Veerendra

We have compiled the NCERT MCQ Questions for Class 10 Economics Chapter 4 Globalisation and the Indian Economy with Answers Pdf free download covering the entire syllabus. Practice MCQ Questions for Class 10 Economics with Answers on a daily basis and score well in exams. Refer to the Globalisation and the Indian Economy Class 10 MCQs Questions with Answers here along with a detailed explanation.

Globalisation and the Indian Economy Class 10 MCQs Questions with Answers

Question 1.
Multinational corporations have succeeded in entering global markets through
(a) WTO
(b) UNO
(c) UNESCO
(d) none of the above

Question 2.
What attracts an MNC?
(a) Cheap labour
(b) Ready demand for the product
(c) Both (a) and (b)
(d) None of the above

Question 3.
Investment means spending on
(a) factory building
(b) machines
(c) equipments
(d) all the above

Question 4.
Globalisation results in
(a) inflow of labour from abroad
(b) inflow of capital from abroad
(c) inflow of tourists from abroad
(d) all the above

Question 5.
Which of the following contributes to globalisation?
(a) internal trade
(b) external trade
(c) large scale trade
(d) small scale trade

Question 6.
Benefits enjoyed by companies who set up production units in the SEZs are:
(a) they do not have to pay taxes for some years
(b) reduction in excise duty
(c) reduced tariffs and barriers
(d) none of the above

Question 7.
Integration of markets means
(a) operating beyond the domestic markets
(b) wider choice of goods
(c) competitive price
(d) all the above

Question 8.
Special Economic Zones (SEZ) developed by the Government of India aim
(a) to attract foreign companies to invest in India
(b) to encourage small investors
(c) to encourage regional development
(d) none of the above

Question 9.
Which one of the following is not true regarding the World Trade Organisation?
(a) It allows free trade to all countries without any trade barriers.
(b) Its aim is to liberalise international trade.
(c) It establishes rules regarding internaional trade.
(d) WTO rules have forced the developing countries to remove trade barriers.

Question 10.
Which one of the following is not true regarding impact of globalisation of India?
(a) It has created jobs in the service sector.
(b) People with education, skill and wealth have not been benefited.
(c) Benefits of globalisation are not shared equally.
(d) Labour laws are not implemented properly and workers are denied their rights.

Question 11.
Which one of the following is a major benefit of joint production between a local company and a Multi-National Company?
(a) MNC can bring latest technology in the production
(b) MNC can control the increase in the price
(c) MNC can buy the local company
(d) MNC can sell the products under their brand name

Question 12.
Which one among the following is a far reaching change in the policy made in India in 1991?
(a) Removing barriers or restrictions set by the government which is known as liberalisation.
(b) Put barriers to foreign trade and foreign investments.
(c) Restrictions set by the government to protect the producers within the country from foreign competition.
(d) By giving protection to domestic producers through a variety of means.

Question 13.
Which one of the following has benefited least because of globalisation in India?
(a) Agriculture Sector
(b) Industrial Sector
(c) Service Sector
(d) Secondary Sector

Question 14.
By 2006, how many countries were the members of the World Trade Organisation?
(a) 139
(b) 149
(c) 159
(d) 169

Question 15.
Entry of MNCs in a domestic market may prove harmful for:
(a) all large scale producers.
(b) all domestic producers.
(c) all substandard domestic producers.
(d) all small scale producers.

Question 16.
The most common route for investments by MNCs in countries around the world is to:
(a) set up new factories
(b) buy existing local companies
(c) form partnerships with local companies
(d) None of these

Question 17.
Removing barriers or restrictions set by the government is known as :
(a) privatisation
(b) globalisation
(c) liberalisation
(d) socialisation

Question 18.
Taxes on imports is an example of :
(a) terms of trade
(b) collateral
(c) trade barriers
(d) foreign trade

Question 19.
The most common route for investments by MNCs in countries around the world is to:
(a) set up new factories
(b) buy existing local companies
(c) form partnerships with local companies
(d) None of these

Question 20.
Which one of the following categories refers to investment?
(a) The money that is spent to buy assets such as land, building, machines, etc.
(b) The money that is spent on religious ceremonies.
(c) The money that is spent on social customs.
(d) The money that is spent on household goods.

Question 21.
Why do MNCs set up offices and factories in more than one nation ?
(a) The cost of production is high and the MNCs can earn profit.
(b) The cost of production is low and the MNCs undergoes a loss.
(c) The cost of production is low and the MNCS can earn greater profit.
(d) The MNCs want to make their presence felt globally.

Question 22.
Liberalisation refers to
(a) freeing the economy from direct control
(b) putting an end to various restrictions
(c) opening up the economy
(d) all the above

Question 23.
FDI (Foreign Direct Investment) attracted by globalisation in India belongs to the
(a) World Bank
(b) multinationals
(c) foreign governments
(d) none of the above

Question 24.
When was the WTO established?
(a) 1985
(b) 1995
(c) 2000
(d) 2005

Question 25.
Which of the following factors has not facilitated globalisation?
(a) Technology
(b) Liberlisation of trade
(c) WTO
(d) Nationalisation of banks

Question 26.
Globalisation leads to rapid movements of the following between countries :
(a) goods and services
(b) investments
(c) people
(d) all the above

Question 27.
Globalisation so far has been more in favour of:
(a) developed countries
(b) developing countries
(c) poor countries
(d) none of the above

Question 28.
Which has played a big role in spreading globalisation?
(a) Information technology (IT)
(b) Transport technology
(c) Both (a) and (b)
(d) None of the above

Question 29.
Cheaper imports, inadequate investment in infrastructure lead to
(a) slowdown in agricultural sector
(b) replace the demand for domestic production
(c) slowdown in industrial sector
(d) all the above

Question 30.
Globalisation results in
(a) lesser competition among producers
(b) greater competition among producers
(c) no change in competition among producers
(d) none of the above

Question 31.
Which sector has not benefited by the policy of globalisation?
(a) Agricultural sector
(b) Manufacturing sector
(c) Service sector
(d) All the above

Question 32.
Globalisation has led to improvement in
(a) choice to consumers
(b) quality of goods and services
(c) foreign investment
(d) all the above

Question 33.
Fair globalisation refers to ensuring benefits to:
(a) labourers
(b) producers
(c) consumers
(d) all the above

Hope the information shed above regarding NCERT MCQ Questions for Class 10 Economics Chapter 4 Globalisation and the Indian Economy with Answers Pdf free download has been useful to an extent. If you have any other queries of CBSE Class 10 Economics Globalisation and the Indian Economy MCQs Multiple Choice Questions with Answers, feel free to reach us so that we can revert back to us at the earliest possible.

Free PDF Download of CBSE Business Studies Multiple Choice Questions for Class 12 with Answers Chapter 10 Financial Market. Business Studies MCQs for Class 12 Chapter Wise with Answers PDF Download was Prepared Based on Latest Exam Pattern. Students can solve NCERT Class 12 Business Studies Financial Market MCQs Pdf with Answers to know their preparation level.

Financial Market Class 12 Business Studies MCQs Pdf

1. Yash had severe pain in his throat, so he called up the doctor and asked for a telephonic advice. The doctor prescribed him a sachet of Throat Reliever Hot Sip. He asked his servant to get a sachet from a local chemist with a cash memo. After consuming the sachet, he started feeling more ill, so he picked up the empty sachet and started reading the label. To his utter dismay, the sachet had already expired last month. Which of the following remedies is not available to him any longer as a consumer?
(a) To withdraw the hazardous goods from sale.
(b) To replace the defective product with a new one.
(c) To refund the price paid for the product.
(d) To pay a reasonable amount of compensation for any loss suffered by the consumer due to the negligence of the opposite party.

2. Due to the negligence of the doctors, Johar passed away within a week’s time after his surgery of the spine. Which of the following parties can not file a case in this regard?
(a) The consumer
(b) Any registered consumers’ association
(c) A legal heir or representative of a deceased consumer
(d) All of the above

3. Which of the following activities lie within the scope of consumer protection?
(a) Educating consumers about their rights and responsibilities
(b) Helping consumers in getting their grievances redressed
(c) Protecting the interests of consumers
(d) All of the above

4. Jagga started a small stationery shop in the nearby market. In pursuit of earning higher profits in a short term, he overpriced all his products by 20%. Gradually, the consumers understood his pricing strategy and stopped coming to his shop for making any purchase. Identify the related point highlighting the importance of consumer protection from businessmen’s point of view.
(a) Long-term interest of business is assured
(b) Business uses society’s resources so they need to safeguard consumer’s interests.
(c) Social responsibility towards consumers as an important interest group.
(d) It is the moral obligation of the businessmen to give due consideration to the consumer’s interests.

5. Dipika Pallikal, the Padma Shri recipient, in a petition filed in 2012 said that she had faced humiliation and loss of reputation, as a transaction using a bank’s debit card at a hotel in the Netherlands’ Rotterdam failed, though she had a balance of more than 10 times the billed amount in her account. The bank claimed that the incident was a case of “force majeure”, which means a natural and unavoidable catastrophe or an act of God, and was beyond is control. A consumer court in Chennai has directed the bank to pay a compensation of lakh to Dipika Pallikal for “deficiency in service”. The bank was also directed to pay her ₹5,000 as expenses. Identify the right of consumers being exercised in the given case.
(a) Right to safety
(b) Right to be heard
(c) Right to seek redressal
(d) Right to consumer education

6. When Aaradhya, inspite of paying the full price of the plot as per the terms and conditions of the allotment letter, was not given the possession of the plot by the builder, she filed a case in the State Commission. Identify the right of consumers being exercised in the given case.
(a) Right to safety
(b) Right to be heard
(c) Right to seek redressal
(d) Right to consumer education

7. Ranjan bought a bottle of soft drink of a famous beverage company and found a gutka pouch floating inside the bottle. He forwarded a legal notice to the company, accusing it of the deficiency in service that could cause health hazard to the consumer. Identify the right of consumer being violated in the given case.
(a) Right to safety
(b) Right to be heard
(c) Right to seek redressal
(d) Right to consumer education

8. Siddhartha booked several rooms in a reputed five-star hotel in Goa for his destination wedding. On the day of his wedding, when his friend Ramandeep, after attending the lunch party, returned to his room to take a shower, he had a fall in the bathroom. The bathroom was three stairs down to the bathing area and there was a handle bar to the right. On the second step, Ramandeep slipped badly and fell on his face with a great force, resulting in multiple fractures. He filled a case against the hotel for compensation for the injuries suffered due to faulty designing of its room. Identify the right of consumers being violated in the given case.
(a) Right to be heard
(b) Right to seek redressal
(c) Right to consumer education
(d) Right to safety

9. A consumer court in Pune slapped a ₹55,000 fine on a reputed online food-delivery company along with a hotel for delivering non-vegetarian food to a lawyer who had ordered a vegetarian dish. He had ordered paneer butter masala but was delivered butter chicken instead. When he reportedly registered the complaint, the hotel promised to replace it and send another parcel of food with the correct dish. However, Deshmukh allegedly received butter chicken instead of paneer butter masala the second time as well. Deshmukh sent notices to both the restaurant and the online food-delivery cpmpany for ‘hurting religious sentiments’. Identify the right of consumers being violated in the given case.
(a) Right to be heard
(b) Right to seek redressal
(c) Right to choose
(d) Right to safety

10. A popular nationalised bank has been fined ₹8 lakh by the country’s highest consumer court, National Consumer Disputes Redressal Commission (NCDRC), for not sharing complete insurance policy details with a customer. The bank has been ordered to pay the full amount as compensation to the customer. Identify the right of consumers being violated in the given case.
(a) Right to be heard
(b) Right to seek redressal
(c) Right to information
(d) Right to safety

11. Naina, her husband and her two minor daughters were travelling from Mumbai to Delhi, availing a company’s flight services in 2018. The airlines had issued boarding passes to all of them. Naina claimed in her plea that the airlines left all her family at the Mumbai Airport without informing them, despite their being in the airport premises. The family had to stay in a hotel and purchase new tickets the next day. The State Consumer Disputes Redressal Commission (SCDRC). on hearing the plea, asked an airline company to pay ₹50,000 to Naina and her family. Identify the right of consumers being exercised in the given case.
(a) Right to safety
(b) Right to be heard
(c) Right to seek redressal
(d) Right to consumer education

12. Identify the right of consumers being promoted in the picture given on the right.

(a) Right to safety
(b) Right to be heard
(c) Right to seek redressal
(d) Right to consumer education

13. Identify the right of consumers being exhibited in the picture on your right.

(a) Right to choose
(b) Right to be heard
(c) Right to seek redressal
(d) Right to consumer education

14. Identify the right of consumers being promoted in the picture.

(a) Right to safety
(b) Right to be heard
(c) Right to seek redressal
(d) Right to consumer education

15. Identify the right of consumers being promoted in the given picture.

(a) Right to seek redressal
(b) Right to consumer education
(c) Right to information
(d) Right to be heard

16. Identify the responsibility of consumers being promoted in the picture.

(a) Buy only standardised goods
(b) Read labels carefully
(c) Assert yourself to ensure that you get a fair
(d) Be honest in your dealings

17. Identify the responsibility of consumers being highlighted in the picture given below.

(a) Be honest in your dealings
(b) Learn about the risks associated with products and services
(c) Assert yourself to ensure that you get a fair deal
(d) Respect the environment.

18. Recently, Yamini purchased a pack of dog food for her pet. It was nowhere mentioned on the pack that it had to be mixed in lukewarm water in order to ensure easy digestion. Therefore, Yamini kept serving the food to her pet by mixing it in cold water. As a result, her pet fell ill and had to be hospitalised. Identify the right of consumers being ignored by the company marketing the pet food.
(a) Right to consumer education
(b) Right to information
(c) Right to choose
(d) Right to be heard

19. Which of the following types of cases are filed in the State Commission?
(a) When the value of the goods or services in question, along with the compensation claimed, exceeds ₹20 lakhs but does not exceed ₹1 crore.
(b) When the value of the goods or services in question, along with the compensation claimed, exceeds ₹20 lakhs but does not exceed ₹2 crore.
(c) When the value of the goods or services in question, along with the compensation claimed, exceeds ₹40 lakhs but does not exceed ₹1 crore.
(d) None of the above

20. Where can the aggrieved party appeal further in case he is not satisfied with the order of the District Forum?
(a) National Commission
(b) State Commission
(c) Supreme Court of India
(d) All of the above

21. In case an aggrieved consumer is not satisfied with the decision of the State Commission, he can make a further appeal in
(a) National Commission
(b) District Forum
(c) Supreme Court of India
(d) All of the above

22. In case an aggrieved consumer is not satisfied with the decision of the National Commission, he can make a further appeal in
(a) State Commission
(b) District Forum
(c) Supreme Court of India
(d) All of the above

23. Which of the following statements is not true with regard to the District Forum?
(a) It consists of a President and three other members, one of whom should be a woman.
(b) The members are appointed by the District Government.
(c) A complaint can be made to the appropriate District Forum when the value of the goods or services in question, along with the compensation claimed, does not exceed ?10 lakhs.
(d) All of the above

24. Which of the following statements is true with regard to the State Commission?
(a) It consists of a President and not less than two other members, one of whom should be a woman.
(b) The members are appointed by the State Government concerned.
(c) A complaint can be made to the appropriate State Commission when the value of the goods or services in question, along with the compensation claimed, exceeds ₹20 lakhs but does not exceed ₹1 crore.
(d) All of the above

25. Which of the following statements is not true with regard to the National Commission?
(a) It consists of a President and at least five other members, one of whom should be a woman.
(b) The members are appointed by the Central Government.
(c) A complaint can be made to the National Commission when the value of the goods or services in question, along with the compensation claimed, exceeds ₹1 crore.
(d) Where the aggrieved party was not satisfied with the order of the National Commission, the case can be taken to the Supreme Court of India.

