Answer the question on basis of passage given below :
P block elements are placed in groups 13 to 18 of the periodic table. Their valence shell electronic configuration is \(ns^2 np^{1-6}\). Group 16 of the p block elements are known as the group of chalcogens having \(ns^2 np^4\) as their general electronic configuration. They exhibit number of oxidation states but the stability of \(- 2\) oxidation state decreases down the group. They are sometimes also known as group of chalcogens as the name is derived from the Greek word for brass and points to the association of sulphur and its congeners with copper. Their ionisation enthalpy decreases down the group. Oxygen shows anomalous behaviour due to its small size and high electronegativity.
Identify the epsom salt out of the following salts :

The correct structure representing N,N-dimethylethanamine is

The number of unpaired electrons in gaseous ions \(Mn ^{3+}, V ^{3+}, Cr ^{3+}\) are respectively:

Read the passage carefully and answer the questions:
The degeneracy of the \(d\) orbitals has been removed due to ligand electron-metal electron repulsions in the octahedral complex to yield three orbitals of lower energy, \(t_{2 g}\) set and two orbitals of higher energy, \(e_g\) set. This splitting of the degenerate levels due to the presence of ligands in a definite geometry is termed as crystal field splitting and the energy separation is denoted by \(\Delta_0\). Thus energy of the two \(e_g\) orbitals will increase by \((3 / 5) \Delta_{\circ}\) and that of three \(t_{2 g}\) will decrease by \((2 / 5) \Delta_0\). The crystal field splitting \(\Delta_{ o }\) depends upon the field produced by the ligand and charge on the metal ion. Some ligands are able to produce strong fields, in which case the splitting will be large, whereas others produce weak fields and consequently result in small splitting of \(d\) orbitals. Relative magnitude of crystal field splitting energy \(\Delta_{\circ}\) and pairing energy, \(P\) (energy required for electron pairing in a single orbital) determine the formation of low spin ( \(\Delta_0>P\) ) or high spin ( \(\Delta_0<P\) ) complex. In tetrahedral coordination entity formation, the \(d\)-orbital splitting is inverted and is smaller as compared to the octahedral field splitting. The crystal field theory attributes the colour of the complex to \(d-d\) transition of the electron. The colour of the coordination compounds depends on the crystal field splitting. In the absence of ligand, crystal field splitting does not occur and hence the substance is colourless.
Choose the correct order of the ligands in their increasing crystal field splitting:

For a reaction
\(2A + B_{2} \rightarrow 2A_{2}B\)
The reactant A will be consumed at:

When we consider an inert electrode in a cell; which statement is not suitable for it?
(A) It provides surface either for oxidation or for reduction reaction.
(B) It does not participate in the cell reaction.
(C) It provides surface for redox reaction.
(D) It provides surface for conduction of electrons.
Choose the correct answer from the options given below:

What will happen during the electrolysis of aqueous solution of \(CuSO_4\) by using platinum electrodes?
A. Copper will deposit at cathode.
B. Copper will deposit at anode.
C. Oxygen will be released at anode.
D. Copper will dissolve at anode.
Choose the correct answer from the options given below:

\(y=\log _e\left(\frac{1-x^2}{1+x^2}\right)\), then \(\frac{d y}{d x}\) is equal to:

8. An ammeter having internal resistance of \( 0.81 \, \Omega \) can read upto 1A. To convert it into an ammeter reading 0 - 10 A we have to connect :

Match List - I with List - II.

LIST I Differential equation	LIST II Integrating Factor (I.F)
A. \(\frac{d y}{d x}-\frac{y}{x}=2 x\)	I. \(x^2-1\)
B. \(\frac{d y}{d x}+\left(\frac{2 x}{x^2-1}\right) y=\frac{2}{\left(x^2-1\right)^2}\)	II. \(\sqrt{1-x^2}\)
C. \(\frac{d y}{d x}-\left(\frac{x}{1-x^2}\right) y=\frac{1}{1-x^2}\)	III. \(\frac{1}{x}\)
D. \(\frac{d y}{d x}+\frac{2 x y}{1+x^2}=\frac{\cot x}{1+x^2}\)	IV. \(1+x^2\)

Choose the correct answer from the options given below:

\(100 \text{ cm}^3\) of \(1\text{M } \text{CH}_3\text{COOH}\) and \(100 \text{cm}^3\) of \(2\text{M } \text{CH}_3\text{OH}\) were mixed to form an ester, which follows Ist order kinetics with respect to both \(\text{CH}_3\text{COOH}\) and \(\text{CH}_3\text{OH}\). The change in their initial rate, if each solution is mixed with equal number of volume of water would be :

Gause's 'Competitive Exclusion Principle' states that :

The number of vectors of unit length perpendicular to both the vectors \(\vec{a} = \hat{i} + 2\hat{j} + 3\hat{k}\) and \(\vec{b} = \hat{i} - \hat{j} + 3\hat{k}\) is: