The decomposition of N\(_2\)\(\mathrm{O}_5\) in CCl\(_4\) at 318K has been studied by monitoring the concentration of N\(_2\)\(\mathrm{O}_5\) in the solution. Initially, the concentration of N\(_2\)\(\mathrm{O}_5\) is 2.33 mol/L and after 184 minutes, it is reduced to 2.08 mol/L. The reaction takes place according to the equation
2N\(_2\)\(\mathrm{O}_5\)(g) \(\rightarrow\) 4NO\(_2\)(g) + O\(_2\)(g)
The average rate of this reaction in different units will be:

Read the passage carefully and answer the questions
The osmotic pressure is one of the four colligative properties which depends on the number of particles of solute in the solution, irrespective of their nature. The osmotic pressure is equal to the product of concentration, gas constant and temperature. It is the most commonly used property for the determination of the molar mass of biomolecules. In many situations, the molecules get dissociated or associated when they are dissolved in a solvent, thereby changing the number of molecules in the solution. As a result, an abnormal molecular mass is obtained. The extent of dissociation or association is given by van't Hoff factor (i), which is the ratio of normal molar mass to abnormal molar mass. It is related with the degree of association or ionization. The introduction of van't Hoff factor in the osmotic pressure equation modifies the equation.
Which one of the following has minimum osmotic pressure at 298 K ?

Answer the questions on the basis of passage given below :
As aldehydes ketones possess the carbonyl functional group, they show similar reactions. They exhibit nucleophilic addition reactions, reduction, oxidations, reactions due to alpha-Hydrogen atom, and many other reactions, like Cannizzaro reaction to electrophilic substitution reactions (in case of aromatic aldehydes ketones).
These reactions help in the preparation of a number of important compounds, like acetic acid, vinyl acetate, polymers and in perfume and dye industries.
Nucleophilic addition reactions form cyanohydrins, acetals, alcohols and N -substituted derivatives like imine, oxime, semicarbazone, phenylhydrazone Schiff's base. Reactions due to alpha-hydrogen atoms help in formation of aldols and alpha, beta-unsaturated aldehydes ketones.
Which of the following combinations of Grignard's reagent and carbonyl compound can give \(C _6 H _5- C ( OH )\left( CH _3\right)- CH \left( CH _3\right)_2\)
A. \(C _6 H _5 CH _2 MgBr +\left( CH _3\right)_2 CH - CHO\)
B. \(C _6 H _5 MgBr + CH _3- CO - CH \left( CH _3\right)_2\)
C. \(CH _3 MgBr + C _6 H _5- CO - CH \left( CH _3\right)_2\)
D. \(C _6 H _5- CO - CH _3+\left( CH _3\right)_2 CHMgBr\)
E. \(C _6 H _5 CH ( MgBr ) CH _3+\left( CH _3\right)_2 CO\)
Choose the correct answer from the option 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.
Which amongst the following is a better oxidising agent than other ?

Answer the question on the basis of passage given below :
For the transition elements
Sc \(\quad\) Ti \(\quad\) V \(\quad\) Cr \(\quad\) Mn\(\quad\) Fe \(\quad\) Co \(\quad\) Ni \(\quad\) Cu \(\quad\) Zn
Atomic numbers :
21 \(\quad\) 22 \(\quad\) 23 \(\quad\) 24 \(\quad\) 25 \(\quad\) 26 \(\quad\) 27 \(\quad\) 28 \(\quad\) 29 \(\quad\) 30 \(\quad\)
Which transition metal has the greatest number of oxidation state?

Which of the following is not correct?
A. \(La(OH)_3\) is less basic than \(Lu(OH)_3\)
B. In Lanthanoid series, ionic radius of \(M^{3+}\) ion decreases from \(La\) to \(Lu\).
C. \(La\) is an element of transition series rather than a Lanthanoid series.
D. Atomic radii of \(Zr\) and \(Hf\) are the same because of Lanthanoid contraction.
Choose the correct answer from the options given below:

Choose the incorrect statement from the following:

A battery of emf 3 V and internal resistance r is connected in series with a resistor of \( 55 \text{ } \Omega \). An ammeter of resistance \( 2 \text{ } \Omega \) connected in circuit reads 50 mA. The value of r is

We use microbes and microbially derived products almost every day. Bacteria called lactic acid bacteria (LAB) grow in milk to convert it into curd. The dough, which is used to make bread, is fermented by yeast called Saccharomyces cerevisiae. Microbes are used to produce industrial products like lactic acid, acetic acid and alcohol, which are used in a variety of processes in the industry. However, certain bacteria, which grow anaerobically on cellulosic material, produce large amount of methane along with CO2 and H2. These bacteria are collectively called methanogens, and one such common bacterium is Methanobacterium. These bacteria are commonly found in the anaerobic sludge during sewage treatment. Microbes are also used for commercial and industrial production of certain chemicals like organic acids, alcohols and enzymes.
Examples of acid producers are Aspergillus niger (a fungus) of citric acid. You are familiar with the commonly used antibiotic Penicillin. Do you know that Penicillin was the first antibiotic to be discovered, and it was a chance discovery? Statins produced by the yeast Monascus purpureus have been commercialised as blood-cholesterol lowering agents. It acts by competitively inhibiting the enzyme responsible for synthesis of cholesterol.
Statins produced by the yeast Monascus purpureus have been commercialised as blood-cholesterol lowering agents. It acts by:

\(P, Q, R\) and \(S\) are four wires of resistances \(3,3,3\) and \(4 \Omega\) respectively. They are connected to form the four arms of a wheatstone bridge circuit. The resistance with which S must be shunted in order that the bridge may be balanced is

A random sample of size 16 has 53 as mean. The sum of the squares of the deviations taken from mean is 150 . If the population mean is 56 then the value of \(t\)-test statistic is :

Read the following paragraph and answer the given questions.
RNAi takes place in all eukaryotic organisms as a method of cellular defense. The source of this complementary RNA could be from an infection by viruses having RNA genomes or mobile genetic elements (transposons) that replicate via an RNA intermediate. Insulin from an animal source, though caused some patients to develop allergy or other types of reactions to the foreign protein. Insulin consists of two short polypeptide chains: chain A and chain B, that are linked together by disulphide bridges. Transgenic mice are being developed for use in testing the safety of vaccines before they are used on humans. Transgenic mice are being used to test the safety of the polio vaccine. If successful and found to be reliable, they could replace the use of monkeys to test the safety of batches of the vaccine. Specific Bt toxin genes were isolated from Bacillusthuringiensis} and incorporated into the several crop plants such as cotton. The choice of genes depends upon the crop and the targeted pest, as most Bt toxins are insect-group specific. The toxin is coded by a gene cryIAc named cry. There are a number of them, for example, the proteins encoded by the genes cryIAc and cryIIAb control the cotton bollworms, that of cryIAb controls corn borer.

Identify the incorrect fact about the genetic modification?

A pair of dice is thrown 7 times. If getting a total of 7 is considered a success, the probability of exactly 6 successe, is: