Extra Questions for Class 10 Maths Chapter 14 Statistics. According to new CBSE Exam Pattern, MCQ Questions for Class 10 Maths Carries 20 Marks.
You can also download NCERT Solutions For Class 10 to help you to revise complete syllabus and score more marks in your examinations.
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Here is the list of Extra Questions for Class 10 Maths with Solutions and Answers Chapter wise based on latest NCERT syllabus (https://ncert.nic.in/) prescribed by CBSE. According to new CBSE Exam Pattern, MCQ Questions for Class 10 Maths Carries 20 Marks.
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Chapter Wise CBSE Quick Revision Notes and Key Points for Class 10 Maths Pdf free download was designed by expert teachers at from latest edition of NCERT books to get good marks in board exams. NCERT Class 10 Maths Notes contains all chapters are part of Revision Notes for Class 10. Here we have given CBSE Maths Notes for Class 10. According to new CBSE Exam Pattern, MCQ Questions for Class 10 Maths Carries 20 Marks.
We hope the given Chapter Wise CBSE Quick Revision Notes and Key Points for Class 10 Maths Pdf free download of physics, chemistry and biology notes will help you. If you have any query regarding NCERT Class 10 Maths Notes, drop a comment below and we will get back to you at the earliest.
Free PDF Download of CBSE Class 10 Maths Chapter 15 Probability Multiple Choice Questions with Answers. MCQ Questions for Class 10 Maths with Answers was Prepared Based on Latest Exam Pattern. Students can solve NCERT Class 10 Maths Probability MCQs with Answers to know their preparation level.
MCQ On Probability Class 10 Question 1. The probability of getting exactly one head in tossing a pair of coins is
(a) 0
(b) 1
(c) 1/3
(d)1/2
Answer: d
Explaination: Reason: S = [HH, HT, TH, TT] = 4
∴ P(exactly 1 head) =24=12
MCQ Questions For Class 10 Maths Probability Question 2. The probability of getting a spade card from a well shuffled deck of 52 cards is
Answer: b
Explaination: Reason: Total cards = 52,
Spade cards = 13
∴ P(a spade card) =1352=14
Probability MCQ Class 10 Question 3. The probability of getting less than 3 in a single throw of a die is
Answer: a
Explaination: Reason: Here S = [1, 2, 3, 4, 5, 6]
∴ n(S) = 6
E = (Less than 3) = [1, 2
∴ P(Less than 3) =26=13
Probability Class 10 MCQ Question 4. The total number of events of throwing 10 coins simultaneously is
(a) 1024
(b) 512
(c) 100
(d) 10
Answer: a
Explaination: Reason: Total events 210 = 1024
MCQ Of Probability For Class 10 Question 5. Which of the following can be the probability of an event?
(a) – 0.4
(b) 1.004
(c) 1823
(d) 107
Answer: c
Explaination: Reason: The probability of an event can neither be a negative value, nor it can exceed unity.
Probability MCQs With Answers Pdf Question 6. Three coins are tossed simultaneously. The probability of getting all heads is
Answer: d
Explaination: Reason: Here S = [HHH, HHT, HTH, THH, HTT, THT, TTH, TTT] = 8
∴ P(all heads) = 18
Probability MCQ Question 7. One card is drawn from a well shuffled deck of 52 cards. The probability of getting a king of red colour is
Answer: a
Explaination: Reason: Total cards = 52
Total events «(S) = 52
a king of red colour = 2
P(a king of red colour) =252=126
MCQ Questions For Class 10 Maths With Answers Question 8. One card is drawn from a well shuffled deck of 52 playing cards. The probability of getting a non-face card is
Answer: b
Explaination: Reason; Total cards = 52,
Total face cards = 12
∴ Non-face cards = 52 – 12 = 40
∴ P(a non-face card) =4052=1013
9. The chance of throwing 5 with an ordinary die is
Answer: a
Explaination: Reason: Here S = [1, 2, 3,4, 5, 6]
∴ n(S) = 6
∴ P(throwings) = 16
MCQ Questions For Class 10 Maths Question 10. The letters of the word SOCIETY are placed at random in a row. The probability of getting a vowel is
Answer: c
Explaination: Reason: Totle letters = 7
No. of vowel = 3 [∵ Vowel are O, I, E]
∴ P(a vowel) = 37
Probability Questions And Answers Pdf Question 11. Cards bearing numbers 3 to 20 are placed in a bag and mixed thoroughly. A card is taken out from the bag at random. The probability that the number on the card taken out is an even number, is
Answer: d
Explaination: Reason: Total cards = 18
Cards with even numbers are 4, 6, 8, 10, 12, 14, 16, 18, 20 = 9
∴ P(even number) =918=12
Maths MCQ For Class 10 Question 12. The total events to throw three dice simultaneously is
(a) 6
(b) 18
(c) 81
(d) 216
Answer: d
Explaination: Reason: Total cards = (6)3= 216
10 Class Maths MCQ With Answers Question 13. The probability of getting a consonant from the word MAHIR is
Answer: b
Explaination: Reason: Total characters in MAHIR = 5,
Consonants are M, H, R i.e., 3
∴ P(getting a consonant) = 35
Probability Multiple Choice Questions Question 14. A girl calculates that the probability of her winning the first prize in a lottery is 8100. If 6,000 tickets are sold, how many tickets has she bought?
(a) 400
(b) 750
(c) 480
(d) 240
Answer: c
Explaination: Reason: No. of tickets sold = 8100 × 6000 = 8 ×60 = 480
Multiple Choice Questions On Probability Question 15. A card is drawn from a well shuffled deck of 52 cards. The probability of a seven of spade is
Answer: b
Explaination: Reason: Total cards = 52, A seven of spade = 1
∴ P(a seven of spade) = 152
Probability Multiple Choice Questions And Answers Question 16. A bag contains 3 red balls and 5 black balls. A ball is drawn at random from the bag. The probability that a red ball drawn is
Answer: a
Explaination: Reason: Total balls = 3 + 5 = 8
∴ Total events = 8
P(a red ball) = 38
Probability MCQ Pdf Question 17. A child has a die whose six faces show the letters as given below:
| A | B | C | D | E | F |
The die is thrown once. The probability of getting a ‘D’ is
Answer: d
Explaination: Reason: Sample space S = [A, B, C, D, E, F] = 6
∴ n(S) = 6
∴ P(getting D) = 16
Probability Multiple Choice Questions And Answers Pdf Question 18. One card is drawn from a well-shuffled deck of 52 cards. The probability that the card will not be an ace is
Answer: c
Explaination: Reason: Total cards = 52
∴ Total events = 52
No. of ace cards = 4
Non-ace cards = 52 – 4 = 48
∴ P(not an ace) =4852=1213
Probability Multiple Choice Questions Pdf Question 19. A lot consists of 144 ball pens of which 20 ae defective and the others are good. Tanu will buy a pen if it is good but will not buy if it is defective. The shopkeeper draws one pen at random and gives it to her. The probability that she will buy that pen is
Answer: c
Explaination: Reason: Total ball pens = 144
Defective ball pens = 20
Good ball pens = 144 – 20 = 124
∴ P(she will buy a pen) = P(good ball pen) =124144=3136
Multiple Choice Probability Questions Question 20. A ticket is drawn at random from a bag containing tickets numbered from 1 to 40. The probability that the selected ticket has a number which is a multiple of 5 is
Answer: b
Explaination: Reason: Total number = 40
∴ n(S) = 40
Number of favourable events are 5,10,15, 20, 25, 30, 35, 40 = 8
∴ Probability (multiple of 5) =840=15
Probability Questions Multiple Choice Question 21. Which of the following cannot be the probability of an event? [Delhi 2011]
(a) 1.5
(b) 35
(c) 25%
(d) 0.3
Answer: a
Explaination:
(a) ∵ Probability of any event cannot be more than 1.
∴ 1.5 can not be the probability of any event.
∴ (a) is the answer.
Basic Probability Multiple Choice Questions Pdf Question 22. A coin is tossed twice. The probability of getting both heads is [Foreign 2013]
Answer: c
Explaination:
(c) Sample space = {HH, HT, TH, TT}
Number of total possible outcomes =4
Number of favourable outcome (both heads) = 1
∴ Probability of getting both heads = 14
Probability MCQs With Answers Question 23. A fair dice is rolled. Probability of getting a number x such that 1 ≤ x ≤ 6, is
(a) 0
(b) > 1
(c) between 0 and 1
(d) 1
Answer: d
Explaination: (d) 1, ∵ It is a sure event.
24. The sum of the probabilities of all elementary events of an experiment is p, then
(a) 0 < p < 1
(b) 0 ≤ p < 1
(c) p = 1
(d) p = 0
Answer: c
Explaination: (c) p = 1
25. If an event cannot occur, then its probability is [NCERT Exemplar Problems]
(a) 1
(b) 34
(c) 12
(d) 0
Answer: d
Explaination: (d) 0. ∵ event cannot occur.
26. An event is very unlikely to happen. Its probability is closest to [NCERT Exemplar Problems]
(a) 0.0001
(b) 0.001
(c) 0.01
(d) 0.1
Answer: a
Explaination: (a) 0.0001
27. Match the columns:
(a) (1) → (A), (2) → (B), (3) → (C)
(b) (1) → (B), (2) → (A), (3) → (C)
(c) (1) → (C), (2) → (B), (3) → (E)
(d) (1) → (C), (2) → (B), (3) → (D)
Answer: d
Explaination: (d) Probability facts
28. A card is drawn from a well-shuffled deck of 52 playing cards. The probability that the card will not be an ace is
Answer: c
Explaination:
(c) Total number of cards = 52
Number of ace = 4
P(not be an ace) = 4852=1213
29. An experiment whose outcomes has to be among a set of events that are completely known but whose exact outcomes is unknown is a
(a) sample space
(b) elementary event
(c) random experiment
(d) none of these
Answer: c
Explaination: (c) Random experiment
30. The experiments which when repeated under identical conditions produce the same results or outcomes are known as
(a) random experiments
(b) probabilistic experiment
(c) elementary experiment
(d) deterministic experiment
Answer: d
Explaination: (d) Deterministic experiment
31. For an event E, P(E) + P(E→) = q, then
(a) 0 ≤ q < 1
(b) 0 < q ≤ 1
(c) 0 < q < 1
(d) none of these
Answer: d
Explaination:
(d) ∵ P(E) + P(E→) = 1
∴ q = 1
32. A man is known to speak truth 3 out of 4 times. He throws a die and a number other than six comes up. Find the probability that he reports it is a six.
Answer: b
Explaination:
(b) When a number other than six appears
and man reports it is a six, it means man is telling a lie.
∴ Probability = 1 – 14=14
33. One ticket is selected at random from 100 tickets numbered 0.0, 01, 02, ……, 99. Suppose x is the sum of digits and y is the product of digits, then probability that x = 9 and y = 0 is
Answer: c
Explaination:
(c) Sum of digits = 9 and product = 0
∴ Number is either 09 or 90.
∴ Required probability = 2100=150
34. A bag contains 5 black balls, 4 white balls and 3 red balls. If a ball is selected randomwise, the probability that it is a black or red ball is ____ .
Answer:
Explaination:
Number of black or red balls = 5 + 3
= 8
∴ Required probability = 812=23
35. The probability of a non-leap year having 53 Mondays is _______. [Foreign 2012]
Answer:
Explaination:
No. of days in a non-leap year = 365
No. of complete weeks = 52(52 × 7 = 364)
No. of days left = 1
∴ Probability of this day being a Monday = Probability of 53 Mondays = 17
36. If a random experiment is performed, then each of its outcomes is known as ______ .
Answer:
Explaination: elementary event
37. The probability of selecting a rotten apple randomly from a heap of 900 apples is 0.18. What is the number of rotten apples in the heap? [AI2017]
Answer:
Explaination:
Total apples in the heap = 900
∴ Total number of elementary events = 900
One rotten apple is randomly selected from this heap
Hence, there are 162 rotten apples in the heap.
38. From a well shuffled pack of cards, a card is drawn at random. Find the probability of getting a black queen.
Answer:
Explaination:
Total number of ways to draw a card = 52
Number of ways to draw a black queen = 2
∴ Probability of getting a black queen 252=126
39. If three different coins are tossed together, then find the probability of getting two heads. [AI 2017 (C)]
Answer:
Explaination:
Three coins are tossed together.
Possible outcomes
{HHH, HHT, HTH, THH, TTT, TTH, THT, HTT}
Number of 2 heads together = 3 Probability of getting two heads = 38
40. A die is thrown once. Find the probability of getting a number less than 3.
Answer:
Explaination:
Total number of ways = 6
Number of ways to get a number less than 3 = 2
∴ Required probability = 26=13
41. Cards bearing numbers 3 to 20 are placed in a bag and mixed thoroughly. A card is taken out from the bag at random. What is the probability that the number on the card taken out is an even number?
Answer:
Explaination:
Total number of cards =18
Even numbers from 3 to 20 are 4, 6, 8, 10, 12, 14, 16, 18, 20 = 9 numbers
Probability that the number on the card taken out is an even number
42. Two coins are tossed simultaneously. Find the probability of getting exactly one head.
Answer:
Explaination:
When two coins are tossed simultaneously
Total number of outcomes = {HH, HT, TH, TT}
Total number of outcomes = 4
Favourable outcomes = {HT, TH} = 2
Probability of getting exactly one head = 24=12
43. An unbiased die is thrown, what is the probability of getting an even number.
Answer:
Explaination:
Total outcomes = {1, 2, 3, 4, 5, 6}
Favourable outcomes = {2, 4, 6}
∴ Probability of getting an even number = 36=12
44. If the probability of winning a game is 0.3, what is the probability of losing it?
Answer:
Explaination:
Probability of winning a game = 0.3
∴ Probability of losing the game
= 1 – Probability of winning the game
= 1 – 0.3 = 0.7
45. A man is known to speak truth 5 out of 7 times. He throws a die and a number other than 6 comes up. Find the probability that he reports it is a six.
Answer:
Explaination:
P(man will speak the truth) = 57
∴ P(man will not speak the truth) = 1 – 57=27
when a number other than 6 comes up the probability of man’s reporting it is a six the probability of man not speaking the truth 57
We hope the given MCQ Questions for Class 10 Maths Probability with Answers will help you. If you have any query regarding CBSE Class 10 Maths Chapter 15 Probability Multiple Choice Questions with Answers, drop a comment below and we will get back to you at the earliest.
Free PDF Download of CBSE Class 10 Maths Chapter 14 Statistics Multiple Choice Questions with Answers. MCQ Questions for Class 10 Maths with Answers was Prepared Based on Latest Exam Pattern. Students can solve NCERT Class 10 Maths Statistics MCQs with Answers to know their preparation level.
MCQ on Statistics Class 10 Question 1. One of the methods for determining mode is
(a) Mode = 2 Median -3 Mean
(b) Mode = 3 Median – 2 Mean
(c) Mode = 2 Mean – 3 Median
(d) Mode = 3 Mean – 2 Median
Statistics Class 10 MCQ with Answer: b
2. Mode is the
(a) middle most frequent value
(b) least frequent value
(c) maximum frequent value
(d) none of these
Answer: c
3. The algebraic sum of the deviations of a frequency distribution from its mean is always,
(a) greater than zero
(b) less than zero
(c) zero
(d) a non-zero number
Answer: c
MCQ Questions for Class 10 Maths Statistics Question 4. While computing mean of grouped data, we assume that the frequencies are
(a) centred at the upper limits of the classes
(b) centred at the lower limits of the classes
(c) centred at the classmarks of the classes
(d) evenly distributed over all the classes
5. Construction of a cumulative frequency table is useful in determining the
(a) mean
(b) median
(c) mode
(d) none of these
Answer: c
6. Which of the following can not be determined graphically?
(a) Mean
(b) Median
(c) Mode
(d) None of these
Answer: a
Statistics MCQ Class 10 Question 7. The absccissa of the point of intersection of the less than type and of the more than type cumulative frequency curves of a grouped data gives its
(a) Mean
(b) Median
(c) Mode
(d) None of these
Answer: b
8. For the following distribution
| C.I. | 0-10 | 10-20 | 20-30 | 30-40 | 40-50 |
| f | 20 | 30 | 24 | 40 | 18 |
the sum of lower limits of the modal class and the median class is
(a) 20
(b) 30
(c) 40
(d) 50
Answer: d
9. For the following distribution
| C.I. | 0-5 | 6-11 | 12-17 | 18-23 | 24-29 |
| f | 26 | 20 | 30 | 16 | 22 |
the upper limit of the median class is
(a) 18.5
(b) 18
(c) 17.5
(d) 17
Answer: c
MCQ of Statistics Class 10 Question 10. For the following distribution
| Marks | No. of students |
| Less than 20 | 4 |
| Less than 40 | 12 |
| Less than 60 | 25 |
| Less than 80 | 56 |
| Less than 100 | 74 |
| Less than 120 | 80 |
the modal class is
(a) 20 – 40
(b) 40 – 60
(c) 60 – 80
(d) 80 -100
Answer: c
11. For the following distribution
| Monthly Expenditure (?) | No. of families |
| Expenditure les than ? 10,000 | 15 |
| Expenditure les than ? 13,000 | 31 |
| Expenditure les than ? 16,000 | 50 |
| Expenditure les than ? 19,000 | 67 |
| Expenditure les than ?22,000 | 85 |
| Expenditure les than ?25,000 | 100 |
The number of families having expenditure range (in ?) 16,000 – 19,000 is
(a) 15
(b) 16
(c) 17
(d) 19
Answer: c
12. In the given data:
| C.I. | f |
| 65-85 | 4 |
| 85 – 105 | 5 |
| 105 – 125 | 13 |
| 125 – 145 | 20 |
| 145 – 165 | 14 |
| 165 – 185 | 7 |
| 185 – 205 | 4 |
the difference of the upper limit of the median class and the lower limit of the modal class is
(a) 38
(b) 20
(c) 19
(d) 0
Answer: b
Statistics Class 10 MCQ Question 13. For the following distribution
| Cl | 0-5 | 5-10 | 10-15 | 15-20 | 20-25 |
| f | 10 | 15 | 12 | 20 | 9 |
the difference of the upper limit of the median class and the lower limit of the modal class is
(a) 0
(b) 5
(c) 10
(d) -5
Answer: a
14. For the following distribution
| Marks | 0-10 | 10-20 | 20-30 | 30-40 | 40-50 |
| No. of students | 3 | 9 | 13 | 10 | 5 |
the number of students who got marks less than 30 is
(a) 13
(b) 25
(c) 10
(d) 12
Answer: b
15. For the following distribution
| Marks obtained | No. of students |
| More than or equal to 0 | 63 |
| More than or equal to 10 | 58 |
| More than or equal to 20 | 55 |
| More than or equal to 30 | 51 |
| More than or equal to 40 | 48 |
| More than or equal to 50 | 42 |
the frequency of the class 20-30 is
(a) 35
(b) 4
(c) 48
(d) 51
Class 10 Maths MCQ Questions with Answer: b
MCQ Questions for Class 10 Maths with Answers Question 16. The times, in seconds, taken by 150 atheletes to run a 100 m hurdle race are tabulated below:
| C.I. | f |
| 13.8-14 | 3 |
| 14 – 14.2 | 4 |
| 14.2 – 14.4 | 6 |
| 14.4 – 14.6 | 69 |
| 14.6 – 14.8 | 48 |
| 14.8-15 | 20 |
The number of atheletes who completed the race in less than 14.6 seconds is
(a) 13
(b) 69
(c) 82
(d) 130
Answer: c
17. di is the deviation of xi from assumed mean a. If mean = x+∑fidi∑fi, then x is
(a) class size ‘
(b) number of observations
(c) assumed mean
(d) none of these
Answer: c
Explaination:
(c) ∵ Mean = assumed mean + ∑fidi∑fi
∴ x = assumed mean.
18. Mean of 100 items is 49. It was discovered that three items which should have been 60, 70, 80 were wrongly read as 40, 20, 50 respectively. The correct mean is
(a) 48
(b) 49
(c) 50
(d) 60
Maths MCQ for Class 10 CBSE with Answer: cExplaination:
(c) Sum of 100 observations
= 100 × 49 = 4900
Correct sum
= 4900 – [40 + 20 + 50 ] + [60 + 70 + 80] = 5000
∴ Correct mean = 5000100 = 50.
MCQ on Statistics Class 9 Question 19. Choose the correct answer from the given four options : In the formula
for finding the mean of grouped data d1 s are deviation from a of [NCERT Exemplar Problems]
(a) lower limits of the classes
(b) upper limits of the classes
(c) mid points of the classes
(d) frequencies of the class marks
Answer: c
Explaination: (c) mid-points of the classes.
20. While computing mean of grouped data, we assume that the frequencies are [NCERT Exemplar Problems]
(a) evenly distributed over all the classes
(b) centred at the classmarks of the classes
(c) centred at the upper limits of the classes
(d) centred at the lower limits of the classes
MCQ for Class 10 Maths with Answer: bExplaination: (b) centred at the classmarks of the classes.
CBSE Class 10 Maths MCQ Pdf Question 21. A car travels from city A to city B, 120 km apart at an average speed of 50 km/h. It then makes a return trip at an average speed of 60 km/h. It covers another 120 km distance at an average speed of 40 km/h. The average speed over the entire 360 km will be
Answer: b
Explaination:
22. Mean of n numbers x1, x2, … xn is m. If xn is replaced by x, then new mean is
Answer: b
Explaination:
Statistics MCQ Question 23. In the formula x¯=a+h(∑fiui∑fi) finding the mean of grouped frequency distribution, ui = [NCERT Exemplar Problems]
Answer: c
Explaination: xi−ah
24. The abscissa of the point of intersection of the less than type and of the more than type cumulative frequency curves of a grouped data gives its [NCERT Exemplar Problems]
(a) mean
(b) median
(c) mode
(d) all the three above
Answer: b
Explaination: median
25. For the following distribution:
| Marks | Number of Students |
| Below 10 | 3 |
| Below 20 | 12 |
| Below 30 | 27 |
| Below 40 | 57 |
| Below 50 | 75 |
| Below 60 | 80 |
the modal class is
(a) 10 – 20
(b) 20 – 30
(c) 30 – 40
(d) 50 – 60
Answer: c
26. The times, in seconds, taken by 150 atheletes to run a 110 m hurdle race are tabulated below:
| Class | Frequency |
| 13.8 – 14.0 | 2 |
| 14.0 – 14.2 | 4 |
| 14.2 – 14.4 | 5 |
| 14.4 – 14.6 | 71 |
| 14.6 – 14.8 | 48 |
| 14.8 – 15.0 | 20 |
The number of atheletes who completed the race in less then 14.6 seconds is: [NCERT Exemplar Problems]
(a) 11
(b) 71
(c) 82
(d) 130
Answer: c
Explaination: (c) 82
27. Mode is the value of the variable which has:
(a) maximum frequency
(b) minimum frequency
(c) mean frequency
(d) middle most frequency [CBSE 2012]
Answer: a
Explaination: (a) maximum frequency.
28. Mode and mean of a data are 12k and 15A. Median of the data is
(a) 12k
(b) 14k
(c) 15k
(d) 16k
Answer: b
Explaination:
(b) ∵ Mode = 3 median – 2 mean
⇒ 12k = 3 median – 2 × 15k
⇒ 42k = 3 median
⇒ Median = 14k.
29. If mean = (3 median – mode) . k, then the value of k is
(a) 1
(b) 2
(C) 12
(d) 32
Answer: c
Explaination:
(c) ∵ Mode = 3 median – 2 mean
⇒ 2 mean = 3 median – mode
⇒ mean = 12 (3 median – mode)
⇒ k= 12
30. The median of set of 9 distinct observations is 20.5. If each of the largest 4 observations of the set is increased by 2, then the median of the new set
(a) is increased by 2
(b) is decreased by 2
(c) is two times of the original number
(d) Remains the same as that of the original set.
Answer: d
Explaination:
(d) No. of observations = 9
∴ median = 5th observation
∵ The largest four observations are increased
∴ 5th observation remains unchanged.
Maths Multiple Choice Questions with Answers for Class 10 Question 31. The median from the table is
| Value | Frequency |
| 7 | 2 |
| 8 | 1 |
| 9 | 4 |
| 10 | 5 |
| 11 | 6 |
| 12 | 1 |
| 13 | 3 |
(a) 11
(b) 10
(c) 12
(d) 11.5
Answer:
Explaination:
32. The relationship between mean, median and mode for a moderately skewed distribution is
(a) mode = median – 2 mean
(b) mode = 3 median – 2 mean
(c) mode = 2 median – 3 mean
(d) mode = median – mean
Answer: b
Explaination: (b) Mode = 3 median – 2 mean
33. The abscissa of the point of intersection
of both types (less than & more than) of cumulative frequency curves help in finding
(a) mean
(b) median
(c) mode
(d) None of these
Answer: b
34. Cumulative frequency curve is also called
(a) histogram
(b) ogive
(c) bar graph
(d) median
Answer: b
35. The A.M. of a set of 50 numbers is 38. If two numbers of the set namely 55 and 45 are discarded, the A.M. of the remaining set of numbers is ______ .
Answer:
Explaination: 37.5
36. If x is the mean of a distribution, then Σfi(xi – x) is eclual t0 _____ .
Answer:
Explaination: (zero)
Maths MCQ for Class 10 CBSE with Answers Pdf Question 37. Find the class marks of classes 10 – 25 and 35 – 55.
Answer:
Explaination:
38. If Σfi = 11, Σfixi = 2p + 52 and the mean of any distribution is 6, find the value of p.
Answer:
Explaination:
39. A set of numbers consists of four 5’s, six 7’s, ten 9’s, eleven 12’s, three 13’s, two 14’s. The mode of this set of numbers is ____ .
Answer:
Explaination: 12
40. The mode of the numbers 2, 3, 4, 4. 3, 5, 3, 6 is ______ .
Answer:
Explaination: 3
41. Find the value of x, if the mode of the following data is 25.
15, 20, 25, 18, 14, 15, 25, 15, 18, 16, 20. 25, 20, x, 18
Answer:
Explaination:
| Observations | Tally Marks | f |
| 14 | 1 | 1 |
| 15 | III | 3 |
| 16 | 1 | 1 |
| 18 | III | 3 |
| 20 | III | 3 |
| 25 | III | 3 |
Observations 15,18,20, and 25 all have the same frequency i.e., 3. For 25 be the mode of the data it should have the maximum frequency.
∴ 25 should repeat itself at least once more i.e., x should be 25.
42. If the mode of a data is 18 and the mean is 24. then median is _____ .
Answer:
Explaination: Median = 663 = 22.
43. Construction of cumulative frequency table is useful in determining the
Answer:
Explaination: Median
Statistics Questions And Answers for Class 10 Question 44. In an arranged series of an even number of 2n terms the median is _______.
Answer:
Explaination: mean of nth term and (n + 1)th term
45.
| x | f | c.f. |
| 1 | 8 | 8 |
| 2 | 10 | 18 |
| 3 | 11 | 29 |
| 4 | 16 | 45 |
| 5 | 20 | 65 |
| 6 | 25 | 90 |
| 7 | 15 | 105 |
| 8 | 9 | 114 |
| 9 | 6 | 120 |
Find the median distribution.
Answer:
Explaination:
n = 120
⇒ n2 = 60
∴ Median is average of 60th and 61st observation
⇒ Median =5+52 = 5
46.
| Marks | Number of students |
| 0 and above | 80 |
| 10 and above | 77 |
| 20 and above | 72 |
| 30 and above | 65 |
| 40 and above | 55 |
| 50 and above | 43 |
| 60 and above | 28 |
| 70 and above | 16 |
| 80 and above | 10 |
| 90 and above | 8 |
| 100 and above | 0 |
Write the proper data (marks) and frequency (Number of students).
Answer:
Explaination:
| Marks | Frequency |
| 0 – 10 | 3 |
| 10 – 20 | 5 |
| 20 – 30 | 7 |
| 30 – 40 | 10 |
| 40 – 50 | 12 |
| 50 – 60 | 15 |
| 60 – 70 | 12 |
| 70 – 80 | 6 |
| 80 – 90 | 2 |
| 90 – 100 | 8 |
47. Find the median class of the following data:
| Marks obtained | Frequency |
| 0-10 | 8 |
| 10-20 | 10 |
| 20-30 | 12 |
| 30-40 | 22 |
| 40-50 | 30 |
| 50-60 | 18 |
Answer:
Explaination:
48. There are ____ types of cumulative frequency curve.
Answer:
Explaination: two
49. Which measure of central tendency is given by the x-coordinate of the point of intersection of the “more than ogive” and “less than ogive”?
Answer:
Explaination: Median
50. In drawing ogive, cumulative frequencies are marked on _____ axis.
Answer:
Explaination: y
51. Which measure of central tendency is given by the x-coordinate of the point of intersection of “more than ogive”.and “less than ogive”?
Answer:
Explaination: Median
We hope the given MCQ Questions for Class 10 Maths Statistics with Answers will help you. If you have any query regarding CBSE Class 10 Maths Chapter 14 Statistics Multiple Choice Questions with Answers, drop a comment below and we will get back to you at the earliest.
Free PDF Download of CBSE Class 10 Maths Chapter 13 Surface Areas and Volumes Multiple Choice Questions with Answers. MCQ Questions for Class 10 Maths with Answers was Prepared Based on Latest Exam Pattern. Students can solve NCERT Class 10 Maths Surface Areas and Volumes MCQs with Answers to know their preparation level.
MCQ On Surface Area And Volume Class 10 Question 1. A cylindrical pencil sharpened at one edge is the combination of
(a) two cylinders
(b) a hemisphere and a cylinder
(c) a cone and a cylinder
(d) frustum of a cone and a cylinder
Answer: c
Question 2. A shuttlecock used for playing badminton has the shape of the combination of
(a) a cylinder and a sphere
(b) a sphere and a cone
(c) a cylinder and a hemisphere
(d) frustum of a cone and a hemisphere
Answer: d
MCQ Questions On Surface Area And Volume 10th NCERT Question 3. The slant height of the frustum of a cone having radii of two ends as 5 cm and 2 cm respectively and height 4 cm is
(a) √26 cm
(b) 5 cm
(c) √65 cm
(d) 25 cm
Answer: b
Explaination:
Surface Area And Volume Class 10 MCQ Question 4. The total surface area of a hemispherical solid having radius 7 cm is
(a) 462 cm²
(b) 294 cm²
(c) 588 cm²
(d) 154 cm²
Answer: a
Explaination: Reason: Total surface area of hemisphere = 3πr² = 3 × 227 × 7 × 7 = 462 cm²
MCQ Of Surface Area And Volume Class 10 Question 5. A solid formed on revolving a right angled triangle about its height is
(a) cylinder
(b) sphere
(c) right circular cone
(d) two cones
Answer: c
Explaination: Reason: Right circular cone is formed.
Surface Area And Volume MCQ Questions Question 6. The surface area of a sphere is 616 cm2. Its radius is
(a) 7 cm
(b) 14 cm
(c) 21 cm
(d) 28 cm
Answer: a
Explaination:
Multiple Choice Questions On Surface Area And Volume Question 7. A cylinder and a cone are of same base radius and of same height. The ratio of the volume of the cylinder to that of the cone is
(a) 2 : 1
(b) 3 : 1
(c) 2 : 3
(d) 3 : 2
Answer: b
Explaination:
Volume And Surface Area Multiple Choice Questions Question 8. The volume of a sphere is 4851 cm3. Its diameter is
(a) 3.5 cm
(b) 7 cm
(c) 14 cm
(d) 21 cm
Answer: d
Explaination:
Surface Area And Volume Class 10 MCQ Question 9. A piece of paper is in the shape of a semi¬circular region of radius 10 cm. It is rolled to form a right circular cone. The slant height is
(a) 5 cm
(b) 10 cm
(c) 15 cm
(d) 20 cm
Answer: b
Explaination: Reason: Slant height l = r
MCQs On Surface Area And Volume Question 10. The base radii of two circular cones of the same height are in the ratio 3 : 5. The ratio of their volumes are
(a) 9 : 25
(b) 5 : 3
(c) 9 : 5
(d) 3 : 25
Answer: a
Explaination:
Surface Area And Volume Multiple Choice Questions Question 11. The curved surface area of glass having radii 3 cm and 4 cm respectively and slant height 10 cm is
(a) 55 cm²
(b) 110 cm²
(c) 220 cm²
(d) 440 cm²
Answer: c
Explaination: Reason: Here r = 3 cm, R = 4 cm, l = 10 cm
∴ Curved surface area = πl(r + R) = 227 × 10(3 + 4)=227 × 10 × 7 = 220 cm²
MCQ On Surface Area And Volume Question 12. If two solid hemispheres of same base radius are joined together along their bases, then curved surface area of this new solid is
(a) 3πr²
(b) 4πr²
(c) 5πr²
(d) 6πr²
Answer: b
13. The radii of the top and bottom of a bucket of slant height 13 cm are 9 cm and 4 cm respectively. The height of the bucket is
(a) 10 cm
(b) 12 cm
(c) 15 cm
(d) 16 cm
Answer: b
Explaination: l² = h² + (R-r)² => 13² = h² + (9 – 4)²
⇒ 169 = h² + 25
⇒ h² = 169 – 25
⇒ h² = 144
⇒ h = 12
14. A surahi is the combination of [NCERT Exemplar Problems]
(a) a sphere and a cylinder
(b) a hemisphere and a cylinder
(c) two hemispheres
(d) a cylinder and a cone
Answer: a
Explaination: (a) A sphere and a cylinder.
