If the reaction sequence given below is carried out with $15$ moles of acetylene, the amount of the product $\mathrm{D}$ formed (in $\mathrm{g}$) is The yields of $\mathrm{A},\mathrm{B},\mathrm{C}$ and $\mathrm{D}$ are given in parentheses. [Given: Atomic mass of $\mathrm{H}=1,\mathrm{C}=12,\mathrm{O}=16,\mathrm{Cl}=35$]

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The coordination number of \(\mathrm{Ni}^{2+}\) is 4 .
\(\mathrm{NiCl}_2+\mathrm{KCN}\) (excess) \(\rightarrow A\) (cyano complex)
\(\mathrm{NiCl}_2+\) conc. \(\mathrm{HCl}\) (excess) \(\rightarrow B\) (chloro complex)
Question:
The IUPAC name of \(A\) and \(B\) are

The acidic hydrolysis of ether (X) shown below is fastest when

A sample \((5.6 \mathrm{~g})\) containing iron is completely dissolved in cold dilute \(\mathrm{HCl}\) to prepare a \(250 \mathrm{~mL}\) of solution. Titration of \(25.0 \mathrm{~mL}\) of this solution requires \(12.5 \mathrm{~mL}\) of \(0.03 \mathrm{M} \mathrm{KMnO}_{4}\) solution to reach the end point. Number of moles of \(\mathrm{Fe}^{2+}\) present in \(250 \mathrm{~mL}\) solution is \(\mathbf{x} \times 10^{-2}\) (consider complete dissolution of \(\mathrm{FeCl}_{2}\) ). The amount of iron present in the sample is \(\mathbf{y} \%\) by weight.
(Assume: \(\mathrm{KMnO}_{4}\) reacts only with \(\mathrm{Fe}^{2+}\) in the solution Use: Molar mass of iron as \(56 \mathrm{~g} \mathrm{~mol}^{-1}\) )
The value of $\mathrm{y}$ is________ .

In a neutral or faintly alkaline solution, $8$ moles of permanganate anion quantitatively oxidize thiosulphate anions to produce $\mathrm{X}$ moles of a sulphur containing product. The magnitude of $\mathrm{X}$ is:

In the following monobromination reaction, the number of possible chiral products is

The structure of a peptide is given below.
If the absolute values of the net charge of the peptide at $\mathrm{pH}=2,\mathrm{pH}=6,$ and $\mathrm{pH}=11$ are $\left|{\mathrm{z}}_1\right|,\left|{\mathrm{z}}_2\right|,$ and $\left|{\mathrm{z}}_3\right|,$ respectively, then what is $\left|{\mathrm{z}}_1\right|+\left|{\mathrm{z}}_2\right|+\left|{\mathrm{z}}_3\right|$?

Let \(X\) be a random variable, and let \(P(X=x)\) denote the probability that \(X\) takes the value \(x\). Suppose that the points \((x, P(X=x)), x=0,1,2,3,4\), lie on a fixed straight line in the \(x y\)-plane, and \(P(X=x)=0\) for all \(x \in \mathbb{R}-\{0,1,2,3,4\}\). If the mean of \(X\) is \(\frac{5}{2}\), and the variance of \(X\) is \(\alpha\), then the value of \(24 \alpha\) is ___

A student skates up a ramp that makes an angle $30°$ with the horizontal. He/she starts (as shown in the figure) at the bottom of the ramp with speed $v_0$ and wants to turn around over a semicircular path $xyz$ of radius $R$ during which he/she reaches a maximum height $h$ (at point $y$) from the ground as shown in the figure. Assume that the energy loss is negligible and the force required for this turn at the highest point is provided by his/her weight only. Then ($g$ is the acceleration due to gravity)

The value(s) of \(\int_0^1 \frac{x^4(1-x)^4}{1+x^2} d x\) is (are)

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When liquid medicine of density \(\rho\) is to be put in the eye, it is done with the help of a dropper. As the bulb on the top of the dropper is pressed, a drop forms at the opening of the dropper. We wish to estimate the size of the drop.
We first assume that the drop formed at the opening is spherical because that requires a minimum increase in its surface energy. To determine the size, we calculate the net vertical force due to the surface tension \(T\) when the radius of the drop is \(R\). When this force becomes smaller than the weight of the drop, the drop gets detached from the dropper.
Question :
If \(r=5 \times 10^{-4} \mathrm{~m}, \rho=10^3 \mathrm{~kg} \mathrm{~m}^{-3}\), \(g=10 \mathrm{~ms}^{-2}, T=0.11 \mathrm{Nm}^{-1}\), the radius of the drop when it detaches from the dropper is approximately

The \(\beta\)-decay process, discovered around 1900 , is basically the decay of a neutron \((n)\). In the laboratory, a proton \((p)\) and an electron \(\left(e^{-}\right)\)are observed as the decay products of the neutron. Therefore, considering the decay of a neutron as a two-body decay process, it was predicted theoretically that the kinetic energy of the electron should be a constant. But experimentally, it was observed that the electron kinetic energy has continuous spectrum. Considering a three-body decay process, i.e.
\(n \rightarrow p+e^{-}+\bar{v}_{e}\), around 1930, Pauli explained the observed electron energy spectrum. Assuming the anti-neutrino \(\left(\bar{v}_{e}\right)\) to be massless and possessing negligible energy, and the neutron to be at rest, momentum and energy conservation principles are applied. From this calculation, the maximum kinetic energy of the electron is \(0.8 \times 10^{6} \mathrm{eV}\). The kinetic energy carried by the proton is only the recoil energy.

Question:
If the anti-neutrino had a mass of \(3 \mathrm{eV} / \mathrm{c}^{2}\) (where \(\mathrm{c}\) is the speed of light) instead of zero mass, what should be the range of the kinetic energy, \(K\), of the electron?

In a Young's double slit experiment, the separation between the two slits is \(d\) and the wavelength of the light is \(\lambda\). The intensity of light falling on slit 1 is four times the intensity of light falling on slit 2 . Choose the correct choice(s),