26. Which of the following functions are carried out by the consumer organisations?
(a) Publishing periodicals to impart knowledge about consumer issues.
(b) Providing legal assistance to consumers.
(c) Filing complaints in appropriate consumer courts on behalf of the consumers,
(d) All of the above

27. In case a consumer is not satisfied with the order passed in the State Commission, he can further make an appeal in the National Commission within a time period of
(a) 10 days
(b) 20 days
(c) 30 days
(d) 45 days

We hope the given Business Studies MCQs for Class 12 with Answers Chapter 10 Financial Market will help you. If you have any query regarding CBSE Class 12 Business Studies Financial Market MCQs Pdf, drop a comment below and we will get back to you at the earliest.

Free PDF Download of CBSE Accountancy Multiple Choice Questions for Class 12 with Answers Chapter 13 Common Size Statements. Accountancy MCQs for Class 12 Chapter Wise with Answers PDF Download was Prepared Based on Latest Exam Pattern. Students can solve NCERT Class 12 Accountancy Common Size Statements MCQs Pdf with Answers to know their preparation level.

Common Size Statements Class 12 Accountancy MCQs Pdf

Multiple Choice Questions
Select the best alternative and check your answer with the answers given at the end of the book.
1. Main objective of Common Size statement is :
(A) To present the changes in various items
(B) To provide for a common base for comparison
(C) To establish relationship between various items
(D) All of the Above

2. Main objective of Common Size Balance Sheet is :
(A) To establish relationship between revenue from operations and other items of statement of profit & loss
(B) To present changes in assets and liabilities
(C) To present changes in various items of income and expenses
(D) All of the Above

3. Common Size Statements are prepared
(A) In the form of Ratios
(B) In the form of Percentages
(C) In both of the Above
(D) None of the Above

4. Which of the following is untrue :
(A) Common size Balance Sheet
(B) Common size Statement of Profit & Loss
(C) Common size cash Flow Statement
(D) None of the Above

5. Main objective of Common Size Statment of Profit & Loss is :
(A) To present changes in assets and liabilities
(B) To judge the financial soundness
(C) To establish relationship between revenue from operations and other items of statement of Profit & Loss
(D) All of the Above

6. In the Statement of Profit & Loss of a Common Size Statement :
(A) Figure of net revenue from operations is assumed to be equal to 100
(B) Figure of gross profit is assumed to be equal to 100
(C) Figure of net profit is assumed to be equal to 100
(D) Figure of assets is assumed to be equal to 100

7. In the Balance Sheet of a Common Size Statement:
(A) Figure of share capital is assumed to be 100
(B) Figure of current liabilities is assumed to be 100
(C) Figure of fixed assets is assumed to be 100
(D) Figure of total assets is assumed to be 100

8. Total assets of a firm are ₹20,00,000 and its fixed assets are ₹8,00,000. What will be the percentage of fixed assets on total assets?
(A) 60%
(B) 40%
(C) 29%
(D) 71%

9. If total assets of a firm are ₹8,20,000 and its fixed assets are ₹5,90,400, what will be the percentage of current assets on total assets?
(A) 42%
(B) 58%
(C) 28%
(D) 72%

10. If net revenue from operations of a firm are ₹1,20,000; cost of revenue from operations is ₹66,000 and operating expenses are ₹21,600, what will be the percentage of operating income on net revenue from operations?
(A) 55%
(B) 45%
(C) 73%
(D) 27%

11. If net revenue from operations of a firm are ₹15,00,000; Gross Profit is ₹9,00,000 and operating expenses are ₹75,000, what will be percentage of operating income on net revenue from operations?
(A) 45%
(B) 55%
(C) 35%
(D) 65%

12. Main objective of Trend Analysis is
(A) To make comparative study of the financial statements for a number of years
(B) To indicate the direction of movement
(C) To help in forecasts of various items
(D) All of the Above

13, What will be the trend percentage, if the Inventory of a firm is ?2,00,000; ?2,40,000; ?3,00,000 and ?4,00,000 respectively?
(A) 1, 1.2, 1.5,2
(B) 10, 12, 15,20
(C) 100, 120, 150, 200
(D) None of the Above

14. In a common size Balance Sheet, total liabilities are assumed to be equal to
(A) 1
(B) 10
(C) 100
(D) 1,000

15. In a common size Statement of Profit & Loss, the amount of net revenue from operations is assumed to be equal to
(A) 1
(B) 10
(C) 100
(D) 1,000

16. The objective of common size Statement of Profit & Loss is not to
(A) Present Changes in Various items of incomes and expenses
(B) Judge the cost items
(C) Establish relationship between revenue from operations and other items of statement of profit & loss
(D) Judge the relative financial soundness for different enterprises

We hope the given Accountancy MCQs for Class 12 with Answers Chapter 13 Common Size Statements will help you. If you have any query regarding CBSE Class 12 Accountancy Common Size Statements MCQs Pdf, drop a comment below and we will get back to you at the earliest.

Free PDF Download of CBSE Accountancy Multiple Choice Questions for Class 12 with Answers Chapter 9 Redemption of Debentures. Accountancy MCQs for Class 12 Chapter Wise with Answers PDF Download was Prepared Based on Latest Exam Pattern. Students can solve NCERT Class 12 Accountancy Redemption of Debentures MCQs Pdf with Answers to know their preparation level.

Redemption of Debentures Class 12 Accountancy MCQs Pdf

Multiple Choice Questions
Choose the Best Alternate :
1. As per SEBI Guidelines an amount equal to ………………….. of the debenture issue must be transferred to Debenture Redemption Reserve before redemption begins.
(A) 25%
(B) 80%
(C) 50%
(D) 100%

2. A company issuing debentures with a maturity period of not more than 18 months, in that case the creation of Debentures Redemption Reserve will be :
(A) 50% of the amount of debentures issued
(B) 25% of the amount of debentures issued
(C) 100% of the amount of debentures issued
(D) None of the above

3. According to the guidelines issued by Securities and Exchange Board of India (SEBI) what percentage of the amount of debentures must be transferred to ‘Debentures Redemption Reserve’ before the commencement of redemption of debentures, in case of convertible debentures?
(A) 25%
(B) 50%
(C) 100%
(D) Zero

4. A Ltd. wants to redeem 5,000, 5% Debentures of ₹100 each at 5% premium. How much amount it must transfer to Debenture Redemption Reserve, if it has already a balance of ₹1,00,000 in Debenture Redemption Reserve Account?
(A) ₹4,00,000
(B) ₹1,50,000
(C) ₹2,00,000
(D) ₹2,50,000

5. A Company issuing debentures with a maturity periof of not more than …………….. need not create Debenture Redemption Reserve.
(A) 2 months
(B) 6 months
(C) 12 months
(D) 18 months

6. Where is ‘Debenture Redemption Reserve’ transferred after the redemption of all debentures?
(A) Capital Reserve Account
(B) General Reserve Account
(C) Statement of Profit and Loss
(D) Sinking Fund Account

We hope the given Accountancy MCQs for Class 12 with Answers Chapter 9 Redemption of Debentures will help you. If you have any query regarding CBSE Class 12 Accountancy Redemption of Debentures MCQs Pdf, drop a comment below and we will get back to you at the earliest.

Free PDF Download of CBSE Maths Multiple Choice Questions for Class 12 with Answers Chapter 13 Probability. Maths MCQs for Class 12 Chapter Wise with Answers PDF Download was Prepared Based on Latest Exam Pattern. Students can solve NCERT Class 12 Maths Probability MCQs Pdf with Answers to know their preparation level.

Probability Class 12 Maths MCQs Pdf

Question 1.
The variance of random variable X i.e. \(\sigma_{x}^{2}\) or var (X) is equal to
(a) E(X²) + [E(X²)₂]²
(b) E(X) – [E(X²)]
(c) E(X²) – [E(X)]²
(d) None of these
Answer:
(c) E(X²) – [E(X)]²

Question 2.
A coin is biased so that the head is 3 times likely to occur as a tail. If the coin is tossed twice, then find the probability distribution of the number of tails.

Answer:

Question 3.
A pair of the die is thrown 4 times. If getting a doubled is considered a success, then find the probability distribution of a number of successes.

Answer:

Question 4.
Find the probability of throwing atmost 2 sixes in 6 throws of a single die.
(a) \(\frac{35}{18}\left(\frac{5}{6}\right)^{3}\)
(b) \(\frac{35}{18}\left(\frac{5}{6}\right)^{4}\)
(c) \(\frac{18}{29}\left(\frac{2}{3}\right)^{4}\)
(d) \(\frac{18}{29}\left(\frac{2}{3}\right)^{3}\)
Answer:
(b) \(\frac{35}{18}\left(\frac{5}{6}\right)^{4}\)

Question 5.
A die is thrown again and again until three sixes are obtained. Find the probability of obtaining third six in the sixth throw of the die.
(a) \(\frac{625}{23329}\)
(b) \(\frac{621}{25329}\)
(c) \(\frac{625}{23328}\)
(d) \(\frac{620}{23328}\)
Answer:
(c) \(\frac{625}{23328}\)

Question 6.
Ten eggs are drawn successively with replacement from a lot containing 10% defective eggs. Then, the probability that there is atleast one defective egg is
(a) \(1-\frac{7^{10}}{10^{10}}\)
(b) \(1+\frac{7^{10}}{10^{10}}\)
(c) \(1+\frac{9^{10}}{10^{10}}\)
(d) \(1-\frac{9^{10}}{10^{10}}\)
Answer:
(d) \(1-\frac{9^{10}}{10^{10}}\)

Question 7.
The probability of a man hitting a target is \(\frac{1}{4}\). How many times must he fire so that the probability of his hitting the target at least once is greater than \(\frac{2}{3}\)?
(a) 4
(b) 3
(c) 2
(d) 1
Answer:
(a) 4

Question 8.
Eight coins are thrown simultaneously. Find the probability of getting atleast 6 heads.
(a) \(\frac{31}{128}\)
(b) \(\frac{37}{256}\)
(c) \(\frac{37}{128}\)
(d) \(\frac{31}{256}\)
Answer:
(b) \(\frac{37}{256}\)

Question 9.
A bag contains 6 red, 4 blue and 2 yellow balls. Three balls are drawn one by one with replacement. Find the probability of getting exactly one red ball.
(a) \(\frac{1}{4}\)
(b) \(\frac{3}{8}\)
(c) \(\frac{3}{4}\)
(d) \(\frac{1}{2}\)
Answer:
(b) \(\frac{3}{8}\)

Question 10.
Eight coins are thrown simultaneously. What is the probability of getting atleast 3 heads?
(a) \(\frac{37}{246}\)
(b) \(\frac{21}{256}\)
(c) \(\frac{219}{256}\)
(d) \(\frac{19}{246}\)
Answer:
(c) \(\frac{219}{256}\)

Question 11.
For the following probability distribution, the standard deviation of the random variable X is

(a) 0.5
(b) 0.6
(c) 0.61
(d) 0.7
Answer:
(d) 0.7

Question 12.
A bag contains 5 red and 3 blue balls. If 3 balls are drawn at random without replecement the probability of getting exactly one red ball is
(a) \(\frac{45}{196}\)
(b) \(\frac{135}{392}\)
(c) \(\frac{15}{56}\)
(d) \(\frac{15}{29}\)
Answer:
(c) \(\frac{15}{56}\)

Question 13.
A die is thrown and card is selected a random from a deck of 52 playing cards. The probability of gettingan even number on the die and a spade card is
(a) \(\frac{1}{2}\)
(b) \(\frac{1}{4}\)
(c) \(\frac{1}{8}\)
(d) \(\frac{3}{4}\)
Answer:
(c) \(\frac{1}{8}\)

Question 14.
A box contains 3 orange balls, 3 green balls and 2 blue balls. Three balls are drawn at random from the box without replacement. The probability of drawing 2 green balls and one blue ball is
(a) \(\frac{3}{28}\)
(b) \(\frac{2}{21}\)
(c) \(\frac{1}{28}\)
(d) \(\frac{167}{168}\)
Answer:
(a) \(\frac{3}{28}\)

Question 15.
A flashlight has 8 batteries out of which 3 are dead. If two batteries are selected without replacement and tested, the probability that both are deal is
(a) \(\frac{33}{56}\)
(b) \(\frac{9}{64}\)
(c) \(\frac{1}{14}\)
(d) \(\frac{3}{28}\)
Answer:
(d) \(\frac{3}{28}\)

Question 16.
Two dice are thrown. If it is known that the sum of numbers on the dice was less than 6, the probability of getting a sum 3, is
(a) \(\frac{1}{18}\)
(b) \(\frac{5}{18}\)
(c) \(\frac{1}{5}\)
(d) \(\frac{2}{5}\)
Answer:
(c) \(\frac{1}{5}\)

Question 17.
Two cards are drawn from a well shuffled deck of 52 playing cards with replacement. The probability, that both cards are queens, is
(a) \(\frac{1}{13} \times \frac{1}{13}\)
(b) \(\frac{1}{13}+\frac{1}{13}\)
(c) \(\frac{1}{13} \times \frac{1}{17}\)
(d) \(\frac{1}{13} \times \frac{4}{51}\)
Answer:
(a) \(\frac{1}{13} \times \frac{1}{13}\)

Question 18.
The probability of guessing correctly at least 8 out of 10 answers on a true-false type examiniation is
(a) \(\frac{7}{64}\)
(b) \(\frac{7}{128}\)
(c) \(\frac{45}{1024}\)
(d) \(\frac{7}{41}\)
Answer:
(b) \(\frac{7}{128}\)

Question 19.
The probability distribution of a discrete random variable X is given below:

The value of k is
(a) 8
(b) 16
(c) 32
(d) 48
Answer:
(c) 32

Question 20.
For the following probability distribution:

E(X) is equal to
(a) 0
(b) -1
(c) -2
(d) -1.8
Answer:
(d) -1.8

Question 21.
For the following probability distribution

E(X²) is equal to
(a) 3
(b) 5
(c) 7
(d) 10
Answer:
(d) 10

Question 22.
Suppose a random variable X follows the binomial distribution with parameters n and p, where 0 < p < 1. If p(x = r) / P(x = n – r) is dindependent of n and r, then p equals
(a) \(\frac{1}{2}\)
(b) \(\frac{1}{3}\)
(c) \(\frac{1}{5}\)
(d) \(\frac{1}{7}\)
Answer:
(a) \(\frac{1}{2}\)

Question 23.
A box has 100 pens of which 10 are defective. What is the probability that out of a sample of 5 pens drawn one by one with replacement at most one is defective?
(a) \(\left(\frac{9}{10}\right)^{5}\)
(b) \(\frac{1}{2}\left(\frac{9}{10}\right)^{4}\)
(c) \(\frac{1}{2}\left(\frac{9}{10}\right)^{5}\)
(d) \(\left(\frac{9}{10}\right)^{5}+\frac{1}{2}\left(\frac{9}{10}\right)^{4}\)
Answer:
(d) \(\left(\frac{9}{10}\right)^{5}+\frac{1}{2}\left(\frac{9}{10}\right)^{4}\)

Question 24.
P has 2 children. He has a son, Jatin. What is the probability that Jatin’s sibling is a brother?
(a) \(\frac{1}{3}\)
(b) \(\frac{1}{4}\)
(c) \(\frac{2}{3}\)
(d) \(\frac{1}{2}\)
Answer:
(a) \(\frac{1}{3}\)

Question 25.
If A and B are 2 events such that P(A) > 0 and P (b) ≠ 1, then \(P(\bar{A} / \bar{B})=\)
(a) 1 – P(A|B)
(b) \(1-P(A / \bar{B})\)
(c) \(\frac{1-P(A \cup B)}{P(B)}\)
(d) \(\frac{1(\bar{A})}{P(B)}\)
Answer:
(b) \(1-P(A / \bar{B})\)

