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(a) Force on the seventh coin is exerted by the weight of the three coins on its top. 

Weight of one coin = mg 

Weight of three coins = 3mg 

Hence, the force exerted on the 7^th coin by the three coins on its top is 3mg. This force acts vertically downward. 

(b) Force on the seventh coin by the eighth coin is because of the weight of the eighth coin and the other two coins (ninth and tenth) on its top. 

Weight of the eighth coin = mg 

Weight of the ninth coin = mg 

Weight of the tenth coin = mg 

Total weight of these three coins = 3mg 

Hence, the force exerted on the 7^th coin by the eighth coin is 3mg. This force acts vertically downward. 

(c) The 6^th coin experiences a downward force because of the weight of the four coins (7^th , 8^th , 9^th , and 10^th) on its top. 

Therefore, the total downward force experienced by the 6^th coin is 4mg. 

As per Newton’s third law of motion, the 6^th coin will produce an equal reaction force on the 7^th coin, but in the opposite direction. 

Hence, the reaction force of the 6^th coin on the 7^th coin is of magnitude 4mg. 

This force acts in the upward direction

 (a) 3mg (down) 

(b) 3mg (down) 

(c) 4mg (up) 

Note, answer to  (b) is not mg but 3mg

Lencho had the expectations of a downpour or a shower for a good harvest of corn.

i. 11, 22, 33, ......

Common difference a = 22 - 1 1 = 11

First term = 11 a + b = 11

b = 11 - 11 = 0 n = 25

Sum = 1/2 an (n + 1) + nb

= 1/2 x 11 x 25 x 26 + 25 x 0 = 3575

ii. 12, 23, 34, ......

Common difference a = 23 - 1 2 = 11

First term = 12 a + b = 12

b = 12 - 11 = 1 n = 25

Sum = 1/2 an (n + 1) + nb

= 1/2 x 11 x 25 x 26 + 25 x 1 = 3600

iii. 21, 32, 43, ......

Common difference a = 32 - 2 1 = 11

First term = 21 a + b = 21

b = 21 - 11 = 10 n = 25

Sum = 1/2 an (n + 1) + nb

= 1/2 x 11 x 25 x 26 + 25 x 10 = 3825

iv. 19, 28, 37, ......

Common difference a = 28 - 1 9 = 9

First term = 19 

a + b = 19

b = 19 - 9 = 10 

n = 25

Sum = 1/2 an(n + 1) + nb

= 1/2 x 9 x 25 x 26 + 25 x 10 = 3175

First term = 1

a + b = 1

b = 1 - 5 = -4

n = 25

Sum = 1/2 an (n + 1) + nb

= 1/2 x 5 x 25 x 26 + 25 x -4 = 1525

Midpoint of the line joining (2, 3) and (6, 5) is

\((\frac{x_1+x_3}{2},\frac{y_1+y_3}{2})=(\frac{2+6}{2},\frac{3+5}{2})\)

\((\frac{8}{2},\frac{8}{2})=(4,4)\)

∴ Centre of the circle is (4,4)

Midpoint of line joining the points (4, 5) and (1, 3) is

\((\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})=(\frac{4+1}{2},\frac{5+3}{2})\)

\((\frac{6}{2},\frac{8}{2})=(3,4)\)

The coordinates of the point of intersection of its diagonal is (3, 4).

Change in x is 2 and y is -2

When change in x be 1 then change in y = \(\frac{-2}{2}=-1\)

Let change in x be 1 then change in y will be 3.

Coordinate of y = 4 + 3 x – 1 = 1

Point (2, 1)

Let change in x be 3 then change in y will be 4.

∴ Coordinate of y = 4 + 4 x – 1 = 0

∴ Point (3, 0)

Two points are (2, 1), (3, 0)

First three digit number which is divisible by 9 is 108.

Last three digit number which is divisible by 9 is 999.

\(\therefore a_1 = 108, \,d = 9, \, a_n = 999\)

Also, \(a_n = a_1+(n - 1)d\)

⇒ \(999 = 108 + (n - 1)9\)

⇒ \((n -1) = \frac{999-108}{9}= \frac{891}9= 99\)

⇒ \(n = 100\)

\(\therefore S_n =\frac n2(a + a_n)\)

\(= \frac{100}2(108 +99)\)

\(= 50 \times 1107\)

\(= 55350\)

(35 x 4) - 5 = 135

(24 x 4) - 5 = 91

Hence, (17 x 4) - 5 = 63

Answer is : (a) Maharashtra

The Indian Hotel Company ( IHC)

Nature of management principles can be described as follows:
1. Universal Applicability: The principles of management are applicable to all types of organisations irrespective of their size and nature.
2. General Guidelines: They are only guidelines for action and don’t provide direct or readymade solution for a managerial problem.
3. Formed by practice and experimentation: The principles of management have been developed through experimentation as well as experience and wisdom of managers.
4. Flexible: They are flexible i.e. they can be modified by the managers according to a given situation.
5. Mainly behavioural: They are mainly behavioural in nature since they are devised to influence human behaviour.
6. Cause and effect relationship: The principles of management establishes relationship between cause and effect. They guide us as to what would be the effect if a particular principle were to be applied in a given situation.
7. Contingent: The use of principles of management is contingent or dependent upon the prevailing conditions.

Learning mathematics serves both as a means and an end. It is a means to develop logical and quantitative thinking abilities.

