The number of structural isomers for \(\mathrm{C}_6 \mathrm{H}_{14}\) is

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Copper is the most noble of the first row transition metals and occurs in small deposits in several countries. Ores of copper include chalcanthite \(\left(\mathrm{CuSO}_4 \cdot 5 \mathrm{H}_2 \mathrm{O}\right)\), atacamite \(\left(\mathrm{Cu}_2 \mathrm{Cl}(\mathrm{OH})_3\right)\), cuprite \(\left(\mathrm{Cu}_2 \mathrm{O}\right)\), copper glance \(\left(\mathrm{Cu}_2 \mathrm{~S}\right)\) and malachite \(\left(\mathrm{Cu}_2(\mathrm{OH})_2 \mathrm{CO}_3\right)\). However, 80\% of the world copper production comes from the ore chalcopyrite \(\left(\mathrm{CuFeS}_2\right)\). The extraction of copper from chalcopyrite involves partial roasting, removal of iron and self-reduction.
Question:
In self-reduction, the reducing species is

In the scheme given below, the total number of intramolecular aldol condensation products formed from ' \(Y\) ' is

Columns 1, 2 and 3 contain starting materials, reaction conditions and type of reactions respectively.

Column 1	Column 2	Column 3
(I) Toulene	(i) \(NaOH\) \( /Br _2\)	(P) Condensation
(II) Acetophenone	(ii) \(B r_2 / h v\)	(Q) Carboxylation
(III) Benzaldehyde	(iii) \(\left( CH _3 CO \right)_2\) \(O / CH _3\) \(COOK\)	(R) Substitution
(IV) Phenol	(iv) \(NaOH\) \(/CO _2\)	(S) Haloform

For the synthesis of benzoic acid the only correct combination is

The synthesis of 3-octyne is achieved by adding a bromoalkane into a mixture of sodium amide and an alkyne. The bromoalkane and alkyne respectively are

The correct statements (s) about intermolecular forces is(are)

Bleaching powder and bleach solution are produced on a large scale and used in several household products. The effectiveness of bleach solution is often measured by iodometry.
Question :
Bleaching powder contains a salt of an oxoacid as one of its components. The anhydride of that oxoacid is

Statement \(\mathbf{1}\left[\mathrm{Fe}\left(\mathrm{H}_2 \mathrm{O}\right)_5 \mathrm{NO}\right] \mathrm{SO}_4\) is paramagnetic.
Statement 2 The \(\mathrm{Fe}\) in \(\left[\mathrm{Fe}\left(\mathrm{H}_2 \mathrm{O}\right)_5 \mathrm{NO}\right] \mathrm{SO}_4\) has three unpaired electrons.

Let \(a_1, a_2, a_3, \ldots, a_{11}\) be real numbers satisfying \(a_1=15,27-2 a_2>0\) and \(a_k=2 a_{k-1}-a_{k-2}\) for \(k=3,4, \ldots, 11\).
If \(\frac{a_1^2+a_2^2+\ldots+a_{11}^2}{11}=90\), then the value of \(\frac{a_1+a_2+\ldots+a_{11}}{11}\) is equal to

The correct statement(s) about surface properties is(are)

Statement 1 For practical purposes, the earth is used as a reference at zero potential in electrical circuits.
and Statement 2 The electrical potential of a sphere of radius \(R\) with charge \(Q\) uniformly distributed on the surface is given by \(\frac{Q}{4 \pi \varepsilon_0 R}\).

Let \(\mathbb{R}\) denote the set of all real numbers. For a real number \(x\), let \([x]\) denote the greatest integer less than or equal to \(x\). Let \(n\) denote a natural number.
Match each entry in List-I to the correct entry in List-II and choose the correct option.

	LIST - I		LIST - II
(P)	The minimum value of \(n\) for which the function \(f(x)=\left[\frac{10 x^3-45 x^2+60 x+35}{n}\right]\) is continuous on the interval \([1,2]\),is	(1)	8
(Q)	The minimum value of \(n\) for which \(g(x)=\left(2 n^2-13 n-15\right)\left(x^3+3 x\right),x \in \mathbb{R}\),is an increasing function on \(\mathbb{R}\),is	(2)	9
(R)	The smallest natural number \(n\) which is greater than 5,such that \(x=3\) is a point of local minima of \(h(x)=\left(x^2-9\right)^{\mathrm{n}}\left(x^2+2 x+3\right)\),is	(3)	5
(S)	Number of \(x_0 \in \mathbb{R}\) such that \(l(x)=\sum_{k=0}^4\left(\sin |x-k|+\cos \left|x-k+\frac{1}{2}\right|\right),x \in \mathbb{R}\),is NOT differentiable at \(x_0\),is	(4)	6
		(5)	10

Area of the region bounded by the curve \(y=e^x\) and lines \(x=0\) and \(y=e\) is