Question 26.
If two events A and B area such that \(P(\bar{A})\) =0.3, P(B) = 0.4 and \(P(B | A \cup \bar{B})=\)
(a) \(\frac{1}{2}\)
(b) \(\frac{1}{3}\)
(c) \(\frac{2}{5}\)
(d) \(\frac{1}{4}\)
Answer:
(d) \(\frac{1}{4}\)

Question 27.
If E and F are events such that 0 < P(F) < 1, then
(a) \(P(E | F)+P(\bar{E} | F)=1\)
(b) \(P(E | F)+P(E | \bar{F})=1\)
(c) \(P(\bar{E} | F)+P(E | \bar{F})=1\)
(d) \(P(E | \bar{F})+P(\bar{E} | \bar{F})=0\)
Answer:
(a) \(P(E | F)+P(\bar{E} | F)=1\)

Question 28.
P(E ∩ F) is equal to
(a) P(E) . P(F|E)
(b) P(F) . P(E|F)
(c) Both (a) and (b)
(d) None of these
Answer:
(c) Both (a) and (b)

Question 29.
If three events of a sample space are E, F and G, then P(E ∩ F ∩ G) is equal to
(a) P(E) P(F|E) P(G|(E ∩ F))
(b) P(E) P(F|E) P(G|EF)
(c) Both (a) and (b)
(d) None of these
Answer:
(c) Both (a) and (b)

Question 30.
Two cards are drawn at random one by one without replacement from a pack of 52 playing cards. Find the probability that both the cards are black.
(a) \(\frac{21}{104}\)
(b) \(\frac{25}{102}\)
(c) \(\frac{23}{102}\)
(d) \(\frac{24}{104}\)
Answer:
(b) \(\frac{25}{102}\)

Question 31.
A bag contains 20 tickets, numbered 1 to 20. A ticket is drawn and then another ticket is drawn without replacement. Find the probability that both tickets will show even numbers.
(a) \(\frac{9}{38}\)
(b) \(\frac{16}{35}\)
(c) \(\frac{7}{38}\)
(d) \(\frac{17}{30}\)
Answer:
(a) \(\frac{9}{38}\)

Question 32.
Two balls are drawn one after another (without replacement) from a bag containing 2 white, 3 red and 5 blue balls. What is the probability that atleast one ball is red?
(a) \(\frac{7}{15}\)
(b) \(\frac{8}{15}\)
(c) \(\frac{7}{16}\)
(d) \(\frac{5}{16}\)
Answer:
(b) \(\frac{8}{15}\)

Question 33.
Let A and B be independent events with P(A) = 1/4 and P(A ∪ B) = 2P(B) – P(A). Find P(B)
(a) \(\frac{1}{4}\)
(b) \(\frac{3}{5}\)
(c) \(\frac{2}{3}\)
(d) \(\frac{2}{5}\)
Answer:
(d) \(\frac{2}{5}\)

Question 34.
Two events A and B will be independent, if
(a) A and B are mutually exclusive
(b) P(A’ ∩ B’) = [1 – P(A)] [1 – P(B)]
(c) P(A) = P(B)
(d) P(A) + P(B) = 1
Answer:
(c) P(A) = P(B)

Question 35.
If A and B are two independent events such that \(P(\bar{A} \cap B)=\frac{2}{15}\) and \(P(A \cap \bar{B})=\frac{1}{6}\), then find P(A) and P (B) respectively.
(a) \(\frac{5}{4}, \frac{4}{5}\)
(b) \(\frac{1}{5}, \frac{1}{7}\)
(c) \(\frac{1}{6}, \frac{1}{7}\)
(d) \(\frac{1}{7}, \frac{1}{7}\)
Answer:
(a) \(\frac{5}{4}, \frac{4}{5}\)

Question 36.
If A and B are two independent events, then the probability of occurrence of at least of A and B is given by
(a) 1 – P(A) P(b)
(b) 1 – P(A) P(B’)
(c) 1 – P(A’) P(B’)
(d) 1 – P(A’) P(b)
Answer:
(c) 1 – P(A’) P(B’)

Question 37.
If A and B are two indendent events such that \(P(\bar{A})\) = 0.75, P(A ∪ B) = 0.65 and P(b) = P, then find the value of P.
(a) \(\frac{9}{14}\)
(b) \(\frac{7}{15}\)
(c) \(\frac{5}{14}\)
(d) \(\frac{8}{15}\)
Answer:
(d) \(\frac{8}{15}\)

Question 38.
If A and Bare events such that P(A) = \(\frac{1}{3}\), P(b) = \(\frac{1}{4}\) and P(A ∩ B) = \(\frac{1}{12}\), then find P(not A and not B).
(a) \(\frac{1}{4}\)
(b) \(\frac{1}{2}\)
(c) \(\frac{2}{3}\)
(d) \(\frac{1}{3}\)
Answer:
(b) \(\frac{1}{2}\)

Question 39.
Two cards are drawn successively from a well shuffled pack of 52 cards. Find the probability that one is a red card the other is a queen.
(a) \(\frac{103}{1326}\)
(b) \(\frac{101}{1326}\)
(c) \(\frac{101}{1426}\)
(d) \(\frac{103}{1426}\)
Answer:
(b) \(\frac{101}{1326}\)

Question 40.
Given that, the events A and B are such that P(A) = \(\frac{1}{2}\), P(A ∪ B) = \(\frac{3}{5}\) and P(b) = P. Then probabilities of B if A and B are mutually exclusive and independent respetively are
(a) \(\frac{1}{2}, \frac{1}{3}\)
(b) \(\frac{1}{5}, \frac{1}{3}\)
(c) \(\frac{2}{3}, \frac{1}{3}\)
(d) \(\frac{1}{10}, \frac{1}{5}\)
Answer:
(d) \(\frac{1}{10}, \frac{1}{5}\)

Question 41.
Two cards from an ordinary deck of 52 cards are missing. What is the probability that a random card drawn from this deck is a spade?
(a) \(\frac{3}{4}\)
(b) \(\frac{2}{3}\)
(c) \(\frac{1}{2}\)
(d) \(\frac{1}{4}\)
Answer:
(d) \(\frac{1}{4}\)

Question 42.
A man is known to speak truth 3 out of 4 times. He throws a die and reports that it is a six. Find the probability that it is actually a six.
(a) \(\frac{5}{8}\)
(b) \(\frac{3}{8}\)
(c) \(\frac{7}{8}\)
(d) \(\frac{1}{8}\)
Answer:
(b) \(\frac{3}{8}\)

Question 43.
A bag contains 4 balls. Two balls are drawn at random and are found to be white. What is the probability that all balls are white?
(a) \(\frac{2}{5}\)
(b) \(\frac{3}{5}\)
(c) \(\frac{4}{5}\)
(d) \(\frac{1}{5}\)
Answer:
(b) \(\frac{3}{5}\)

Question 44.
A bag contains 3 green and 7 white balls. Two balls are drawn one by one at random without replacement. If the second ball drawn is green, what is the probability that the first ball was drawn in also green?
(a) \(\frac{5}{9}\)
(b) \(\frac{4}{9}\)
(c) \(\frac{2}{9}\)
(d) \(\frac{8}{9}\)
Answer:
(c) \(\frac{2}{9}\)

Question 45.
A card from a pack of 52 cards is lost. From the remaining cards of the pack, two cards are drawn and are found to be both clubs. Find the probability of the lost card being a club.
(a) \(\frac{11}{50}\)
(b) \(\frac{17}{50}\)
(c) \(\frac{13}{50}\)
(d) \(\frac{19}{50}\)
Answer:
(a) \(\frac{11}{50}\)

Question 46.
A random variable X has the following distribution.

For the event E = {X is prime number} and F = {X < 4}, P(E ∪ F) =
(a) 0.87
(b) 0.77
(c) 0.35
(d) 0.50
Answer:
(b) 0.77

Question 47.
A random variable X has the following probability distribution:

Find P(X < 3), P(X ≥ 4), P(0 < X < 5) respectively.
(a) \(\frac{1}{6}, \frac{11}{24}, \frac{33}{48}\)
(b) \(\frac{1}{6}, \frac{33}{48}, \frac{11}{24}\)
(c) \(\frac{1}{4}, \frac{11}{26}, \frac{21}{44}\)
(d) \(\frac{11}{26}, \frac{1}{4}, \frac{21}{44}\)
Answer:
(b) \(\frac{1}{6}, \frac{33}{48}, \frac{11}{24}\)

Question 48.
If the chance that a ship arrives safely at a port is \(\frac{9}{10}\); find the chance that out of 5 expected ships, atleast 4 will arrive safely at the port.
(a) \(\frac{91854}{100000}\)
(b) \(\frac{32805}{100000}\)
(c) \(\frac{59049}{100000}\)
(d) \(\frac{26244}{100000}\)
Answer:
(a) \(\frac{91854}{100000}\)

Question 49.
If the mean and the variance of a binomial distribution are 4 and, then find P(X ≥ 1).
(a) \(\frac{720}{729}\)
(b) \(\frac{721}{729}\)
(c) \(\frac{728}{729}\)
(d) \(\frac{724}{729}\)
Answer:
(c) \(\frac{728}{729}\)

Question 50.
A pair of dice is thrown 200 times. If getting a sum of 9 is considered a success, then find the mean and the variance respectively of the number of successes.
(a) \(\frac{400}{9}, \frac{1600}{81}\)
(b) \(\frac{1600}{81}, \frac{400}{9}\)
(c) \(\frac{1600}{81}, \frac{200}{9}\)
(d) \(\frac{200}{9}, \frac{1600}{81}\)
Answer:
(b) \(\frac{1600}{81}, \frac{400}{9}\)

Question 51.
In a binomial distribution, the sum of its mean and variance is 1.8. Find the probability of two successes, if the event was conducted times.
(a) 0.2623
(b) 0.2048
(c) 0.302
(d) 0.305
Answer:
(b) 0.2048

Question 52.
If the sum and the product of the mean and variance of a binomial distribution are 24 and 128 respectively, then find the distribution.
(a) \(\left(\frac{1}{4}+\frac{3}{4}\right)^{32}\)
(b) \(\left(\frac{1}{2}+\frac{1}{2}\right)^{30}\)
(c) \(\left(\frac{1}{2}+\frac{1}{2}\right)^{32}\)
(d) \(\left(\frac{1}{4}+\frac{3}{4}\right)^{30}\)
Answer:
(c) \(\left(\frac{1}{2}+\frac{1}{2}\right)^{32}\)

Question 53.
If the sum of the mean and variance of a binomial distribution is 15 and the sum of their squares is 17, then find the distribution.
(a) \(\left(\frac{2}{3}+\frac{1}{3}\right)^{25}\)
(b) \(\left(\frac{1}{2}+\frac{1}{2}\right)^{25}\)
(c) \(\left(\frac{1}{2}+\frac{1}{2}\right)^{27}\)
(d) \(\left(\frac{2}{3}+\frac{1}{3}\right)^{27}\)
Answer:
(d) \(\left(\frac{2}{3}+\frac{1}{3}\right)^{27}\)

Question 54.
The mean and the variance of a binomial distribution are 4 and 2 respectively. Find the probability of atleast 6 successes.
(a) \(\frac{37}{256}\)
(b) \(\frac{32}{255}\)
(c) \(\frac{34}{259}\)
(d) \(\frac{31}{256}\)
Answer:
(a) \(\frac{37}{256}\)

Question 55.
If P(A ∩ B) = \(\frac{7}{10}\) and P(b) = \(\frac{17}{20}\), P(A|B) equals
(a) \(\frac{14}{17}\)
(b) \(\frac{17}{20}\)
(c) \(\frac{7}{8}\)
(d) \(\frac{1}{8}\)
Answer:
(a) \(\frac{14}{17}\)

Question 56.
If P(A) = \(\frac{3}{10}\), P(b) = \(\frac{2}{5}\) and P(A ∪ B) = \(\frac{3}{5}\), then P(B|A) + P(A|B) equals
(a) \(\frac{1}{4}\)
(b) \(\frac{1}{3}\)
(c) \(\frac{5}{12}\)
(d) \(\frac{7}{12}\)
Answer:
(d) \(\frac{7}{12}\)

Question 57.
If P(A) = \(\frac{2}{5}\), P(B) = \(\frac{3}{10}\) and P(A ∩ B) = \(\frac{1}{5}\), then P(A’|B’) . (P(B’|A’) is equal to
(a) \(\frac{5}{6}\)
(b) \(\frac{5}{7}\)
(c) \(\frac{25}{42}\)
(d) 1
Answer:
(b) \(\frac{5}{7}\)

Question 58.
If A and B are two events sue that P(A) = \(\frac{1}{2}\), P(b) = \(\frac{1}{3}\), P(A|B) = \(\frac{1}{4}\) then (A’ ∩ B’) equals
(a) \(\frac{1}{12}\)
(b) \(\frac{3}{4}\)
(c) \(\frac{1}{4}\)
(d) \(\frac{3}{16}\)
Answer:
(c) \(\frac{1}{4}\)

Question 59.
If P(A) = 0.4, P(b) = 0.8 and P(B|A) = 0.6, then P(A ∪ B) equal to
(a) 0.24
(b) 0.3
(c) 0.48
(d) 0.96
Answer:
(c) 0.48

Question 60.
If A and B are two events and A ≠ Φ, B ≠ Φ, then
(a) P(A|B) = P(A) . P(b)
(b) P(A|B) = \(\frac{P(A \cap B)}{P(B)}\)
(c) P(A|B) . P(B|A) = 1
(d) P(A|B) = P(A)|P(b)
Answer:
(b) P(A|B) = \(\frac{P(A \cap B)}{P(B)}\)

Question 61.
A and B are events such that P(A) = 0.4, P(b) = 0.3 and P(A ∪ B) = 0.5. Then P(B’ ∩ A) equals
(a) \(\frac{2}{3}\)
(b) \(\frac{1}{2}\)
(c) \(\frac{3}{10}\)
(d) \(\frac{1}{5}\)
Answer:
(d) \(\frac{1}{5}\)

Question 62.
You are given that A and B are two events such that P(b) = \(\frac{3}{5}\), P(A|B) = \(=\frac{4}{5}\), then P(A) equals
(a) \(\frac{3}{10}\)
(b) \(\frac{1}{5}\)
(c) \(\frac{1}{2}\)
(d) \(\frac{3}{5}\)
Answer:
(c) \(\frac{1}{2}\)

We hope the given Maths MCQs for Class 12 with Answers Chapter 13 Probability will help you. If you have any query regarding CBSE Class 12 Maths Probability MCQs Pdf, drop a comment below and we will get back to you at the earliest.

Free PDF Download of CBSE Maths Multiple Choice Questions for Class 12 with Answers Chapter 11 Three Dimensional Geometry. Maths MCQs for Class 12 Chapter Wise with Answers PDF Download was Prepared Based on Latest Exam Pattern. Students can solve NCERT Class 12 Maths Three Dimensional Geometry MCQs Pdf with Answers to know their preparation level.

Three Dimensional Geometry Class 12 Maths MCQs Pdf

Question 1.

Answer:
(b) \(\frac{\pi}{2}\)

Question 2.
The angle between the lines passing through the points (4, 7, 8), (2, 3, 4) and (-1, -2, 1), (1, 2, 5) is
(a) 0
(b) \(\frac{\pi}{2}\)
(c) \(\frac{\pi}{4}\)
(d) \(\frac{\pi}{6}\)
Answer:
(a) 0

Question 3.

Answer:
(d) Both (a) and (b)

Question 4.

Answer:
(a) \(\frac{x-1}{1}=\frac{y-2}{3}=\frac{z+3}{4}\)

Question 5.

Answer:
(a) \(-\frac{10}{7}\)

Question 6.
Equation of the plane passing through three points A, B, C with position vectors

Answer:
(a) \(\pi(\hat{i}-\hat{j}-2 \hat{k})+23=0\)

Question 7.
Four points (0, -1, -1) (-4, 4, 4) (4, 5, 1) and (3, 9, 4) are coplanar. Find the equation of the plane containing them.
(a) 5x + 7y + 11z – 4 =0
(b) 5x – 7y + 11z + 4 = 0
(c) 5x – 7y – 11z – 4 = 0
(d) 5x + 7y – 11z + 4 = 0
Answer:
(b) 5x – 7y + 11z + 4 = 0

Question 8.
Find the equation of plane passing through the points P(1, 1, 1), Q(3, -1, 2), R(-3, 5, -4).
(a) x + 2y = 0
(b) x – y = 2
(c) -x + 2y = 2
(d) x + y = 2
Answer:
(d) x + y = 2

Question 9.
The vector equation of the plane passing through the origin and the line of intersection of the plane r.a = λ and r.b = µ is
(a) r.(λa – µb) = 0
(b) r.(λb – µa) = 0
(c) r.(λa + µb)= 0
(d) r.(λb + µa) = 0
Answer:
(b) r.(λb – µa) = 0

Question 10.
The vector equation of a plane passing through the intersection of the planes \(r_{\cdot}(\hat{i}+\hat{j}+\hat{k})=6\) and \(r_{\cdot}(2 \hat{i}+3 \hat{j}+4 \hat{k})=-5\) and the point (1, 1, 1) is

Answer:
(c) \(r_{\cdot}(20 \hat{i}+23 \hat{j}+26 \hat{k})=69\)

Question 11.

Answer:
(b) -4

Question 12.

(a) coplanar
(b) non-coplanar
(c) perpendicular
(d) None of the above
Answer:
(a) coplanar

Question 13.
The angle between the planes 3x + 2y + z – 5 = 0 and x + y – 2z – 3 = 0 is

Answer:
(c) \(\cos ^{-1}\left(\frac{3}{2 \sqrt{21}}\right)\)

Question 14.
The equation of the plane through the point (0, -4, -6) and (-2, 9, 3) and perpendicular to the plane x – 4y – 2z = 8 is
(a) 3x + 3y – 2z = 0
(b) x – 2y + z = 2
(c) 2x + y – z = 2
(d) 5x – 3y + 2z = 0
Answer:
(c) 2x + y – z = 2

Question 15.
The angle between the planes \(r \cdot(\hat{i}+2 \hat{j}+\hat{k})=4\) and \(r(-\hat{i}+\hat{j}+2 \hat{k})=9\) is
(a) 30°
(b) 60°
(c) 45°
(d) None of these
Answer:
(b) 60°

Question 16.

Answer:
(b) \(\frac{70}{11}\)

Question 17.
The shortest distance between the lines

Answer:
(d) \(\frac{1}{\sqrt{6}}\)

Question 18.
The shortest distance between the lines \(\frac{x-3}{3}=\frac{y-8}{-1}=\frac{z-3}{1}\) and \(\frac{x+3}{-3}=\frac{y+7}{2}=\frac{z-6}{4}\) is equal
(a) 3√30
(b) √30
(c) 2√30
(d) None of these
Answer:
(a) 3√30

Question 19.
The shortest distance between the lines x = y = z and x + 1 – y = \(\frac{z}{0}\) is
(a) \(\frac{1}{2}\)
(b) \(\frac{1}{\sqrt{2}}\)
(c) \(\frac{1}{\sqrt{3}}\)
(d) \(\frac{1}{\sqrt{6}}\)
Answer:
(d) \(\frac{1}{\sqrt{6}}\)

Question 20.
The shortest distance between the lines x = y + 2 = 6z – 6 and x + 1 = 2y = -12z is
(a) \(\frac{1}{2}\)
(b) 2
(c) 1
(d) \(\frac{3}{2}\)
Answer:
(b) 2

Question 21.
The angle θ between the line r = a + λb is given by

Answer:
(a) \(\sin ^{-1}\left(\frac{\tilde{h}_{\hat{\pi}}^{\pi}}{|\vec{b}|}\right)\)

Question 22.

Answer:
(a) \(\sin ^{-1}\left(\frac{2 \sqrt{2}}{3}\right)\)

Question 23.
The angle between the straight line \(\frac{x-1}{2}=\frac{y+3}{-1}=\frac{z-5}{2}\) and the plane 4x – 2y + 4z = 9 is
(a) 60°
(b) 90°
(c) 45°
(d) 30°
Answer:
(b) 90°

Question 24.
Distance of the point (α, β, γ) from y-axis is
(a) β
(b) |β|
(c) |β| + |γ|
(d) \(\sqrt{\alpha^{2}+\gamma^{2}}\)
Answer:
(d) \(\sqrt{\alpha^{2}+\gamma^{2}}\)

Question 25.
The distance of the plane \(r \cdot\left(\frac{2}{7} \hat{i}+\frac{3}{7} \hat{j}-\frac{6}{7} \hat{k}\right)=1\) from the origin is
(a) 1
(b) 7
(c) \(\frac{1}{7}\)
(d) None of these
Answer:
(a) 1

Question 26.

Answer:
(d) \(\frac{\sqrt{2}}{10}\)

Question 27.
The reflection of the point (α, β, γ) in the xy-plane is
(a) (α, β, 0)
(b) (0, 0, γ)
(c) (-α, -β, -γ)
(d) (α, β, -y)
Answer:
(d) (α, β, -y)

Question 28.
The area of the quadrilateral ABCD, where A(0, 4, 1), B(2, 3, -1), C(4, 5, 0) and D(2, 6, 2), is equal to
(a) 9 sq. units
(b) 18 sq. units
(c) 27 sq. units
(d) 81 sq. units
Answer:
(a) 9 sq. units

Question 29.
The locus represented by xy + yz = 0 is
(a) A pair of perpendicular lines
(b) A pair of parallel lines
(c) A pair of parallel planes
(d) A pair of perpendicular planes
Answer:
(d) A pair of perpendicular planes

Question 30.
Direction cosines of the line that makes equal angles with the three axes in space are

Answer:
(c) \(\pm \frac{1}{\sqrt{3}}, \pm \frac{1}{\sqrt{3}}, \pm \frac{1}{\sqrt{3}}\)

Question 31.
If the direction ratios of a line are 1, -3, 2, then its direction cosines are

Answer:
(a) \(\frac{1}{\sqrt{14}}, \frac{-3}{\sqrt{14}}, \frac{2}{\sqrt{14}}\)

Question 32.
The cosines of the angle between any two diagonals of a cube is
(a) \(\frac{1}{3}\)
(b) \(\frac{1}{2}\)
(c) \(\frac{2}{3}\)
(d) \(\frac{1}{\sqrt{3}}\)
Answer:
(a) \(\frac{1}{3}\)

Question 33.
Which of the following is false?
(a) 30°, 45°, 60° can be the direction angles of a line is space.
(b) 90°, 135°, 45° can be the direction angles of a line is space.
(c) 120°, 60°, 45° can be the direction angles of a line in space.
(d) 60°, 45°, 60° can be the direction angles of a line in space.
Answer:
(a) 30°, 45°, 60° can be the direction angles of a line is space.

Question 34.
A line makes angles α, β and γ with the co-ordinate axes. If α + β = 90°, then γ is equal to
(a) 0°
(b) 90°
(c) 180°
(d) None of these
Answer:
(b) 90°

Question 35.
If a line makes an angle θ₁, θ₂, θ₃ with the axis respectively, then cos 2θ₁ + cos 2θ₂ + cos 2θ₃ =
(a) -4
(b) -2
(c) -3
(d) -1
Answer:
(d) -1

Question 36.
The coordinates of a point P are (3, 12, 4) w.r.t. origin O, then the direction cosines of OP are

Answer:
(d) \(\frac{3}{13}, \frac{12}{13}, \frac{4}{13}\)

Question 37.
Find the direction cosines of the line joining A(0, 7, 10) and B(-1, 6, 6).

