Explore topic-wise InterviewSolutions in Current Affairs.

 (i) \(a^2-4\)

= \((a)^2-(2)^2=(a+2)(a-2)\)

 (ii) \(a^2-49b^2\)

= \((a)^2-(7b)^2=(a+7b)(a-7b)\)

 (iii) \(x^3-121x\)

\(=x[(x)^2-(11)^2]\)

\(=x(x-11)(x+11)\)

 (iv) \(4a^2-\frac{9}{4a^2}\)

\(=(2a)^2-(\frac{3}{2a})^2\)

\(=(2a+\frac{3}{2a})(2a-\frac{3}{2a})\)

 (v) \(\frac{18}{x^2}-\frac{2x^2}{9}\)

\(=2(\frac{9}{x^2}-\frac{x^2}{9})=2[(\frac{3}{x})^2-(\frac{x}{3})^2]\)

\(=2(\frac{3}{x}-\frac{x}{3})(\frac{3}{x}+\frac{x}{3})\)

Correct option is (B) 2

\(5^{3x-1}\div25\) = 125

\(\Rightarrow\frac{5^{3x-1}}{25}=125\)

\(\Rightarrow\) \(5^{3x-1}=5^2\times5^3=5^{2+3}=5^5\)

\(\Rightarrow\) \(3x-1=5\)

\(\Rightarrow\) 3x = 5+1 = 6

\(\Rightarrow x=\frac63=2\)

 Correct option is  B) 2

\((a-b)^2-c^2\)

\(=(a-b-c)(a-b+c)\)

\((a-3b)^2-36b^2\)

\(= (a-3b)^2-(6b)^2\)

\(= (a-3b+6b)(a-3b-6b)\)

\(= (a+3b)(a-9b)\)

a) Molecular mass of a substance expressed in grams is called gram molecular mass. 

b) Volume of one mole of any substance is called its Molar volume.

Because it is number of moles of solute per litre of solution, and volume varies with temperature.

External indicator is added in between the titration process by taking a drop of titrated mixture. 

Example: Potassium ferrocynide is used when ferrous ammonium sulphate is titrated against K₂Cr₂O₇.

A quantity of substance whose mass in grams is numerically equal to its molecular mass is called gram molecular mass. In simple terms, molecular mass of a substance expressed in grams is called gram molecular mass. 

e.g., the molecular mass of oxygen = 32 amu 

Therefore, gram molecular mass of oxygen = 32 g

When in titration one of the solution acts as a self indicator. 

Example: KMnO₄.

The volume occupied by one gram mole of a substance in the gaseous or is the vapour state at STP is called the gram molecular volume. The gram molecular volume of all the substance is found to be 22.4 dm³ or 22400 cm³. The mass in gram of 22.4 dm³ of a gas or vapour at STP is equal to its gram molecular weight. 

1 g molecule of chlorine or 1 gram molecule of carbon di-oxide or 1 gram of any other substance in the gaseous state occupies a volume of 22400 cm³ (22.4 dm³). 

1 g molecule weight of hydrogen = 2.016 g, 2.016 g of hydrogen occupies 22.4 dm³ of volume at STP. But 1 g equivalent weight of hydrogen is 1.008 g occupies 11.2 dm³ of volume at STP or mass of 11200 cm³ of hydrogen = its equivalent weight.

Allotropes of oxygen : 

• Oxygen O₂ 
• Ozone O₃ 

(i) The existence of an element in two or more chemically similar but physically different forms is called allotropy and the different forms are called allotropes, e.g., diamond, graphite, wood charcoal, lamp black etc., are allotropes of carbon. 

(ii) The existence of a compound in different crystalline forms is called polymorphism and the different forms are called polymorphs, e.g., ZnS has two polymorphs called zinc blende and wurtzite. 

(iii) The existence of different compounds with similar chemical composition in the same crystalline form is called [M₂SO₄M₂ (SO₄)₃ 24H₂O] are isomorphs.

Option : (d) H₂Te

In the vapour state, sulphur partly exists as S₂ molecule, which has two unpaired electrons in the antibonding π^* orbitals like O₂. Hence it exhibits paramagnetism.

• All the elements of group 16 exhibit allotropy. 
• These elements exist in different allotropic modifications. 
• Oxygen exists as O₂ and ozone O₃. 
• Sulphur exists as α-sulphur, β-sulphur, γ-sulphur, homocyclic sulphur, plastic sulphur, etc. Rhombic sulphur (α sulphur) and mono-clinic sulphur (β sulphur) are the important allotropes. Both are non-metallic in nature. 
• Selenium exists in two allotropic forms red (nonmetallic) and grey (metallic). 
• Tellurium exists in two allotropic forms crystalline form and the amorphous form.
• Po has two forms namely α-form and β-form both being metallic.  

Option : (d) +2

• Allotropy is the existence of an element in more than one physical form. It means that under different conditions of temperature and pressure an element can exist in more than one physical forms.
• Coal, graphite and diamond etc., are different allotropic forms of carbon.
• Polymorphism is the existence of a substance in more than one crystalline form.
• It means that under different conditions of temperature and pressure, a substance can form more than one type of crystal. 

For example,

Mercuric iodide exists in the orthorhombic and trigonal form.

The property of some elements to exist in two or more different forms in the same physical state is called allotropy.

Oxygen combines with the most electronegative element fluorine to form OF₂ and exhibits positive oxidation state (+ 2). Since, oxygen does not have vacant J-orbitals it cannot exhibit higher oxidation states. 

Sulphur has vacant d-orbitals and hence can exhibit + 6 oxidation state to form SF₆.

