mathrm{I}_2+7 \mathrm{H}_2 \mathrm{O}\)
IV. \(\mathrm{Na}_2 \mathrm{Cr}_2 \mathrm{O}_7+2 \mathrm{KCl} \longrightarrow \mathrm{K}_2 \mathrm{Cr}_2 \mathrm{O}_7+2 \mathrm{NaCl}\)

If \(x \in\left(\frac{-\pi}{2}, \frac{\pi}{2}\right)\), then \(\log \sec x=\)

If \(y=x \operatorname{Tan}^{-1}\left(\frac{x}{y}\right)\), then \(\frac{d y}{d x}=\)

Two cells with same emf \(\mathrm{E}\) but different inteınal resistances, \(r_1\), and \(r_2\) are connected in series to an external resistance \(\mathrm{R}\). If the potential difference across the first cell is zero then the value of \(\mathrm{R}\) is

If a line is moving between the coordinate axes such that the sum of the intercepts made by it on the coordinate axes is always 12 , then the equation of that line which forms a triangle of maximum area with the coordinate axes is

The solution of \(\frac{d y}{d x}+\frac{1}{3} y=1\) is

An LCR series circuit is connected to an external emf, \(e=200 \sin 100 \pi \mathrm{t} v\). The values of capacitance and resistance in the circuit are \(1 \mu \mathrm{F}\) and \(100 \Omega\) respectively. The amplitude of current in the circuit is maximum when the inductance is (in henry)