Answer:
(b) \(\frac{1}{3 \sqrt{2}}, \frac{1}{3 \sqrt{2}}, \frac{4}{3 \sqrt{2}}\)

Question 38.
The direction cosines of a line passing through two points P(x₁, y₁, z₁) and Q(x₂, y₂, z₂) are

Answer:
(c) \(\frac{x_{2}-x_{1}}{P Q}, \frac{y_{2}-y_{1}}{P Q}, \frac{z_{2}-z_{1}}{P Q}\)

Question 39.
The equation of a line which passes through the point (1, 2, 3) and is parallel to the vector \(3 \hat{i}+2 \hat{j}-2 \hat{k}\), is

Answer:
(b) \(r=(\hat{i}+2 \hat{j}+3 \hat{k})+\lambda(3 \hat{i}+2 \hat{j}-2 \hat{k})\)

Question 40.
The equation of line passing through the point (-3, 2, -4) and equally inclined to the axes are
(a) x – 3 = y + 2 = z – 4
(b) x + 3 = y – 2 = z + 4
(c) \(\frac{x+3}{1}=\frac{y-2}{2}=\frac{z+4}{3}\)
(d) None of these
Answer:
(b) x + 3 = y – 2 = z + 4

Question 41.
If l, m and n are the direction cosines of line l, then the equation of the line (l) passing through (x₁, y₁, z₁) is

Answer:
(a) \(\frac{x-x_{1}}{l}=\frac{y-y_{1}}{m}=\frac{z-z_{1}}{n}\)

Question 42.
In the figure, a be the position vector of the point A with respect to the origin O. l is a line parallel to a
vector b. The vector equation of line l is

Answer:
(c) r = a + λb

Question 43.
The certesian equation of the line l when it passes through the point (x₁, y₁, z₁) and parallel to the vector
b = \(a \hat{i}+b \hat{j}+c \hat{k}\), is
(a) x – x₁ = y – y₁ = z – z₁
(b) x + x₁ = y + y₁ = z + z₁
(c) \(\frac{x+x_{1}}{a}=\frac{y+y_{1}}{b}=\frac{z+z_{1}}{c}\)
(d) \(\frac{x-x_{1}}{a}=\frac{y-y_{1}}{b}=\frac{z-z_{1}}{c}\)
Answer:
(d) \(\frac{x-x_{1}}{a}=\frac{y-y_{1}}{b}=\frac{z-z_{1}}{c}\)

Question 44.
The equation of the straight line passing through the point (a, b, c) and parallel to Z-axis is

Answer:
(d) \(\frac{x-a}{0}=\frac{y-b}{0}=\frac{z-c}{1}\)

Question 45.
The coordinates of a point on the line \(\frac{x+2}{3}=\frac{y+1}{2}=\frac{z-3}{2}\) at a distance of \(\frac{6}{\sqrt{12}}\) from the point (1, 2, 3) is
(a) (56, 43, 111)
(b) \(\left(\frac{56}{17}, \frac{43}{17}, \frac{111}{17}\right)\)
(c) (2, 1, 3)
(d) (-2, -1, -3)
Answer:
(b) \(\left(\frac{56}{17}, \frac{43}{17}, \frac{111}{17}\right)\)

Question 46.
Find the coordinatets of the point where the line through the points (5, 1, 6) and (3, 4, 1) crosses the yz-plane.
(a) \(\left(0,-\frac{17}{2}, \frac{13}{2}\right)\)
(b) \(\left(0, \frac{17}{2},-\frac{13}{2}\right)\)
(c) \(\left(10, \frac{19}{2}, \frac{13}{2}\right)\)
(d) (0, 17, 13)
Answer:
(b) \(\left(0, \frac{17}{2},-\frac{13}{2}\right)\)

Question 47.
The point A(1, 2, 3), B(-1, -2, -1) and C(2, 3, 2) are three vertices of a parallelogram ABCD. Find the equation of CD.

Answer:
(d) \(\frac{x-2}{1}=\frac{y-3}{2}=\frac{z-2}{2}\)

Question 48.
The equation of the line joining the points (-3, 4, 11) and (1, -2, 7) is

Answer:
(b) \(\frac{x+3}{-2}=\frac{y-4}{3}=\frac{z-11}{2}\)

Question 49.
The vector equation of the line through the points A(3, 4, -7) and B(1, -1, 6) is

Answer:
(c) \(r=(3 \hat{i}+4 \hat{j}-7 \hat{k})+\lambda(-2 \hat{i}-5 \hat{j}+13 \hat{k})\)

Question 50.

Answer:
(d) \(\frac{\pi}{6}\)

Question 51.
The angle between the line 2x = 3y = -z and 6x = -y = -4z is
(a) 30°
(b) 45°
(c) 90°
(d) 0°
Answer:
(c) 90°

Question 52.
The angle between the lines 3x = 6y = 2z and \(\frac{x-2}{-5}=\frac{y-1}{7}=\frac{z-3}{1}\) is
(a) \(\frac{\pi}{6}\)
(b) \(\frac{\pi}{4}\)
(c) \(\frac{\pi}{3}\)
(d) \(\frac{\pi}{2}\)
Answer:
(d) \(\frac{\pi}{2}\)

Question 53.
Find the angle between the pair of lines given by

Answer:
(a) \(\cos ^{-1}\left(\frac{19}{21}\right)\)

Question 54.
The angle between the lines x = 1, y = 2 and y = -1, z = 0 is
(a) 90°
(b) 30°
(c) 60°
(d) 0°
Answer:
(a) 90°

Question 55.

Answer:
(a) 0

Question 56.

Answer:
(b) \(\frac{\left|\left(\tilde{a}_{2}-a_{1}\right) \times b\right|}{|b|}\)

Question 57.

Answer:
(b) \(\sqrt{\frac{59}{7}}\)

Question 58.

Answer:
(d) \(\sqrt{\frac{129}{5}}\)

Question 59.
The direction cosines of the unit vector perpendicular to the plane \(r \cdot(6 \hat{i}-3 \hat{j}-2 \hat{k})+1=0\) passing through the origin are
(a) \(\frac{6}{7}, \frac{3}{7}, \frac{2}{7}\)
(b) 6, 3, 2
(c) \(-\frac{6}{7}, \frac{3}{7}, \frac{2}{7}\)
(d) -6, 3, 2
Answer:
(c) \(-\frac{6}{7}, \frac{3}{7}, \frac{2}{7}\)

Question 60.
The coordinate of the foot of perpendicular drawn from origin to the plane 2x – 3y + 4z – 6 = 0 is

Answer:
(d) \(\left(\frac{12}{\sqrt{29}}, \frac{-18}{\sqrt{29}}, \frac{24}{\sqrt{29}}\right)\)

Question 61.
The vector equation of a plane which is at a distance of 7 units from the origin and normal to the vector
\(3 \hat{i}+5 \hat{j}-6 \hat{k}\) is

Answer:
(d) \(r \cdot\left(\frac{3 \hat{i}}{70}+\frac{5 \hat{j}}{70}-\frac{6 \hat{k}}{70}\right)=7\)

Question 62.
Find the vector equation of the plane which is at a distance of 8 units from the origin and which is normal to the vector \(2 \hat{i}+\hat{j}+2 \hat{k}\).

Answer:
(c) \(r_{\cdot}(2 \hat{i}+\hat{j}+2 \hat{k})=24\)

Question 63.
Find the length of perpendicular from the origin to the plane \(r(3 \hat{i}-4 \hat{j}+12 \hat{k})\).
(a) \(\frac{5}{13}\)
(b) \(\frac{5}{\sqrt{13}}\)
(c) \(\frac{5}{23}\)
(d) \(\frac{\sqrt{5}}{13}\)
Answer:
(a) \(\frac{5}{13}\)

Question 64.
The equation of the plane passing through three non- collinear points with position vectors a, b, c is
(a) r.(b × c + c × a + a × b) = 0
(b) r.(b × c + c × a + a × b) = [abc]
(c) r.(a × (b + c)) = [abc]
(d) r.(a + b + c) = 0
Answer:
(b) r.(b × c + c × a + a × b) = [abc]

We hope the given Maths MCQs for Class 12 with Answers Chapter 11 Three Dimensional Geometry will help you. If you have any query regarding CBSE Class 12 Maths Three Dimensional Geometry MCQs Pdf, drop a comment below and we will get back to you at the earliest.