The conversions which are represented correctly are


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Answer the question on the basis of passage given below:
Second period elements of p-Block differs from the rest of their group members due to their small atomic size, high electronegativity, high ionization enthalpy and absence of d-orbitals. The elements from the second period like C, N, O have unique property of forming \(p \pi-p \pi\) multiple bonds whereas other heavier elements of p-block form \(d \pi-p \pi\) multiple bonds. This changes the properties of second period elements to great extent. Also the single bond strength of the p-block elements with their own atoms gets affected by their atomic size and presence of lone pairs.
Inert pair effect also affects the properties of the p-Block elements especially for those elements which are present from 4th period onward and this happens due to poor screening effect of inner (n-1)d subshell electrons.
Among the elements mentioned below, some are not stable in their +3 oxidation state and undergoes disproportionation reactions easily:
A. N
B. \(P\)
C. As
D. Sb
E. Bi
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Identify the biodegradable polymer in the following :

Which of the following statements is not correct with reference to a catalyst?

In the formation of a Leclanche cell, the space between electrodes is filled with:
(A) \(ZnCl _2\)
(B) \(NH _4 Cl\)
(C) \(AlCl _3\)
(D) ZnS
(E) \(NH _4 NO _3\)
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A first order reaction is found to have a rate constant \(k = 5.5 \times 10^{-14}\ s^{-1}\).
Find the half-life of the reaction.

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The crystal field theory (CFT) is an electrostatic model which considers the metal-ligand bond to be ionic arising purely from electrostatic interactions between the metal ion and the ligand. Ligands are treated as point charges in case of anions or dipoles in case of neutral molecules. The five d orbitals in an isolated gaseous metal atom/ion have same energy, i.e., they are degenerate. This degeneracy is maintained if a spherically symmetrical field of negative charges surrounds the metal atom/ion. However, when this negative field is due to ligands (either anions or the negative ends of dipolar molecules like NH3 and H2O) in a complex, it becomes asymmetrical and the degeneracy of the d orbitals is lifted. It results in splitting of the d orbitals. The pattern of splitting depends upon the nature of the crystal field.
The hybridisation and magnetism of the complexes \(\left[\mathrm{Co}\left(\mathrm{C}_2 \mathrm{O}_4\right)_3\right]^{3-}\) and \(\left[\mathrm{Mn}(\mathrm{CN})_6\right]^{3-}\) respectively is:

The shortest distance between the lines \(\vec{r}_1=\hat{i}+\hat{j}+\lambda(2 \hat{i}-\hat{j}+\hat{k})\) and \(\vec{r}_2=2 \hat{i}+\hat{j}-\hat{k}+\mu(4 \hat{i}-2 \hat{j}+2 \hat{k})\) is :

Let \(X\) denote the number of hours a student studies on a selected day. The probability distribution of \(X\) is given by (where \(k\) is some unknown constant)
\(P\left(X=x_i\right)=\left\{\begin{array}{ll}0.5, & \text { if } x_i=0 \\k x_i, & \text { if } x_i=1 \\k\left(4-x_i\right), & \text { if } x_i=2 \text { or } 3 \\0, & \text { otherwise }\end{array}\right.\)
Then the value of \(k\) is

The value of \(\tan \frac{1}{2}\left\{\sin ^{-1}\left(\frac{2 x}{1+x^2}\right)+\cos ^{-1}\left(\frac{1-y^2}{1+y^2}\right)\right\}\) if \(|x|<1, y>0\) and \(x y<1\) is:

Which of the following are first order linear differential equations?
(A)\(\frac{d x}{d y}+P_1(y) x=Q_1(y): P_1(y)\) and \(Q_1(y)\) are functions of y or constant functions
(B)\(\frac{d y}{d x}+P_2(x) y=Q_2(x): P_2(x)\) and \(Q_2(x)\) are functions of a or constant functions
(C)\((x+y) \frac{d y}{d x}=x-2 y\)
(D)\(\left(1+x^2\right) \frac{d y}{d x}-2 x y=x^2+3\)
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When strong magnetic field is applied on a stationary electron, the electron :

A non conducting solid sphere of radius R is uniformly charged. The magnitude of the electric field due to the sphere at a distance r from its center :
A. decreases as r increases, for 0 < r < \(\infty\)
B. increases as r increases, for r < R
C. becomes zero.
D. decreases as r increases, for R < r < \(\infty\)
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