Which of the following vitamin is water soluble ?

Match List I with List II.

List-I	List-II
A. aq \(N a C l\) solution with \(P t\) electrodes	I.oxygen gas evolution at the anode
B. Dilute solution of \(H _2 SO _4\) with Pt electrode	II. Metal loss at anode.
C. aq \(CuCl _2\) with Pt electrode	III. Hydrogen gas evolved at cathode
D. aq \(CuCl _2\) with Cu electrode	IV. Metal deposited at cathode.

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If two substances A and B have \(P^o_A: P^o_B = 1 : 2\) and have mole fraction in the ratio \(1:2\), then mole fraction of A in vapours is:

Read the passage carefully and answer the Questions
In the formation of coordination complexes, if the inner \(d\) orbital \((n - 1)d\) is used in hybridisation, the complex, is called an inner orbital or low spin or spin paired complex. And if it uses outer \(d\) orbital \((nd)\) in hybridisation (like \(sp^3d^2\)), it is called outer orbital or high spin or spin free complex. The degeneracy of the \(d\) orbitals has been removed due to ligand electron-metal electron repulsions in the complex. This splitting of the degenerate levels due to the presence of ligands in a definite geometry is termed as crystal field splitting. For coordination complexes, the magnetic moment is determined by the number of unpaired electrons and is calculated by using the 'spin-only' formula, \(\mu = \sqrt{n(n+2)}\) where \(n\) is the number of unpaired electrons and \(\mu\) is the magnetic moment in units of Bohr magneton \((BM)\). The coordination compounds are of great importance. These compounds are widely present in the mineral, plant and animal worlds and are known to play many important functions in the area of analytical chemistry, metallurgy, biological systems, industry and medicine.
Which of the following complex has the highest magnetic moment?

On heating, \(\left[ Ti \left( H _2 O \right)_6\right] Cl _3\) becomes colorless because \(\backslash\) ldots \(\backslash\) ldots \(\backslash\) ldots

In the conversion of ethanol to ethene, the first step of the reaction involves the formation of

Match the statement of set of orbitals given in List-I with orbitals and energy separation given in List-II

List – I (Statements)	List-II (Orbitals and energy separation)
(A) \(t_{2 g}\) set of orbitals in octahedral crystal field and energy separation from barycentre	(I) \(d_{x^2-y^2}, d_{z^2}\) and \(3 / 5 \Delta_t\)
(B) \(e_g\) set of orbitals in octahedral crystal field and energy separation from barycentre	(II) \(d_{x y}, d_{x z}, d_{y z}\) and \(2 / 5 \Delta_t\)
(C) \(t_2\) set of orbitals in tetrahedral crystal field and energy separation from barycentre	(III) \(d_{x^2-y^2}, d_{z^2}\) and \(3 / 5 \Delta_0\)
(D) \(e\) set of orbitals in tetrahedral crystal field and energy separation from barycentre	(IV) \(d_{x y}, d_{x z}, d_{y z}\) and \(2 / 5 \Delta_0\)

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The solution of the differential equation \(\frac{d y}{d x}=\left(1+x^2\right)\left(1+y^2\right)\) is (Here \(C\) is an arbitrary constant)

A small company manufactures necklaces and bracelets. The combined number of necklaces and bracelets it can handle per day is at the most 24 .A bracelet takes 1 hour to make and a necklace takes half hour to be made.Maximum number of hours available per day is 16 .If the number of necklaces and bracelets made per day is \(x\) and \(y\)
respectively then the time constraint for the L.P.P.is :

The slope of the normal to the curve \(y=x^3+3 x-2\) at its point of intersection with y-axis is:

Let \(f(x)=\left\{\begin{array}{ll}\frac{|x|}{x}, & x \neq 0 \\ 1, & x=0\end{array}\right.\), and \(g(x)=\left\{\begin{array}{ll}x \sin \frac{1}{x}, & x \neq 0 \\ 0, & x=0\end{array}\right.\). Then at the origin, which one is true?

The depletion layer has large electrical resistance because:

In an interference experiment, the two slits are 1 mm apart and the screen is placed 1 m away from the slits.
The width of a bright fringe for the light of wavelength 500 nm is