15. Match the column :
(a) 1 → A, 2 → C, 3 → D, 4 → E
(b) 1 → F, 2 → B, 3 → C, 4 → E
(c) 1 → B, 2 → C, 3 → D, 4 → E
(d) 1 → F, 2 → E, 3 → C, 4 → A
Answer: b
Explaination: (b) Formulae.
MCQ Questions For Class 10 Maths Surface Area And Volume Question 16. A cube whose edge is 20 cm long, has circles on each of its faces painted black. What is the total area of the unpainted surface of the cube if the circles are of the largest possible areas?
(a) 90.72 cm²
(b) 256.72 cm²
(c) 330.3 cm²
(d) 514.28 cm²
Answer: d
Explanation:
(d) Diameter of largest circle = 20 cm.
∴ Area of circle = 100π cm²
∴ Area of 6 circles = 6 × 100π = 600π cm² (∵ there are six faces in a cube)
Also, Area of cube = 6 × (20)² = 2400 cm²
Area of unpainted surface = 2400 – 600π
= 2400 – 600 × 227
= 514.28 cm².
17. If two solid hemispheres of the same base radius r are joined together along their bases, then curved surface area of this new solid is [NCERT Exemplar Problems]
(a) 4πr²
(b) 6πr²
(c) 3πr²
(d) 8πr²
Answer: a
Explanation: (a) 4πr²
18. The radius (in cm) of the largest right circular cone that can be cut out from a cube of edge 4.2 cm is [AI2011]
(a) 4.2
(b) 2.1
(c) 8.1
(d) 1.05
Answer: b
Explaination:
(b) Edge of the cube = 4.2 cm
Diameter of base of largest possible cone = 4.2 cm 4 2
∴ Radius = 4.22 = 2.1 cm
19. How many bags of grain can be stored in a cuboid granary 12 m × 6 m × 5 m. If each bag occupies a space of 0.48 m3?
(a) 750
(b) 75
(c) 1500
(d) 375
Answer: a
Explaination:
20. In a swimming pool measuring 90 m × 40 m, 150 men take a dip. If the average displacement of water by a man is 8 m3, then rise in water level is
(a) 27.33 cm
(b) 30 cm
(c) 31.33 cm
(d) 33.33 cm
Answer: d
Explaination:
(d) Volume of water displaced
= 150 × 8 = 1200 m3
⇒ 90 × 40 × h = 1200
⇒ h = 120090×40 m = 33.33 cm
MCQ Questions on Surface Area and Volume 10th NCERT Question 21. Match the column:
(a) 1 → C, 2 → A, 3 → D, 4 → F
(b) 1 → C, 2 → A, 3 → D, 4 → E
(c) 1 → C, 2 → B, 3 → D, 4 → F
(d) 1 → C, 2 → A, 3 → F, 4 → D
Answer: c
Explaination: (c) Formulae.
22. Given that 1 cu. cm of marble weighs 25 g, the weight of a marble block of 28 cm in width and 5 cm thick, is 112 kg. The length of the block is
(a) 36 cm
(b) 37.5 cm
(c) 32 cm
(d) 26.5 cm
Answer: c
Explaination:
23. A sphere and a cube have equal surface areas. The ratio of the volume of the sphere to that of cube is
Answer: b
Explaination:
Surface Area and Volume MCQ Question 24. A sphere of diameter 18 cm is dropped into a cylindrical vessel of diameter 36 cm, partly filled with water. If the sphere is completely submerged, then the water level rises (in cm) by [Delhi 2011]
(a) 3
(b) 4
(c) 5
(d) 6
Answer: a
Explaination:
25. The shape of a gilli, in the gilli-danda game (see Fig.), is a combination of [NCERT Exemplar Problems]
(a) two cylinders
(b) a cone and a cylinder
(c) two cones and a cylinder
(d) two cylinders and a cone
Answer: c
Explaination: (c) Two cones and a cylinder.
26. A right circular cylinder of radius r cm and height h cm (h > 2r) just encloses a sphere of diameter [NCERT Exemplar Problems]
(a) r cm
(b) 2r cm
(c) h cm
(d) 2h cm
Answer: b
Explaination: (b) 2r cm.
Surface Area and Volume Class 10 MCQ Question 27. During conversion of a solid from one shape to another, the volume of the new shape will [NCERT Exemplar Problems]
(a) increase
(B) decrease
(c) remain unaltered
(d) be doubled
Answer: c
Explaination: (c) Remain unaltered.
28. A rectangular block 6 cm × 12 cm × 15 cm is cut into exact number of equal cubes. The least possible number of cubes will be
(a) 6
(b) 11
(c) 33
(d) 40
Answer: d
Explaination:
(d) Volume of rectangular block = 6 × 12 × 15 = 1080 cm3
Side of largest cube = HCF of 6, 12, 15
= 3
∴ Volume of 1 cube = 33 = 27 cm3
Number of cubes = 6×12×1527 = 40
29. Ariver 1.5 m deep and 36 m wide is flowing at the rate of 3.5 km per hour. The amount of water that runs into the sea per minute (in cubic metres) is
(a) 31500
(b) 3150
(c) 3150000
(d) 6300
Answer:
Explaination:
30. The number of coins, 1.5 cm in diameter and 0.2 cm thick to be melted to form a right circular cylinder of height 10 cm and diameter 4.5 cm is
(a) 350
(b) 400
(c) 450
(d) 500
Answer: c
Explaination:
31. The shape of a glass (tumbler) (see Fig.) is usually in the form of [NCERT Exemplar Problems]
(a) A cone
(b) frustum of a cone
(c) a cylinder
(d) a sphere
Answer: b
Explaination: (b) Frustum of a cone.
32. A shuttle cock used for playing badminton has the shape of the combination of [NCERT Exemplar Problems]
(a) a cylinder and a sphere
(b) a cylinder and a hemisphere
(c) a sphere and a cone
(d) frustum of a cone and a hemisphere
Answer: d
Explaination: (d) Frustum of a cone and a hemisphere.
33. A cone is cut through a plane parallel to its base and then the cone that is formed on one side of that plane is removed. The new part that is left over on the other side of the plane is called [NCERT Exemplar Problems]
(a) a frustum of a cone
(b) cone
(c) cylinder
(d) sphere
Answer: a
Explaination: (a) Frustum of a cone.
Multiple Choice Questions on Surface Area and Volume Question 34. In a right circular cone, the cross-section made by a plane parallel to the base is a [NCERT Exemplar Problems]
(a) circle
(b) frustum of a cone
(c) sphere
(d) hemisphere
Answer: a
Explaination: (a) Circle.
35. A solid is hemispherical at the bottom and
conical (of same radius) above it. If the surface areas of the two parts are equal, then the ratio of its radius and the slant height of the conical part is ____ . [Foreign 2011]
Answer:
Explaination:
C.S.A of conical part = C.S.A. of spherical part
πrl = 2πr²
l = 2r
⇒ 12 = rl
⇒ r : l = 1 : 2
36. Two cubes each with 6 cm edge are joined end to end. The surface area of the resulting cuboid is ____ .
Answer:
Explanation:
[360 cm²]
Hint: Length of resulting cuboid = 12 cm.
Width = 6 cm, height = 6 cm.
∴ Surface area
= 2(12 × 6 +12 × 6 + 6 × 6)
= 2(180) = 360 cm².
37. A solid cylinder of radius r and height h is placed over other cylinders of same height and radius. The total surface area of the shape so formed is 4nrh + 4rcr2. [True/False] [NCERT Exemplar Problems]
Answer:
Explaination:
38. A cube of side 4 cm is cut into cubes of side 1 cm, then total surface area of all the small cubes is ______ .
Answer:
Explaination:
384 cm²
Volume of bigger cube = 4 × 4 × 4 = 64 cm3
Volume of one smaller cube = 1 × 1 × 1 = 1 cm3
Number of smaller cubes = 641 = 64
Surface area of one smaller cube = 6 × 1²
= 6 cm²
∴ Total surface area = 6 × 64 = 384 cm²
39. The ratio of the volume of a cube to that of a sphere which will fit inside the cube is ____ .
Answer:
Explaination:
[6 : π] Hint:
Let side of cube = x
Volume of cube = x3
Diameter of sphere = x
40. A cube of side 6 cm is cut into a number of cubes, each of side 2 cm. The number of cubes will be ______ .
Answer:
Explaination: 27
MCQ on Surface Area and Volume Question 41. Two cubes have their volumes in the ratio 1 : 27. Find the ratio of their surface areas. [CBSE 2018 (C)]
Answer:
Explaination:
42. A conical military tent having diameter of the base 24 m and slant height of the tent is 13 m, find the curved surface area of the cone. [π = 227]
Answer:
Explaination:
43. Volume and surface area of a solid hemisphere are numerically equal. What is the diameter of hemisphere? [Delhi 2017]
Answer:
Explaination:
44. A joker’s cap is in the form of a right circular cone of base radius 7 cm and the slant height is 25 cm. Find the area of the cap. [π = 227]
Answer:
Explaination:
Base radius of Joker’s cap = 7 cm;
slant height = 25 cm
Curved surface area = πrl = 227 × 7 × 25
= 550 cm²
45. A cylinder and a cone are of same base radius and of same height. Find the ratio of the volume of cylinder to that of the cone.
Answer:
Explaination:
Surface Area and Volume Multiple Choice Question 46. Two cylindrical cans have equal base areas. If one of the can is 15 cm high and other is 20 cm high, find the ratio of their volumes.
Answer:
Explaination:
47. A sphere of maximum volume is cut out from a solid hemisphere of radius 7 cm. What is the ratio of the volume of the hemisphere to that of the cut out sphere?
Answer:
Explaination:
48. Three cubes of iron whose edges are 6 cm, 8 cm and 10 cm respectively are melted and formed into a single cube. The edge of the new cube formed is ____ .
Answer:
Explaination:
12 cm
Hint: 63 + 83 + 103 = l3
⇒ 216 + 512+ 1000 = l3
⇒ 1728 = l3
⇒ l = 12 cm.
49. A metal sheet 27 cm long, 8 cm broad and 1 cm thick is melted into a cube. The difference between surface areas of two solids is ____ .
Answer:
Explaination:
[286 cm²]
Hint: Surface area of the metal sheet
= 2 [27 × 8 + 8 × 1 +27 × 1]
= 2[216 + 35] = 502 cm²
Since this sheet is melted to form a cube, therefore,
Volume of cube = Volume of cuboid metal sheet
⇒ side3 = 27 × 8 × 1 cm3
∴ side = 27×8×1−−−−−−−−√3 = 6 cm
∴ Surface area = 6 x 6² = 216 cm²
Difference = 502 – 216 = 286 cm².
50. A copper sphere of radius 3 cm is beaten and drawn into a wire of diameter 0.2 cm. The length of the wire is ___ .
Answer:
Explaination: 36 m
51. The dimensions of a metallic cuboid are 100 cm x 80 cm * 64 cm. It is melted and recast into a cube. Find the surface area of the cube.
Answer:
Explaination:
Dimensions of the metallic cuboid are
100 cm × 80 cm × 64 cm
100 × 80 × 64 = a3 (where a = side of cube)
⇒ 10 × 2 × 4 = a
⇒ a = 80cm
Surface area of the cube = 6a² = 6(80)²
= 6 × 80 × 80 = 38400 cm²
52. The slant height of the frustum of a cone is 5 cm. If the difference between the radii of its two circular ends is 4 cm, write the height of the frustum.
Answer:
Explaination:
53. A farmer wants to dig a well either in the form of a cuboid of dimension 1 m × 1 m and depth 7 m or in the form of a cylinder of diameter 1 m and depth 7 m. The rate of digging the well is ₹ 500/m3. Find the cost to dig both the wells [π = 227]
Answer:
Explaination:
We hope the given MCQ Questions for Class 10 Maths Surface Areas and Volumes with Answers will help you. If you have any query regarding CBSE Class 10 Maths Chapter 13 Surface Areas and Volumes Multiple Choice Questions with Answers, drop a comment below and we will get back to you at the earliest.
Free PDF Download of CBSE Class 10 Maths Chapter 12 Areas Related to Circles Multiple Choice Questions with Answers. MCQ Questions for Class 10 Maths with Answers was Prepared Based on Latest Exam Pattern. Students can solve NCERT Class 10 Maths Areas Related to Circles MCQs with Answers to know their preparation level.
Circle Multiple Choice Question 1. The area of the circle is 154 cm2. The radius of the circle is
(a) 7 cm
(b) 14 cm
(c) 3.5 cm
d) 17.5 cm
Areas Related To Circles Class 10 MCQ With Answer: dExplaination: Reason: Area of circle = 154 cm²
⇒ nr² = 154 cm2
⇒ 227 × r² = 154
⇒ r² = 154 × 227
⇒ r² = 7 × 7 = 49
∴ r = √49 = 7
2. If angle of sector is 60°, radius is 3.5 cm then length of the arc is
(a) 3 cm
(b) 3.5 cm
(c) 3.66 cm
(d) 3.8 cm
Answer: c
Explaination: Reason: Here r = 3.5 cm = 3510 = 72 cm θ = 60°
Length of arc = θ360 × 2πr = 60360 × 2 × 227 = × 72 × 16 × 22 = Undefined control sequence \3 = 3.66 cm
Areas Related To Circles MCQs Question 3. The area of a quadrant of a circle whose circumference is 22 cm, is
Answer: d
Explaination: Reason: Here 2πr = 22 cm
2 × 227 × r = 22
⇒ r = 22 × 722 × 12 = 72 cm
∴ Area of quadrant of circle = 14πr² = 14 × 227 × 72 × 72 = 778 cm²
4. If 0 is the angle in degrees of a sector of a circle of radius V, then area of the sector is
Answer: b
5. A horse is tied to a peg at one corner of a square shaped grass field of side 15 m by means of a 7 m long rope. The area of that part of the field in which the horse can graze, is
(a) 77 cm²
(b) 772 cm²
(c) 154 cm²
(d) 774 cm²
MCQ on Areas Related To Circles With Answer: b
Explaination:
6. The area of the circle whose diameter is 21 cm is
(a) 346.5 cm²
(b) 37.68 cm²
(c) 18.84 cm²
(d) 19.84 cm²
Answer: a
Explaination: Reason: Here diameter = 21 cm
∴ Radius r = 212 cm
Area of the circle, A = πr²
∴ A=227×212×212=11×3×212=6932=346.5cm2
7. The area of the sector of a circle with radius 6 cm and of angle 60° is
(a) 9.42 cm²
(b) 37.68 cm²
(c) 18.84 cm²
(d) 19.84 cm²
Answer: c
Explaination: Reason: Here r = 6 cm, θ = 60°
Area of the sector = θ360
∴ Area = 60360 × 3.14 × 6 × 6 = 16 × 3.14 × 6 × 6 = 3.14 × 6 = 18.84 cm²
8. The area of a circle whose circumference is 22 cm, is
(a) 11 cm²
(b) 38.5 cm²
(c) 22 cm²
(d) 77 cm²
Answer: b
Explaination:
9. The area of a circle is 154 cm2. Its diameter is
(a) 7 cm
(b) 14 cm
(c) 21 cm
(d) 28 cm
Answer: b
Explaination: Reason: Here area of the circle, A = 154 cm², Radius, r = ?
Area of the circle = 154 cm² …(Given)
∴ πr² = 154
⇒ 227 × r² = 154
⇒ r² = 154 × latex]\frac{7}{22}[/latex] = 7 × 7
⇒ r = 7 cm
∴ Diameter of the circle = 2 × r = 2 × 7 = 14 cm
10. The length of the minute hand of a clock is 14 cm. The area swept by the minute hand in 5 minutes is
(a) 153.9 cm²
(b) 102.6 cm²
(c) 51.3 cm²
(d) 205.2 cm²
Answer: c
Explaination: Reason: Angle swept by the minute hand in 1 minute = (360° ÷ 60) = 6°
∴ θ = 30°
∴ Angle swept by the minute hand in 5 minutes = 6° × 5 = 30°
Length of minute hand (r) = 14 cm
∴ Area swept = θ360πr² = 30360 × 227 × 14 × 14 = 1543 = 51.3 cm²
MCQ Questions For Class 10 Maths Areas Related To Circles Question 11. The radii of two circles are 19 cm and 9 cm respectively. The radius of the circle which has circumference equal to the sum of the circumference of two circles is
(a) 35 cm
(b) 10 cm
(c) 21 cm
(d) 28 cm
Answer: d
Explaination: Reason: Let the radii of two circles be r1 and r2 and the radius of large circle be r.
∴ r1 = 19 cm, r2 = 9 cm
Circumference of two circles = C1+ C2 …(where C = circle)
= 2πr1 + 2πr2 = 2π × 19 + 2π × 9 = 38π + 18π = 56π
∴ Circumference of large circle = 56π
⇒ 2πr = 56π
⇒ r = 28
∴ Radius of large circle = 28 cm
12. The area of the circle that can be inscribed in a square of side 6 cm, is
(a) 18π cm²
(b) 12π cm²
(c) 9π cm²
(d) 14π cm²
Answer: c
Explaination: Reason: Size of square = 6 cm, radius = 62 = 3 cm;
Area of the circle = πr² = π × 3 × 3 = 9π cm²
13. The radii of two circles are 4 cm and 3 cm respectively. The diameter of the circle having area equal to the sum of the areas of the two circles (in cm) is [Delhi 2011]
(a) 5
(b) 7
(c) 10
(d) 14
Answer: c
Explaination:
MCQ on Area Related To Circles Class 10 Question 14. The perimeter (in cm) of a square circumscribing a circle of radius a cm, is [AI2011]
(a) 8 a
(b) 4 a
(c) 2 a
(d) 16 a
Answer: a
Explaination:
(a) Side of a square circumscribing a circle of radius a cm = diameter of circle = 2 a cm
∴ Perimeter of the square
= 4 × 2a = 8a cm
15. If the area of a circle is numerically equal to twice its circumference, then the diameter of the circle is
(a) 4 units
(b) n units
(c) 8 units
(d) 2 units
Answer: c
Explaination:
(c) πr² = 2πr × 2
⇒ r = 4
⇒ 2r = 8 units
16. If the circumference of a circle is 352 metres, then its area in square metres is
(a) 5986
(b) 6589
(c) 7952
(d) 9856
Answer: d
Explaination:
Area Related To Circle Class 10 MCQ Question 17. The diameter of a wheel is 1.26 m. The distance travelled in 500 revolutions is
(a) 2670 m
(b) 2880 m
(c) 1980 m
(d) 1596 m
Answer: c
Explaination:
(c) Radius of the wheel = 1.262 = 0.63 m
Distance travelled in one revolution
= 2πr = 2 × 227 × 0.63
= 3.96 m
∴ Distance travelled in 500 revolutions
= 500 × 3.96
= 1980 m.
18. If the sum of the circumferences of two circles with radii Rj and R2 is equal to the circumference of a circle of radius R, then [NCERT Exemplar Problems]
(a) R1 + R2 = R
(b) R1 + R2 > R
(C) R1 + R2 < R
(d) nothing definite can be said about the relation among Rp1, R2 and R.
Answer: a
Explaination:
(a) 2πR1 + 2πR2 = 2πR
⇒ R1 + R2 = R.
19. If the circumference of a circle and the perimeter of a square are equal, then [NCERT Exemplar Problems]
(a) area of the circle = area of the square
(b) area of the circle > area of the square
(c) area of the circle < area of the square
(d) nothing definite can be said about the relation between the areas of the circle and square.
Answer: b
Explaination:
(b) Let circumference of a circle = C
2πr = C C
⇒ r = C2π
Perimeter of a square = C
⇒ 4a = C
⇒ a = C4
MCQ on Area Related To Circles Question 20. Area of the largest triangle that can be inscribed in a semi-circle of radius r units is [NCERT Exemplar Problems]
(a) r² sq. units
(b) 12 r² sq. units
(c) 2 r² sq. units
(d) √2 r² sq. units
Answer: a
Explaination:
21. Match the columns
(a) 1 → A, 2 → C, 3 → D, 4 → E
(b) 1 → B, 2 → C, 3 → F, 4 → E
(c) 1 → D, 2 → B, 3 → A, 4 → F
(d) 1 → D, 2 → B, 3 → E, 4 → F
Answer: c
Explaination: (c) Formulae
22. In the given figure, three sectors of a circle of radius 7 cm, making angles of 60°, 80° and 40° at the centre are shaded. The area of the shaded region (in cm2) is [Using π = 227] [Foreign 2012]
(a) 77
(b) 154
(c) 44
(d) 22
Answer: a
Explaination:
(a) Area of shaded region = area of sector with angle
(60° + 80° + 40°) = 180∘360∘×227×7×7
= 77 cm²
Areas Related To Circles Question 23. If the difference between the and the radius of of a circle is 37 cm, then 22 using π = 227 the circumference (in cm) of the circle is: [Delhi 2013]
(a) 154
(b) 44
(c) 14
(d) 7
Answer: b
Explaination:
24. If 7i is taken as 227, the distance (in metres) covered by a wheel of diameter 35 cm, in one revolution, is [AI2013]
(a) 2.2
(b) 1.1
(c) 9.625
(d) 96.25
Answer: b
Explaination:
(b) Distance covered by a wheel in one
revolution = 2 πr = 2 × 227 × 352
= 110 cm = 1.1 m
Circle MCQ Pdf Question 25. If the circumferences of two circles are in the ratio 4 : 9, then the ratio in their area is
(a) 9 : 4
(b) 4 : 9
(c) 2 : 3
(d) 16 : 81
Answer: d
Explaination:
26. The ratio of the areas of the incircle and circumcircle of a square is
(a) 1 : 2
(b) 1 : 3
(c) 1 : 4
(d) 1 : √2
Answer: a
Explaination:
(a) Let side of square = x units
∴ Diagonal of the square = √2 x units
Diameter of the incircle = x units
Diameter of the circumcircle = √2 x units
27. A circular wire of radius 42 cm is cut and bent into the form of a rectangle whose sides are in the ratio of 6 : 5. The smaller side of the rectangle is
(a) 30 cm
(b) 60 cm
(c) 70 cm
(d) 80 cm
Answer: b
Explaination:
(b) Length of wire = 2πrr = 2πr × 42
= 2 × 227 × 42 = 264 cm
Let sides of rectangle are 6x and 5x
⇒ 2(6x + 5x) = 264
⇒ 11x = 132
⇒ x = 12
∴ Smaller side = 12 × 5 = 60 cm
28. Match the columns.
(a) 1 → B, 2 → C, 3 → D, E → 4
(b) 1 → B, 2 → D, 3 → C, E → 4
(c) 1 → A, 2 → C, 3 → D, E → 4
(d) 1 → B, 2 → C, 3 → D, E → 4
Answer: b
Explaination: (b) Formulae
29. ABC is an equilateral triangle. The area of the shaded region if the radius of each of the circle is 1 cm, is
Answer: c
Explaination:
30. ABCDEF is any hexagon with different vertices A, B, C, D, E and F as the centres of circles with same radius r are drawn. The area of the shaded portion is
(a) πr²
(b) 2πr²
(c) 3πr²
(d) 4πr²
Answer: b
Explaination:
31. In the figure, PQRS is a square and O is centre of the circle. If RS = 10 √2, then area of shaded region is
(a) 90 π – 90
(b) 80 π – 80
(c) 50 π-100
(d) 100 π – 100
Answer: c
Explaination:
(c) Diagonal of square = √2 × (10√2) = 20 units
∴ Diameter of circle = 20 units
Area of circle = π × (10)² = 100π sq.units
Area of square = (10√2)² = 200 sq. units
Area of circle not included in the square = (100π – 200) sq.units
∴ Area of shaded portion = 12(100π – 200)
= 50π – 100.