• At the early grades, children’s learning of mathematics should be a natural outgrowth from children themselves.
• Such experiences must be interesting and should challenge their imagination, so that while observing any natural phenomena they can think mathematically.

Let us now discuss in detail regarding the nature of mathematics:

• Mathematics aims at abstraction.
• Mathematics is logical.
• Mathematics is symbolic.
• Mathematics is precise.
• Mathematics is the study of structures.

Hence, we conclude that Nature of Mathematics is Abstract.

Skill:- A skill is the ability to do something. We are not born with skills, we learn them as we go along.

Mathematical skill:-  Mathematics skills help individuals to deal with basic and everyday tasks.

• Students learn these skills in schools.
• These skills are important for both work and personal life.
• It includes verbal components(number knowledge, counting, reasoning) and non-verbal components(maths notation, reasoning in time and space)

Following are a few mathematical skills:-

• Necessary computation skills
• Estimation and approximation
• Representation of mathematical ideas using words, pictures, and symbols.
• Measurement (finding the length, weight, and height of an object)
• Interpreting graphs
• Spatial sense(Geometry,ideas of shape,size,space,poistion)

Thus, it is concluded that Defining mathematical concepts is not a mathematical skill as it is an ability to learn.

 Multiple choice questions:- It is a type of questionnaire that provides multiple answer options.

A multiple-choice question (MCQ) is composed of two parts: a stem that identifies the question or problem, and a set of alternatives or possible answers that contain a key that is the best answer to the question, and several distractors that are plausible but incorrect answers to the question.

• Multiple-choice or objective type questions are highly reliable and valid questions used to measure educational achievement, intelligence, etc.
• Multiple-choice questions need time to be formulated but it takes very little time for evaluation.
• Effective distractors in multiple-choice items attract lower ability students or low score securing group, those with misconceptions or limited knowledge and skills because they are based on common misconceptions or errors in logic.
• These types of questions involve multiple choices wherein it is required to choose the right answer.
• Distractors constitute the most important element of a multiple-choice item. They also present the most challenging aspects of an item.

Thus, it is concluded that Option 1 is correct.​

• Distractors:- A multiple-choice item consists of a problem, known as the stem, and a list of suggested solutions, known as alternatives. The alternatives consist of one correct or best alternative, which is the answer, and incorrect alternatives known as distractors.

It shows inefficient/underutilization of resources.

The rightward shift of PPC indicates growth of resources or technological progress.

1. A giant lion having many wheels is the symbol of Make in India campaign.

2. The symbol of Make in India campaign indicates courage, strength, tenacity and wisdom.

3. It will help in the creation of 100 smart cities and affordable housing in India.

4. The Prime Minister Narendra Modi launched the Make in India campaign on 25th of September in 2014.

5. The main objective of Make in India campaign is to ensure solid growth and valuable employment creation in the country with the help of top investors.

6. The Government of India has created a dedicated help team and an online portal for the easy and effective communication of investors.

7. Thermal

8. Giant

9. Hub

1. It will take five years to complete Digital India.

2. Digitalization will help government offices in recording attendance and maintaining order, by using biometric identification.

3. Digital India programme was launched by the Prime Minister of India, Shri Narendra Modi on July 1st, 2015.

4. A Digital week was celebrated to finalize the requirements and features of Digital India.

5. The data of the public will be held by a huge cloud of computers and servers.

6. Mobile phones will be used as a personal identity.

7. Gadget

8. Literacy

9. Import

1. The rate of Swachh Bharat Cess is 0.5%.

2. Swachh Bharat Abhiyan is a clean India drive.

3. he PM himself has nominated the names of nine people to participate in the cleanliness drive in their own areas.

4. Approximately 3 million government employees including students from schools and colleges took part in the cleanliness drive.

5. When the PM launched the campaign, he himself cleaned the road.

6. Swachh Bharat Abhiyan was launched by Indian Prime Minister, Narendra Modi on 2nd October in 2014.

7. Approximately

8. Flush

9. Flush

In 1999 Kargil War fought between India and Pakistan 

Correct option is (d) 0.016 bar

DBT = 20°C = 293 K

P_t = 1.013 bar

w = 0.622 x \(\cfrac{P_v}{p_t-p_v}\)

0.0095 = 0.622 x \(\cfrac{p_v}{1.013-p_v}\) 

0.0152 = \(\cfrac{p_v}{1.013-p_v}\) 

0.0153 – 0.0152P_v = P_v

0.0153 = 1.0152P_v 

P_v = 0.016 bar

The correct answer is Collateral.

• Collateral is an asset or property that an individual or entity offers to a lender as security for a loan.
• It is used as a way to obtain a loan, acting as a protection against potential loss for the lender should the borrower default.

• Collateral minimizes the risk for lenders.
• If a borrower defaults on the loan, the lender can seize the collateral and sell it to recoup its losses.
• Mortgages and car loans are two types of collateralized loans.
• A secured loan is a loan in which the borrower pledges some asset (e.g. a car or property) as collateral for the loan, which then becomes a secured debt owed to the creditor who gives the loan.

The correct answer is option 5 i.e Japan

• Reliance Mutual Fund has been renamed as Nippon India Mutual Fund (NIMF).
• The organization was renamed following the purchase of 75% stake in Reliance Nippon Life Asset Management by Nippon Life Insurance.
• Nippon India Mutual Fund has become the largest foreign-owned Asset Management Company in India.
• Sundeep Sikka will continue to lead the company as the CEO.