A first order reaction is found to have a rate constant, k = 5.5 × 10^-14 s^-1. The half life of the reaction will be :

Match List-I with List-II

List-I (Name Reaction)	List-II (Reagent)
(A) Rosemund Reaction	(I) CO/HCl, anhyd.\(AlCl_{3}\), \(CuCl\)
(B) Stephen Reaction	(II) \(CrO_{2}Cl_{2}\)
(C) Etard Reaction	(III) \(SnCl_{2}\) and HCl
(D) Gatterman Koch Reaction	(IV) \(H_{2}\), \(Pd-BaSO_{4}\)

Choose the correct answer from the options given below:

Read the passage given below and answer the question.
The transition elements which give the greatest number of oxidation states occur in or near the middle of the series. Manganese, for example, exhibits all the oxidation states from +2 to +7 . The lesser number of oxidation states at extreme ends stems from either too few electrons to lose or share (Sc, Ti) on too many d-electrons (hence fewer orbitals available in which to share electrons with others) for higher valence \(( Cu , Zn )\). Thus early in the series scandium (II) is virtually unknown and titanium (IV) is more stable than Ti (III) or Ti (II). At the other end, the only oxidation state of zinc is \(+ 2\) (no d electrons are involved). The maximum oxidation states of reasonable stability correspond in value to the sum of the s - and d-electrons upto manganese ( \(Ti ^{I V} O _2, V^V O _2^{+}, Cr ^{V I} O _4^{2-}\), \(Mn ^{\text {VII }} O _4\) ) followed by a rather abrupt decrease in stability of higher oxidation states, so that the typical species to follow are \(Fe ^{I I, I I I}, Co ^{I I, I I I}, Ni ^{I I}, Cu ^{I, I I}, Zn ^{I I}\).
The variability of oxidation states, a characteristic of transition elements, arises out of incomplete filling of d-orbitals in such a way that their oxidation states differ from each other by unity, e.g. \(V ^{I I}, V^{I I I}, V^{I V}, V^V\). This is in contrast with the variability of oxidation states of non transition elements where oxidation states normally differ by a unit of two.
An interesting feature in the variability of oxidation states of the d-block elements is noticed among the groups (groups 4 through 10). Although in the p-block, the lower oxidation states are favoured by the heavier members (due to inert pair effect), the opposite is true in the groups of dblock. For example, in group 6, \(Mo ( VI )\) and \(W ( VI )\) are found to be more stable than \(Cr ( VI )\). The \(Cr ( VI )\) in the form of dichromate in acidic medium is a strong oxidising agent, whereas \(MoO _3\) and \(WO _3\) are not.
Low oxidation states are found when a complex compound has ligands capable of \(\pi\)-acceptor character in addition to the \(\sigma\)-bonding. For example, in \(Ni ( CO )_4\) and \(Fe ( CO )_5\), the oxidation state of nickel and iron is zero.
Identify the stable pair of ions :

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.
Phosphorus forms \(PF _5\) but nitrogen cannot form \(NF _5\) as:

What is the total number of structural isomers possible for the compound with molecular formula \(C _4 H _9 Br\)?

Select the colligative property which is used in the calculation of molar mass of biomolecules.

Identify the correct pKa value order:
A. Phenol
B. 4-Methylphenol (p-Cresol)
C. Benzoic acid
D. 4-Methylbenzoic acid
E. 4-Nitrobenzoic acid
Choose the correct answer from the options given below:

The corner points of the feasible region of LPP \(x+y \leq 200, y \geq 4 x, x \geq 20, x \geq 0, y \geq 0\) are :
(A) \((20,180)\)
(B) \((40,180)\)
(C) \((20,80)\)
(D) \((40,80)\)
(E) \((40,160)\)

Two positive numbers \(x\) and \(y\) such that \(x+y=60\) and \(x y^3\) is maximum are :

Match List-I with List-II

List-I	List-II
(A) Gyromagnetic ratio	(I) \( 4 \times 10^{-5} \text{ T} \)
(B) Permeability of free space	(II) \( 9.27 \times 10^{-24} \text{ Am}^2 \)
(C) Earth's magnetic field at equator	(III) \( 8.8 \times 10^{10} \text{ C/kg} \)
(D) Bohr magneton	(IV) \( 12.56 \times 10^{-7} \text{ TmA}^{-1} \)

Choose the correct answer from the options given below:

Let a pair of dice be thrown and the random variable \(X\) be the sum of the numbers that appear on the two dice.
Match List - I with List - II

X	Probability, \(P ( X )\)
(A) 4	(I) \(\frac{1}{6}\)
(B) 5	(II) \(\frac{5}{36}\)
(C) 6	(III) \(\frac{1}{12}\)
(D) 7	(IV) \(\frac{1}{9}\)

Choose the correct answer from the options given below :

The area bounded by the curve \(y=4+3 x-x^2\) and the \(x\)-axis is equal to

Match List - I with List - II

List - I	List - II
(A) Corner point of a feasible region	(I) The line segment joining any two arbitrary points of the region always lies entirely within the region
(B) Bounded feasible region	(II) can not be enclosed within a circle
(C) Unbounded feasible region	(III) can be enclosed within a circle
(D) Convex region	(IV) is a point of intersection of two boundary lines in the feasible region

Choose the correct answer from the options given below: