Bombardment of aluminium by \(\alpha\)-particle leads to its artificial disintegration in two ways, (i) and (ii) as shown. Products \(X, Y\) and \(Z\) respectively are

In the following reaction, compound $\mathrm{Q}$ is obtained from compound $\mathrm{P}$ via an ionic intermediate.

What is the degree of unsaturation of $\mathrm{Q}$?

Using the data provided, calculate the multiple bond energy \(\left(\mathrm{kJ} \mathrm{mol}^{-1}\right)\) of a \(\mathrm{C} \equiv \mathrm{C}\) bond in \(\mathrm{C}_{2} \mathrm{H}_{2}\). That energy is (take the bond energy of a \(\mathrm{C}-\mathrm{H}\) bond as \(350 \mathrm{~kJ} \mathrm{~mol}^{-1}\) ) \(2 \mathrm{C}(\mathrm{s})+\mathrm{H}_{2}(\mathrm{~g}) \longrightarrow \mathrm{HC}=\mathrm{CH}(\mathrm{g}) ; \Delta \mathrm{H}=\) \(225 \mathrm{~kJ} \mathrm{~mol}^{-1}\) \(2 \mathrm{C}(\mathrm{s}) \longrightarrow 2 \mathrm{C}(\mathrm{g}) ; \Delta \mathrm{H}=1410 \mathrm{~kJ} \mathrm{~mol}^{-1}\) \(\mathrm{H}_{2}(\mathrm{~g}) \longrightarrow 2 \mathrm{H}(\mathrm{g}) ; \Delta \mathrm{H}=330 \mathrm{~kJ} \mathrm{~mol}^{-1}\)

A tin chloride $\mathrm{Q}$ undergoes the following reactions (not balanced)
$\mathrm{Q}+\mathrm{C}{\mathrm{l}}^{-}\to \mathrm{X}$
$\mathrm{Q}+\mathrm{M}{\mathrm{e}}_3\mathrm{N}\to \mathrm{Y}$
$\mathrm{Q}+\mathrm{C}\mathrm{u}\mathrm{C}{\mathrm{l}}_2\to \mathrm{Z}+\mathrm{C}\mathrm{u}\mathrm{C}\mathrm{l}$
$\mathrm{X}$ is a monoanion having pyramidal geometry. Both $\mathrm{Y}$ and $\mathrm{Z}$ are neutral compounds. Choose the correct option(s).

The option(s) with only amphoteric oxides is(are)

The complex(es), which can exhibit the type of isomerism shown by $\left[\mathrm{Pt}{\left({\mathrm{NH}}_3\right)}_2{\mathrm{Br}}_2\right]$, is(are) $\left[\mathrm{en}={\mathrm{H}}_2{\mathrm{NCH}}_2{\mathrm{CH}}_2{\mathrm{NH}}_2\right]$

A positron is emitted from \({ }_{11}^{23} \mathrm{Na}\). The ratio of the atomic mass and atomic number of the resulting nuclide is

If $f:R\to R$ is a differentiable function such that $f^{\prime }\left(x\right)>2f\left(x\right)$ for all $x\in R$ and $f\left(0\right)=1$ then

The inductors of two $LR$ circuits are placed next to each other, as shown in the figure. The values of the self-inductance of the inductors, resistances, mutual-inductance and applied voltages are specified in the given circuit. After both the switches are closed simultaneously, the total work done by the batteries against the induced $EMF$ in the inductors by the time the currents reach their steady-state values is_______$\mathrm{mJ}$.

A container with $1 \mathrm{kg}$ of water in it is kept in sunlight, which causes the water to get warmer than the surroundings. The average energy per unit time per unit area received due to the sunlight is $700 \mathrm{W} {\mathrm{m}}^{-2}$ and it is absorbed by the water over an effective area of $0.05 {\mathrm{m}}^2.$ Assuming that the heat loss from the water to the surroundings is governed by Newton's law of cooling, the difference (in ${}^{\circ }\mathrm{C}$) in the temperature of water and the surroundings after a long time will be_________. (Ignore effect of the container, and take constant for Newton's law of cooling $=0.001 {\mathrm{s}}^{-1},$ Heat capacity of water $=4200 \mathrm{J} {\mathrm{kg}}^{-1} {\mathrm{K}}^{-1}$)

At time $t=0$, a disk of radius $1 \mathrm{m}$ starts to roll without slipping on a horizontal plane with an angular acceleration of $\alpha =\frac{2}{3} \mathrm{rad} {\mathrm{s}}^{-2}$. A small stone is stuck to the disk. At $t=0$, it is at the contact point of the disk and the plane. Later, at time $t=\sqrt{\pi } \mathrm{s}$, the stone detaches itself and flies off tangentially from the disk. The maximum height (in $\mathrm{m}$) reached by the stone measured from the plane is $\frac{1}{2}+\frac{x}{10}$. The value of $x$ is [Take $g=10 \mathrm{m} {\mathrm{s}}^{-2}$.] If the numerical value has more than two decimal places, truncate/round-off the value to TWO decimal places.

A train with cross-sectional area $S_t$ is moving with speed $v_t$ inside a long tunnel of cross-sectional area $S_0\left(S_0=4S_t\right)$. Assume that almost all the air (density $\rho$) in front of the train flows back between its sides and the walls of the tunnel. Also, the airflow with respect to the train is steady and laminar. Take the ambient pressure and that inside the train to be $P_0$. If the pressure in the region between the sides of the train and the tunnel walls is $P$, then $\left(P_0-P\right)=\frac{7}{2N}\rho v_t^2.$ The value of $N$ is _______.

The total number of distinct $x\in \left[0, 1\right]$ for which, ${\int }_0^x\frac{t^2}{1+t^4}dt=2x-1$ is