The order from Berlin brought a sense of shock and surprise in the class. They were all dumbstruck. As per the order, this was the last French class. Alsace and Lorraine had been captured by the Prussians. So only German was to be taught in the schools. Hamel had to leave the next day. Now they all felt passionate about their mother tongue. All the eminent village elders felt guilty for neglecting their mother tongue.

Now they came to the class and showed their love and respect for their mother tongue. They were in awe for their French teacher M. Hamel. The entire school was filled with an air of repentance and guilt. There was complete quietness. The teacher, M. Hamel, was dressed at his best and was full of emotions. Even the students in the class, including little Franz, felt remorse for their indifference to their mother tongue. There was an atmosphere of stillness and quietness in the class.

‘Education prepares you for the future.’

• Oxygen being more electronegative, is capable of forming hydrogen bonding in the compound H₂O.
• The other elements S, Se and Te of Group 16, being less electronegative do not form hydrogen bonds.
• Thus, hydrogen bonding is not present in the other hydrides H₂S, H₂Se and H₂Te.

The order from Berlin shocked the French. It stated that from henceforth only German would be taught at Alsace and Lorraine. The whole environment was tense. The narrator found that the sonorous rapping on the table, and other peculiar loud noises were no more. All mute faces were writing busily disturbing the calm of the place. The villagers had occupied the back benches to attend M. Hamel's class. He was also attired in a formal outfit. His attitudinal change found him gentle in reprimanding everyone present. Including himself for being casual to the most logical language, French. Everyone was engrossed in learning and Hamel made them realize their mistake.

• The nucleus of a hydrogen atom consists of one positively charged proton i.e., nuclear charge of +1 and one extranuclear electron.
• As this electron is in direct influence of nuclear attraction, hydrogen has a little tendency to lose this electron.
• However, it can easily pair with the other electron forming a covalent bond.
• Therefore, it exists in diatomic form as H₂ molecule and hence, it is also referred to as dihydrogen.

Diborane (B₂H₆)

The narrator had not prepared his lesson well and was late for school. As he hurried toward his class, he was counting on the commotion to get to his desk without being noticed but that day everything was as quiet as a Sunday morning.

The order from Berlin to teach only German in the schools of Alsace and Lorraine perturbed the French greatly. Now they realized how important French was. The humdrum inside and outside the class was missing. The silence of the graveyard welcomed each one. Students and village people had a common people feeling of terror and of learning German under pressure. All were settled to take the last lesson seriously. They realized their blunder of not taking French seriously before. All sat with grim faces and their dislike for M. Hamel changes to admiration. Even M. Hamel presented a different facet of his personality. He wished he could teach the entire French in the Last Lesson. His patriotic fervour when he wrote 'Viva La France' inspired the French to earn their freedom back.

(i) Catenation 

(ii) Tetravalency of carbon

(i) Catenation 

(ii) Tetravalency of carbon

Khushwant Singh describes his grandfather as he was painted in the portrait that was hung above the mantlepiece. He wore a big turban and loose-fitting clothes. He had a long white beard and he looked at least 100 years old. He looked like the kind of person who could have only lots and lots of grandchildren.

Thick, stale chapattis with a little butter and sugar spread on it.

The rosary and her prayers were an inseparable part of the grandmother.

She hoped that the author would listen and get to know it by heart.

The sight of her mother's corpse-like face arouses ' that old familiar ache' in her heart. Her childhood fear returns. The fear is that with ageing comes decay and death. Ageing and decay are inevitable. No one avoid them. Perhaps she herself may have to face all these things. This idea is quite painful and fearful to her.

1. Pyruvate dehydrogenase (PDH) requires thiamin (vitamin Bi) as a coenzyme. It cannot function in absence of vitamin B₁ . 

2. Thiamin deficiency causes many disorders such as pyruvic acidosis and lactic acidosis, which are life threatening conditions. Hence, it is required to maintain good health.

(B) Autosomal linked disease

When male and female flowers are borne on the same plant, they are called monoecious, e.g., mango, guava and when male and female flowers are borne on different plants, they are called dioecious plants. e.g., date palm, papaya

Aleurone layer is a layer of cells rich in proteins, that separates the embryo from the endosperm in cereal grains like rice, maize, wheat etc. 

Pseudocarp is a false fruit which develops from the ovary along with adjoining accessory floral parts, e.g., apple.

In 'Fabaceae' the old sepal is anterior.

The endosperm in maize seed is enclosed by aleurone layer (a sheath of special tissue).It contain proteins.

(i) Smallest flower: Wolffia 

(ii) Largest flower- Rafflesia.

The plants with three types of individuals: Male, female and hermaphrodite are called trioecious plant.

The first leaf of the embryo of seed plants which is usually simpler in structure than later formed leaves.

The correct option is (a) Nymphaea

They are called non-endospermic or exalbuminous seeds. In Nymphaea, the food is stored in nucellus or perisperm. The seed is called perispermic seed.

Ratio of circumferences of two circles = 2:3 (given)

Let the two circles be C₁ and C₂ with radii r₁ and r₂.

Circumference of circle = 2πr

Circumference of C₁ = 2πr₁ and

Circumference of C₂ = 2πr₂

(Circumference of C₁) / (Circumference of C₂) = (2πr₁)/(2πr₂)

2/3 = r₁/r₂

Now,

(area of C₁) / (area of C₂) = (πr₁²)/(πr₂²)

= {(r₁)/(r₂)}²

= (2/3)²

=4/9

Therefore, the required ratio is 4:9.

Given,

Diameter of the hemisphere = 14 cm

So, the radius of the hemisphere = 7 cm

Total height of the vessel = 13 cm = h + r

Now,

Inner surface area of the vessel = 2 π r (h + r)

= 2 (22/7)(7) (13)

= 572 cm² 

Therefore, the inner surface area of the vessel is 572 cm².