Explore topic-wise InterviewSolutions in Current Affairs.

This section includes 7 InterviewSolutions, each offering curated multiple-choice questions to sharpen your Current Affairs knowledge and support exam preparation. Choose a topic below to get started.

1.

Statement I :- While preparing Bank Reconciliation statement with Balance as per Cash Book then interest credited by bank will be added. Statement II :- While preparing Bank Reconciliation statement with Balance as per Pass Book then interest charged by bank will be added (a) Both the statements are correct (b) Both the statements are incorrect (c) Only Statement I is correct (d) Only statement II is correct

Answer»

Correct option is (a) Both the statements are correct 

2.

If bank Reconciliation Statement is prepared with Dr. balance as per Cash book, which of the following will be added :- (a) Cheques deposited not yet credited (b) Interest charged by Bank (c) Directly deposited by customer in bank account (d) Bills paid by bank on standing instructions

Answer»

Correct option is (c) Directly deposited by customer in bank account 

3.

Assertion (A) :- Loans raised from Banks and Financial Institutions are categorised under Capital Receipts. Reason (R) :- Capital Receipts are non-recurring in nature. (a) Both A and R are correct and R is the correct explanation of A, (b) Both A and R are correct but R is not the correct explanation of A. (c) A is correct but R is incorrect. (d) A is incorrect but R is correct.

Answer»

Correct option is (b) Both A and R are correct but R is not the correct explanation of A. 

4.

Which derivative product the buyer having a right but obligation to buy the underlying? a. Call optionb. Put option c. Future d. Forward

Answer»

Correct answer is a. Call option

5.

The process by which a life insurance policyholder can transfer all rights, title and interest under a policy contract to a third person is known asA. Assignment of the policyB. Hypothecation of the policyC. Reinvestment of the policyD. Negotiation of the pol~cy

Answer» Correct Answer - A
6.

The NRis while investing in the equity of a company cannot buy more than prescribed percentage of the paid up capital of that company. What is the prescribed percentage?A. 0.02B. 0.03C. 0.04D. 0.05

Answer» Correct Answer - D
An NRl can purchase up to a maximum of 5% of the aggregate paid up capital of the company (equity as well as preference capital) or the aggregate paid up value of each series of convertible debentures as the case may be. Total investment by NRls cannot exceed 10% of the paid-up capital in an Indian company.
7.

Give any three points of difference between advertising and sales promotion

Answer»
AdvertisingSales Promotion
Aim:
Long term building of the brand attitude
Short term tactical goal of ‘moving forward’ sales now
Duration:
Long Term
Short Term
Services:
TV, newspapers, radio, outdoor publicity
Discount coupon, free st
8.

Expenditure on different promotion and advertising media like TV and Radio sales promotion etc. are the examples of _______. A) Fixed cost B) Semi variable cost C) Price D) Variable cost

Answer»

D) Variable cost

Expenditure on different promotion and advertising media like TV and Radio sales promotion etc. are the examples of Variable cost.

9.

Write notes on the following: 1. IP address 2. MAC address 3. Modem

Answer»

1. IP address: 

An IP address has 4 parts numeric address. Each parts contains 8 bits. By using 8 bits we can represent a decimal number between 0 to 255(2 =256 numbers). Each part is separated by dot. A total of 4 × 8=32 bits used. But nowadays 128 bits are used for IP address. 

2. Media Access Control(MAC) address: 

It is a unique 12 digit hexadecimal number(IMEI for mobile phones, it is a 15 digit decimal number) assigned to each NIC by its manufacturer. This address is known as MAC address. It is of the form. MM:MM:MM:SS:SS:SS. 

3. Modem: 

It is a device used to connect the computer to the internet. It converts digital signal into analog signal (modulation) and vice versa (De modulation)

10.

What is MAC address? What is the difference between a MAC address and an IP address?

Answer»

MAC means Media Access Control address. It is a unique 12 digit hexadecimal number(IMEI for mobile phones, it is a 15 digit decimal number) assigned to each NIC by its manufacturer. This address is known as MAC address and it is permanent. It is of the form. MM:MM:MM:SS:SS:SS. 

The first MM:MM:MM contains the ID number of the adapter company and the second SS:SS:SS represents the serial number assigned to the adapter by the company.

IP address means Internet Protocol address. It has 4 parts numeric address. Each parts contains 8 bits. By using 8 bits we can represent a decimal number between 0 to 255(28=256 numbers). Each part is separated by dot. A total of 4 × 8=32 bits used. But nowadays 128 bits are used for IP address.

11.

An agent applies force of constant magnitude `F_(0)` always in the tangential direction as shown in the figure`-3.77`. Find the speed of the bob when string becomes horizontal, assuming that it is at rest at its lowest point: A. `sqrt((l)/(m) (pi F_(0) - 2 mg))`B. `sqrt(lg)`C. `sqrt((l)/(m) (pi F_(0)) - 4 gm)`D. `sqrt((l)/(m) F_(0))`

Answer» Correct Answer - A
`W = Delta KE`
`- mgl + F_(0) xx l (pi)/(2) = (1)/(2) mv^(2) - 0`
`sqrt(-2gl + (F_(0)pi1)/(m)) = v`
12.

The ratio of age of A and B is 5 : 4 and the ratio of age of B and C is 4 : 3. If difference of age of A and C is 14 years, then what will be the ratio of age of C and B after 7 years?1. 14 : 152. 15 : 143. 4 : 54. 5 : 45. None of these

Answer» Correct Answer - Option 3 : 4 : 5

Given:

Ratio of age of A and B = 5 : 4

Ratio of age of B and C = 4 : 3

Difference of age of A and C = 14 years

Calculations:

Let the present age of A and B and C be 5x, 4x and 3x respectively.

5x – 3x = 14

⇒ 2x = 14

⇒ x = 7

Present age of B = 4x

⇒ 4 × 7

⇒ 28 years

Present age of C = 3x

⇒ 3 × 7

⇒ 21 years

After 7 years, age of B = 28 + 7

⇒ 35 years

After 7 years, age of C = 21 + 7

⇒ 28 years

Ratio of age of C and B after 7 years =  28 : 35

⇒ 4 : 5

The ratio of age of C and B after 7 years is 4 : 5

13.

A shopkeeper claims that he is selling rock salt at 20 Rs./kg which cost him 25 Rs./kg but he is giving 800 grams instead of 1 kg. What will be the percentage profit or loss of the shopkeeper?1. 10% loss2. 10% gain3. 20% gain4. No profit no gain5. None of the above

Answer» Correct Answer - Option 4 : No profit no gain

Given:

C.P of 1000 grams rock salt = Rs. 25

S.P of 1000 grams rock salt = Rs. 20

False weight = 800 grams

Calculations:

C.P of 1000 grams rock salt = Rs. 25

C.P of 800 grams of rock salt

⇒ 25/1000 × 800

⇒ Rs. 20

S.P of 1000 grams rock salt = Rs. 20

∴ there is no profit no loss as the shopkeeper bought the rock salt in Rs 20 Rs/kg and sold it for the same.

There is no profit no loss.
14.

Divide Rs. 672 in the ratio 5 : 3.

Answer»

Sum of ratio terms = (5 + 3) = 8.

First part = Rs. (672 x (5/8)) = Rs. 420; 

Second part = Rs. (672 x (3/8)) = Rs. 252.

15.

Three glasses 1,2 and 3 have water and juice in ratio of 1 : 2, 3 : 4 and 2 : 5. Find out which glass contains maximum amount of juice if capacity of glasses is 90 ml, 210 ml and 140 ml respectively and 10 ml of juice was removed from glass 2 and added to glass 3. 1. Second glass2. Both glass 2 and 33. Third glass4. Both glass 1 and 25. None of the above

Answer» Correct Answer - Option 2 : Both glass 2 and 3

Given:

Glass 1 = 1 : 2, 90ml

Glass 2 = 3 : 4, 210 ml

Glass 3 = 2 : 5, 140ml

Calculation:

Glass 1 has capacity of 90 ml and has water to juice in ratio of 1 : 2

⇒ Amount of juice in glass 1 = (2/3) × 90

⇒ Amount of juice in glass 1 = 60

Glass 2 has capacity of 210ml and has water to juice in ratio of 3 : 4

⇒ Amount of juice in glass 2 = (4/7) × 210

⇒ Amount of juice in glass 2 = 120 ml

⇒ 10 ml removed hence, final quantity = 110 ml

Glass 3 has capacity of 140 ml and has water to juice in ratio of 2 : 5

⇒ Amount of juice in glass 3 = (5/7) × 140

⇒ Amount of juice in glass 3 = 100 ml

⇒ 10 ml added hence, final quantity is 110 ml

both glasses 2 and 3 has maximum amount of juice that is 110 ml

16.

Divide Rs. 1162 among A, B, C in the ratio 35 : 28 : 20.

Answer»

Sum of ratio terms = (35 + 28 + 20) = 83. 

A's share = Rs. (1162 x (35/83))= Rs. 490; 

B's share = Rs. (1162 x(28/83))= Rs. 392; 

C's share = Rs. (1162 x (20/83))= Rs. 280.

17.

A container consist of oil and kerosene in ratio of 2 : 7. Recommend the action from below mentioned options to obtain 1 : 1 ratio of mixture.1. Add 5 ml of oil to container2. Remove 50 ml of mixture and replace it with oil3. Add 50 ml of oil to container4. Remove 20 ml of mixture5. Remove 75 ml of oil from container

Answer» Correct Answer - Option 3 : Add 50 ml of oil to container

Given:

Initial ratio of oil : kerosene = 2 : 7

Required ratio = 1 : 1

Calculation:

Let’s assume the container to be of 90 ml

⇒ Oil : kerosene = 2 : 7

⇒ Container has oil = (2/9) × 90

⇒ Container has oil = 20 ml

⇒ Container has kerosene = 70 ml

Now, Required ratio = 1 : 1

⇒ In order to attain this ratio both liquids needs to have equal parts

⇒ By adding 50 ml of oil, oil quantity increases = 20 +50

⇒ Oil quantity = 70 ml

⇒ Kerosene Quantity = 70 ml

50 ml of oil needs to be added to mixture

18.

A bag contains 50 p, 25 P and 10 p coins in the ratio 5: 9: 4, amounting to Rs. 206. Find the number of coins of each type.

Answer»

Let the number of 50 p, 25 P and 10 p coins be 5x, 9x and 4x respectively. 

(5x/2)+( 9x/ 4)+(4x/10)=206

50x + 45x + 8x = 4120

103x = 4120 

x=40. 

Number of 50 p coins = (5 x 40) = 200; 

Number of 25 p coins = (9 x 40) = 360; 

Number of 10 p coins = (4 x 40) = 160.

19.

A bag contains 20 paise, 25 paise, and 50 paise coins in the ratio 8 ∶ 5 ∶ 4, amounting to Rs. 436.5. Find the number coins of 50 P.1. 5802. 3903. 4504. 360

Answer» Correct Answer - Option 4 : 360

Given:

A bag contains 20 paise, 25 paise, and 50 paise coins in the ratio 8 ∶ 5 ∶ 4, and the amount is Rs. 436.5.

Calculations:

A bag contains 20 paise in ratio 8 = (1/5) × 8 = Rs 1.60 

Similarly, 25 paise in ratio 5 = (1/4) × 5 = Rs 1.25

And, 50 paise in ratio 4 = (1/2) × 4 = Rs 2.00

According to question,

⇒ 1.60 + 1.25 + 2.00 = 4.85  

⇒ 4.85  = 436.5 

Then, 1 = 90 

⇒ 90 × 2 = 180 

The number of 50 paise coins = 180 × 2 = 360

20.

According to 2017-2018 data, the share of different sectors in employment (percentage) in India wasPrimary Sector - 44% Secondary Sector - 25% Tertiary Sector - 31%Out of the three sectors, why did the ratio of employment in Primary Sector high? Select the most suitable option from the following : A. Workers in the Primary Sector are underemployed B. Low job opportunities in Secondary Sector C. Efforts of labour are not equivalent in all the sectors D. Outsourcing of job opportunities in Secondary Sector

Answer»

A - Workers in the Primary Sector are underemployed.

21.

Activities in which natural products are changed into other forms come under which one of the following sectors?(a) Primary(b) Secondary(c) Tertiary(d) Quaternary

Answer»

Answer is : (b) Secondary

22.

What is the solution to the problem of double counting in the estimation of national income?

Answer»

1. The value obtained is actually the GNP at market prices. Care must be taken to avoid double counting. 

2. The value of the final product is derived by the summation of all the values added in the productive process.

3. To avoid double counting, either the value of the final output should be taken into the estimate of GNP or the sum of values added should be taken. 

4. Double counting is to be avoided under value added method. 

5. Any commodity which is either raw material or intermediate good for the final production should not be included. 

6. For example, value of cotton enters value of yam as cost, and value of yam in cloth and that of cloth in garments.

7. At every stage value added only should be calculated.

23.

Suppose there are four families in your locality, the average per capita income of whom is Rs. 10,000. If the income of three families is Rs. 6,000, Rs. 8,000 and Rs. 14,000 respectively, what would be the income of the fourth family?(a) Rs. 5,000(b) Rs. 10,000(c) Rs. 12,000(d) Rs. 15,000

Answer»

Answer is : (c) Rs. 12,000

24.

Which one of the following sectors shows the highest share in employment in 2017 - 18, in India?(a) Primary(b) Secondary(c) Tertiary(d) Quaternary

Answer»

Answer is : (a) Primary

25.

Activities that help in the development of Primary and Secondary sectors come under which one of the following sectors?(a) Primary (b) Secondary (c) Tertiary(d) Quaternary

Answer»

Answer is : (c) Tertiary

26.

At the initial stages of development, which one of the following sectors was the most important of economic activity?(a) Primary(b) Secondary(c) Tertiary(d) Quaternary

Answer»

Answer is : (a) Primary

27.

Which one of the following sectors shows the highest share in employment in 2017-18, in India?(a) Primary (b) Secondary (c) Tertiary (d) Quaternary

Answer»

Correct option is: (a) Primary

28.

Activities that help in the development of Primary and Secondary sectors come under which one of the following sectors ? (a) Primary (b) Secondary (c) Tertiary (d) Quaternary

Answer»

Correct option is: (c) Tertiary

29.

At the initial stages of development, which one of the following sectors was the most important of economic activity? (a) Primary (b) Secondary (c) Tertiary (d) Quaternary

Answer»

Correct option is: (a) Primary

30.

Explain the problem of double counting in estimating national income, with the help of an example. Also explain two alternative ways of avoiding the problem.

Answer»

The problem of double counting is the problem of estimating the value of goods and services more than once. 

For example:- A farmer produces 100 kg of wheat and sells it for Rs.4000 to Miller.

For Miller, wheat is an intermediate good. Miller converts wheat into flour. He sells it for Rs.5000 to a baker.

Baker manufactures bread from flour and sells the entire bread to final consumers for Rs.6000.

As a general practice , every producer treats its product as final output. Total value of output=4000+5000+6000=15000.But the value of wheat and flour are counted more than once.

The problem of double counting can be avoided by (i) Final output method and (ii) Value added Method.

31.

Which one of the following sectors shows the highest share in Gross Domestic Product (GDP) in India ? (a) Primary (b) Secondary (c) Tertiary (d) Quaternary

Answer»

Correct option is: (c) Tertiary

32.

Explain the Nature and significant of management.

Answer»

Nature of Management:

  • Universal Process: Wherever there exists human pursuit, there exists management. Without effective management, the intentions of the organisation cannot be accomplished.
  • The factor of Production: Equipped and experienced managers are necessary for the utilisation of funds and labour.
  • Goal-Oriented: The most significant aim of all management pursuit is to achieve the purposes of a firm. The aims must be practical and reachable.
  • Supreme in Thought and Action: Managers set achievable goals and then direct execution on all aspects to achieve them. For this, they need complete assistance from middle and lower degrees of management.
  • The system of authority: Well-defined principles of regulation, the regulation of proper power and efficiency at all degrees of decision-making. This is important so that each self must perform what is required from him or her and to whom he must report.
  • Profession: Managers require to control managerial expertise and education, and have to adhere to a verified law of demeanour and stay informed of their human and social responsibilities.
  • Process: The management method incorporates a range of activities or services directed towards an object.

Significance of Management:

  • Achieving Group Goals: Management encourages collaboration and coordination amongst workers. A general control must be provided to the organisational and personal objectives in order to favourably accomplish the aims.
  • Increases Efficiency: Management improves productivity by managing resources in a reliable conceivable way in order to decrease cost upscale potency.
  • Creates Dynamic organisation: Management undertakes the conditions by assuring that these variations are well accepted privately and that objection to change is controlled.
  • Achieving personal objectives: Management promotes leadership and furnishes motivation to the employees to operate effectively in order to accomplish their personal aims while working towards the organisational goals.
  • Development of Society: Management helps in the enhancement of community by manufacturing reliable quality commodities, establishing employment chances and fostering innovative technologies.
33.

Which of the following approaches to human development consider the provision of health, education, food, water, supply, sanitation and housing? A. income B. welfare C. capability D. basic needs

Answer»

The correct option is (D) Basic needs

  • The ILO report for the 1976 World Employment Conference defined basic needs in terms of food, clothing, housing, education, and public transportation.
  • The ILO was founded in October 1919. It is headquartered in Geneva, Switzerland.
  • The current Director-General of ILO as of March 2021 is Guy Ryder.
  • Employment was both a means and an end, and participation in decision-making was also included.
  • This approach reversed conventional practice, which was to project a desirable annual rate of per capita economic growth into the future.
  • The latter was a forward rolling approach while the basic needs approach achieved more precision by setting specific production targets and deriving the desirable rate of economic growth implied.
  • The basic needs development strategy was also more practical than conventional strategies.
34.

II Answer the following questions in 20 sentences.Explain the short run supply curve of a firm with the help of a diagram.Ans: Supply of a firm refers to the quantity that it chooses to sell at a given price.

Answer»

Short run supply curve: In a perfectly competitive market, the short run supply curve is that part of its Marginal cost curve where the Marginal Cost curve is rising from the Average Variable Cost curve. Thus, it is evident from the diagram that when price rises the quantity supplied also rises and vice versa.

the monopoly firms aims at profit maximum under short run equilibrium with the case of zero cost profit maximization is reached at a point where TR is at maximum
Therefore..TR=TC 
when TC is zero, profit is maximum..when TR is maximum 
let us understand this with the following example
suppose there is a village which has only one well from which water is supplied to villagers. All villagers are completely depended on it. the well is owned by one person who purchase the water has to draw the water out of the well.the well owner is thus a monopolist with zero cost of production
35.

The demand for good rises by 20 percent as a result of all in its price. Its price elasticity of demand `(-) 0.8`. Calculate the precentage fall in price.

Answer» `E_(d) = ("Percentage Change in Quantity Demanded")/("Percentage Change in Price")`
or `0.8 = (20)/("Percentage Change in Price")`
or, Percentage Change in Price `= (20)/(0.8) = 25%`
Thus, the percentage fall in the price 25%
36.

If due to fall in the price of good X, demand for good Y rises, the two goods are : (choose the correct alternative)A. SubstitutesB. ComplementsC. Not relatedD. Competitive

Answer» Correct Answer - B
Complements
37.

With relevant examples, discuss the types of project sustainability.

Answer»

Some dimensions of project sustainability are:

  1. Institutional stability
  2. Continued operation and maintenance of project facilities
  3. Continuous flow of net benefits
  4. Maintenance of environmental stability
  5. Equitable sharing and distribution of project benefits
  6. Continued community participation

Some elements of sustainable development are:

  1. Efficient use of natural resources
  2. Education
  3. Population stabilization
  4. Integrated environmental systems management
  5. Social and cultural changes
  6. Determining environmental limits
  7. Refining market economy
  8. Reduction in waste and prevention of pollution
  9. Protecting soil from pollution
  10. Reducing disparity in life cycle
  11. Restoring landscapes

Some examples of sustainable business are:

  1. Replacing nationally and internationally produced products with those created locally and regionally
  2. Taking responsibility on the effects they have on the natural world
  3. Avoiding exotic sources of capital for business development and growth
  4. Engaging in productive processes that are human, worthy, dignified, and intrinsically satisfying
  5. Creating objects of durability and long-term utility whose ultimate use or disposition will not be harmful to future generations
  6. Changing of consumers to customers through education
  7. Promoting transparency and systematic dealings with risks, uncertainty, and irreversibility
  8. Ensuring appropriate valuation, appreciation, and restoration
  9. Integrating environmental, social, human, and economic goals in business policies and activities
  10. Promoting and implementing continuous quality improvement
  11. Promoting commitment to the best practices
  12. Understanding projects which illustrate the successful application of sustainability principles to business
  13. Demonstrating that market forces can drive the company to conduct business in a way that benefits shareholders, society, and the environment
  14. Integrating sustainability in all business plans
38.

Give two examples of private corporate enterprise.

Answer»

(i) Reliance Industries Ltd. 

(ii) Infosys Ltd.

39.

The Deflection Sensitivity of a Cathode Ray Tube is1. Directly proportional to the deflection voltage2. Directly proportional to the square of the deflection voltage3. Inversely proportional to the deflection voltage4. Independent of the deflection voltage

Answer» Correct Answer - Option 4 : Independent of the deflection voltage

Deflection sensitivity of a cathode ray tube is defined as the deflection of the screen per unit deflection voltage.

\(s = \frac{D}{{{E_d}}} = \frac{{L{t_d}}}{{2d\;{E_a}}}m/v\)

Where,

L = distance between screen and centre of the deflecting plates

D = Distance between deflecting plates

Ld = Length of deflecting plates

Ea = Accelerating voltage

Ed = Potential between deflecting plates

It is clear that, sensitivity is independent of deflection voltage.
40.

An ammeter requires a change of 3 A in its coil to produce a change in deflection of the pointer by 12 mm. What is the static sensitivity ?1. 36 mm/A2. 9 mm/A3. 4 mm/A4. 15 mm/A5.

Answer» Correct Answer - Option 3 : 4 mm/A

Concept:

Static sensitivity:

It is defined as the ratio of the magnitude of response to the magnitude of the quantity being measured. In simple terms, it can also be said as the ratio of output to input.

\(\rm Static\;sensitivity=\frac{\Delta\;Output}{\Delta\;Input}\)

Calculation:

Given:

Output = 12mm, input = 3 A 

As the input of 3A produces a deflection of 12 mm.

\(\rm Static\;sensitivity=\frac{\Delta\;Output}{\Delta\;Input}\)

\(\rm Static\;sensitivity=\frac{12}{3}=4\;mm/A\)

41.

It is established that an electric current through a metallic conductor produces a magnetic field around it. Is there a similar magnetic field produced around a thin beam of moving (i) alpha particles, (ii) neutrons? Justify your answer.

Answer»

Hint— (i) Yes, Alpha particles being positively charged constitutes a current in the direction of motion. (ii) No. The neutrons being electrically neutral constitute no current.

42.

Meena draws magnetic field lines of field close to the axis of a current carrying circular loop. As she moves away from the centre of the circular loop she observes that the lines keep on diverging. How will you explain her observation.

Answer» Strength of the magnetic field falls as distance increases. This is indicated by the decrease in degree of closeness of the lines of field.
43.

What does the direction of thumb indicate in the right-hand thumb rule. In what way this rule is different from Fleming’s left-hand rule?

Answer» The thumb indicates the direction of current in the straight conductor held by curled fingers, whereas the Fleming’s left-hand rule gives the direction of force experienced by current carrying conductor placed in an external magnetic field.
44.

Write a dialogue between a customer and a shop keeper.

Answer»

Customer : Good morning sir. Shop 

Keeper : Good morning. What do you want? 

Customer : I want an LED TV. Shop

Keeper : Which brand do you like, sir?

Customer : I want Philips TV. Shop 

Keeper : What features do you want in it? 

Customer : I want 40 inches along with 3D provision. 

Shop Keeper : Here it is, sir. It costs Rs. 50,000/-. 

Customer : Could I pay the money through debit card? 

Shop Keeper : Yes sir. May I pack this for you? Customer : Yes

45.

