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Given, A²= A.

(E) we need to calculate,

(I + A)³- 7A = I³ + A³ + 3IA (I + A) - 7A { (x + y)³ = x³ + y³ + 3xy (a + y)}

This is a multiple choice type question as classified in NCERT Exemplar

Correct option (i) and (ii)

On moving down the group, as the size increases the hydration enthalpy decreases. The hydration enthalpy of beryllium and magnesium ions are high due to the small size. Thus, sulfates are readily soluble in water.

Given, A is both symmetric and skew-symmetric.

(E) Then, A' = A ____ (1) and A' = -A ____ (2)

So using (2), A' = -A.

A = -A {eqⁿ (I)}

A + A = 0

2A = 0

A = 0.

A is a zero matrix

So, option B is correct.

This is a multiple choice type question as classified in NCERT Exemplar

Correct option (i) and (iii)

Na₂CO₃ is used in paper paints and textile industry. It is used to manufacture soap powders.

NaOH is used in textile industry for mercerising cotton fabrics.

Yes, at Maya Somaiya School of Music and Performing Arts, students who are officially pursuing a MPA course are offered scholarships. The institute has various types of scholarships to cater to a wide range of student needs. The below list contains some of the scholarships offered by the institute:

• EWS (Economically Weaker Section) Scholarship
• For Students with Disabilities (PWD)
• Sports Merit Scholarship

This is a multiple choice type question as classified in NCERT Exemplar

Correct option (ii) and (iv)

Alkali metals have larger atomic size and low density. These metals lose electrons due to less effective nuclear charge. They have a high value of electrode potential.

Lithium has the highest negative reduction potential value. Due to the small size of lithium it has a small atomic size and  the highest ionization enthalpy.

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After completing an MBA course from SRM School of Management, candidates can pursue various job opportunities in the fields of Management, Marketing, Sales, etc. Moreover, the course also prepares the students with the knowledge, skills, and strategic perspectives essential to business leadership and a managerial career in the competitive world. Some of the job roles that candidates can pursue after completing the course are as follows:

• International Marketing Manager
• Global Business Consultant
• Foreign Trade Analyst
• Human Resource Manager
• Business Development Manager, etc. 

Micheal Burns, an American entertainment executive & the vice chairman of Lionsgate Productions, is a notable alumni of the ASU Engineering School.

Lionsgate is a famous entertainment organizations known for producing & distributing a number of movies & TV Shows. Among some of its popular franchises are: The Hunger Games, John Wick, Twilight & Saw.

Some other popular movies produced by it includes: Rambo, The Expendables, Hacksaw Ridge & the Blair Witch project. 

Micheal pursued a Bachelor of Science degree from the institute in 1980 before going on to attend UCLA in 1992 for his MBA studies.

This is a multiple choice type question as classified in NCERT Exemplar

Correct option (iv)

Chlorides of alkaline earth metals are hydrated salts. They can be used as dehydrating agents due to their hygroscopic nature to absorb moisture from air. Extent of hydration decreases from Mg to Ba.

Therefore, dehydration of hydrates of halides of calcium, barium and strontium i.e., CaCl₂.6H₂O, BaCl₂.2H₂O, SrCl₂.2H₂O can be achieved by heating.

Yes candidates can join UHS Bagalkot BTech if they do not want to give the KCET entrance exam. Candidates can apply through the ICAR AIEEA entrance exam to secure admission into the programme. Once the results of either of the exams are announced, candidates can apply for admission into the programme through the university website. 

Yes, BVIMSR admission is open for the current year. The institute offers MMS course at the PG level. Candidates looking for course admission must meet the eligibility criteria set by the college, Aspirants must pass graduation with a 45%-50% aggregate. Student appearing for final year examinations can also apply, but their admission will be subject to obtaining a minimum of 50% aggregate (45% for SC/ST) at qualifying examination. Diploma holders are not eligible. 

Yes, fees play an important role when comparing the MPA course offered by Maya Somaiya School of Music and Performing Arts with other similar institutes/colleges. Drawing a comparison based on fees helps students calculate the affordability of a program. The lower the fees, the greater the affordability. As per official sources, the total tuition fees to pursue the MPA course at the institute is INR 80,000.

Note: The above-mentioned fee is as per the official sources. However, it is indicative and subject to change.

We have, AB = BA. (given)

(E) P (n):AB’ = B’A.

P (i):AB¹ = B¹A. Þ AB = BA

so, the result is true for n = 1.

Let the result be true for n = k.

P (k):AB^k = B^kA

Then,

P (k + 1) : AB^{k + 1} = A. B^k. B = B^kA.B = B^k.BA $\{?\}\; AB=BA$

= Bk + 1.A .

So, AB^{k + 1} = B^{k + 1}A.

The result also holds for n = k + 1.

Hence, AB^n = B^n A^n holds for all natural number ‘n’.

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This is a multiple choice type question as classified in NCERT Exemplar

Correct Option (iii)

The chemical formula of A is Ca (OH)₂ Sodium carbonate is prepared by Solvay's process. In this process, ammonia is recovered when ammonium chloride reacts with calcium hydroxide. On reacting NH₄Cl with Ca (OH)₂, calcium chloride is obtained as a by-product. The reaction is given below.

2NH₄Cl+Ca (OH)₂→2NH₃+CaCl₂+H₂O

When CO₂ is bubbled through an aqueous solution of Ca (OH)₂ the solution turns milky. It is used in whitewashing due to its disinfectant nature.

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