Complete the following dialogue.Customer : I would like to fly to America in this month.Travel Agent : .............Customer : I would choose Jet Airways. Travel Agent : ................Customer : Then I will travel by next month. Travel Agent : .........Customer : I will let you know.Travel Agent : .........

Answer»

Customer : I would like to fly to America in this month.

Travel Agent : Oh! That’s great, which flight do you prefer?

Customer : I would choose Jet Airways. 

Travel Agent : Jet Airways flights are not available this month.

Customer : Then I will travel by next month. 

Travel Agent : Ok. Can I book a ticket for you?

Customer : I will let you know. 

Travel Agent : You are welcome.

46.

WrIte a dialogue with at least 5 utterances between the manager of a restaurant and an angry customer who finds a fly in his soup

Answer»

Waiter : Here’s your soup, Sir. 

Customer : Thank you. (tastes the hot soup). What’s this? Eek! A fly in my soup. (shouts) Waiter! No, I’d better talk to the manager. 

Manager : Is something wrong? 

Customer : It is the soup that is wrong. 

Manager : What happened, sir? 

Customer : I ordered for a vegetarian soup but i was served a non-veg soup.

Manager : A non-veg. soup? In this hotel? 

Customer : Yes, certainly. See this. 

Manager : Oh, I’m extremely sorry. Waiter, get him another bowl of soup. 

Customer : Oh, no, thank you, not another nonveg. soup.

47.

The position- time (x-t) graphs for two rabbits A and B moving from their carrot field O to their homes P and Q respectively along straight line path (taken as x axis ) are shown in figure below. Choose the correct statement(s): A. A lives closer to the carrot field than BB. A starts form the carrot field earlier than BC. A and B have equal average velocities form 0 to`t_(0)`D. B overtakes A on the way

Answer» Correct Answer - A::B::C
48.

The verical of point above the ground is twice that of Q. A particle is projected downward with a speed of `5 ms^(-1)` from P and at the same time another particle is projected upward with the same speed from W. Both particle reach the ground simultaneously, thenA. PQ= 30 mB. PQ = 60 mC. time of glight of the stone = 3sD. time of flight of the stones = `1//3`s

Answer» Correct Answer - A::C
49.

Factorize -X​​​​​​3+6x2​​​​-3x-10

Answer»

\(-x^3+6x^2-3x-10\)

\(\because x=-1\) is a zero of this function.

Therefore \((x+1)\) is a factor of it.

Now,

\(-x^3+6x^2-3x-10\)

\(=(x+1)(-x^2+7x-10)\)

\(=(x+1)(-x^2+2x+5x-10)\)

\(=(x+1)(-x(x-2)+5(x-2))\)

\(=(x+1)(x-2)(-x+5)\)

\(=-(x+1)(x-2)(x-5)\)

50.

Prove that \( \beta(m, 1 / 2)=2^{2 m-1} \beta(m, m) \)

Answer»

β(m, 1/2) = \(\frac{Γ(m)Γ(1/2)}{Γ(m+1/2)}\) \(\left(\because\beta=\frac{\Gamma(m)(n)}{\Gamma(m+n)}\right)\)

\(=\cfrac{\Gamma(m)\Gamma(m)\Gamma(\frac12)}{\Gamma(m)\Gamma(m+\frac12)}\) (Multiplying numerator & denominator by \(\Gamma(m)\))

\(=\cfrac{\Gamma(m)\Gamma(m)\Gamma(\frac12)}{\frac{\sqrt{\pi}}{2^{2m-1}}\Gamma(2m)}\) (\(\because\) \(\Gamma(m)\Gamma(m+\frac12)=\frac{\pi}{2^{2m-1}}\Gamma(2m)\))

\(=2^{2m-1}\frac{\Gamma(m)\Gamma(m)}{\Gamma(2m)}\frac{\sqrt\pi}{\sqrt\pi}\) (\(\because\Gamma(\frac12)=\sqrt\pi\))

= 22m-1β (m, m) \((\because \beta(m, m) = \frac{\Gamma(m)\Gamma(m)}{\Gamma(2m)})\)

Hence Proved