32. The diameter of the wheel of a bus is 1.4 m. The wheel makes 10 revolutions in 5 seconds. The speed of the vehicle (in kmph) is ______ .
Answer:
Explaination:
33. The area of a quadrant of a circle whose circumference is 44 cm is ______ .
Answer:
Explaination:
34. If the wheel of an engine of a train is 427m in circumference makes seven revolutions in 4 seconds, then the speed of the train is _____ km/h.
Answer:
Explaination:
35. The area of the largest possible square inscribed in a circle of unit radius (in sq. units) is ______.
Answer:
Explaination:
2 units
Hints: Diameter of circle = 2 units
∴ Diagonal of the square = 2 units
Side of the square = 22√ = √2 units
∴ Area of the square = (√2)² = 2 sq. units
36. In the fig., O is the centre of a circle. The area of sector OAPB is 518 of the area of the circle. Find x.
Answer:
Explaination:
37. Find the perimeter of the given figure, where AEDˆ is a semicircle and ABCD is a rectangle.
Answer:
Explaination:
Length of AEDˆ = πr
= π x 7 cm = 7π cm
AB + BC + DC = 20 + 14 + 20 = 54 cm
∴ Perimeter of figure = (7π + 54) cm
38. A bicycle wheel makes 5000 revolutions in moving 11 km. Find the diameter of the wheel. (use π = 227)
Answer:
Explaination:
39. A pendulum swings through an angle of 30° and describes an arc 8.8 cm in length. Find the length of pendulum, (use π = 227)
Answer:
Explaination:
40. An arc of a circle is of length 5TI cm and the sector it bounds has an area of 20π cm². Find the radius of the circle.
Answer:
Explaination:
41. If the diameter of a semicircular protractor is 14 cm, then find its perimeter. [π = 227]
Answer:
Explaination:
42. Find the perimeter of the shaded region in figure, if ABCD is a square of side 14 cm and APB and CPD are semicircles. [Use π = 227]
Answer:
Explaination:
Perimeter = AD + BC + length of DPC + length of APB
= 14 + 14 + πr + πr
= 28 + 2 × 227 × 142= 72 cm
We hope the given MCQ Questions for Class 10 Maths Areas Related to Circles with Answers will help you. If you have any query regarding CBSE Class 10 Maths Chapter 12 Areas Related to Circles Multiple Choice Questions with Answers, drop a comment below and we will get back to you at the earliest.
Free PDF Download of CBSE Class 10 Maths Chapter 11 Geometrical Constructions Multiple Choice Questions with Answers. MCQ Questions for Class 10 Maths with Answers was Prepared Based on Latest Exam Pattern. Students can solve NCERT Class 10 Maths Geometrical Constructions MCQs with Answers to know their preparation level.
Construction Class 10 MCQ Question 1. To divide a line segment PQ in the ratio 5 : 7, first a ray PX is drawn so that ∠QPX is an acute angle and then at equal distances points are marked on the ray PX such that the minimum number of these points is
(a) 5
(b) 7
(c) 12
(d) 10
Answer: c
Constructions Maths Question 2. To divide a line segment AB in the ratio 4 : 7, a ray AX is drawn first such that ∠BAX is an acute angle and then points A1 A2 A3, … are located at equal distances on the ray AX and the point B is joined to
(a) A4
(b) A11
(c) A10
(d) A7
Class 10 Maths MCQ Questions with Answer: b
Construction 10 Class Question 3. To draw a pair of tangents to a circle which are inclined to each other at an angle of 35°, it is required to draw tangents at the end-points of those two radii of the circle, the angle between which is
(a) 145°
(b) 130°
(c) 135°
(d) 90°
Answer: a
Construction Class 10 Question 4. When a line segment is divided in the ratio 2 : 3, how many parts is it divided into?
(a) 23
(b) 2
(c) 3
(d) 5
Answer: d
We hope the given MCQ Questions for Class 10 Maths Geometrical Constructions with Answers will help you. If you have any query regarding CBSE Class 10 Maths Chapter 11 Geometrical Constructions Multiple Choice Questions with Answers, drop a comment below and we will get back to you at the earliest.
Free PDF Download of CBSE Class 10 Maths Chapter 10 Circles Multiple Choice Questions with Answers. MCQ Questions for Class 10 Maths with Answers was Prepared Based on Latest Exam Pattern. Students can solve NCERT Class 10 Maths Circles MCQs with Answers to know their preparation level.
Circle Multiple Choice Question 1. The distance between two parallel tangents of acircle of radius 4 cm is
(a) 2 cm
(b) 4 cm
(c) 6 cm
(d) 8 cm
Answer: d
Explaination:
Reason: Here radius, r = 4 cm
Required distance,
AB = OA + OB
= r + r = 2r = 2×4 = 8 cm
2. In the given figure, if ZRPS = 25°, the value of ZROS is
(a) 135°
(b) 145°
(c) 165°
(d) 155°
Circles Class 10 MCQ With Answer: dExplaination: Reason: Since OR ⊥ PR and OS ⊥ PS
∴ ∠ORP = ∠OSP = 90°
In □ ORPS, ∠ROS + ∠ORP + ∠RPS + ∠OSP = 360°
∠ROS + 90° + 25° + 90° = 360°
∠ROS = 360° – 205° = 155°
3. A tangent is drawn from a point at a distance of 17 cm of circle C(0, r) of radius 8 cm. The length of its tangent is
(a) 5 cm
(b) 9 cm
(c) 15 cm
(d) 23 cm
Answer: c
Explaination:
Reason: In rt ∆OAP, AP² + OA² = OP²
⇒ AP² + (8)² = (17)² => AP² + 64 = 289
⇒ AP² = 289 – 64 = 225
∴ AP = √225 = 15 cm
4. The length of tangents drawn from an external point to the circle
(a) are equal
(b) are not equal
(c) sometimes are equal
(d) are not defined
Answer: a
Explaination: Reason: Since the length of tangents drawn from an external point to a circle are equal.
5. Number of tangents drawn at a point of the , circle is/are
(a) one
(b) two
(c) none
(d) infinite
Answer: a
Explaination: Reason: There is only one tangent at a point of the circle.
6. The tangents drawn at the extremities of the diameter of a circle are
(a) perpendicular
(b) parallel
(c) equal
(d) none of these
Answer: b
Explaination:
Reason: Since OP ⊥ AB and OQ ⊥ CD
∴ Z1 = 90° and Z2 = 90°
⇒ ∠1 = Z2, which are alternate angles.
∴ AB || CD
7. Tangents from an external point to a circle are
(a) equal
(b) not equal
(c) parallel
(d) perpendicular
MCQs of Maths for Class 10 With Answer: aExplaination: Reason: Tangents from external points to a circle are equal.
8. The length of a tangent drawn from a point at a distance of 10 cm of circle is 8 cm. The radius of the circle is
(a) 4 cm
(b) 5 cm
(c) 6 cm
(d) 7 cm
Answer: c
Explaination:
Reason: In rt. AOAP, we have
OA² + AP² = OP²
⇒ OA² + (8)² = (10)2
⇒ OA² + 64 = 100
⇒ OA² = 100 – 64 = 36
∴ OA = √36 = 6 cm
MCQ Questions on Circles for Class 10 Question 9. In given figure, CP and CQ are tangents to a circle with centre O. ARB is another tangent touching the circle at R. If CP = 11 cm and BC = 6 cm then the length of BR is
(a) 6 cm
(b) 5 cm
(c) 4 cm
(d) 3 cm
Answer: b
Explaination: Reason: Since
BQ = BR …(i) [∵ Tangents drawn from external points are equal]
CQ = CP …[Using (i)]
BC + BQ = 11
⇒ 6 + BR = 11
⇒ BR = 11 – 6 = 5 cm
10. From a point P which is at a distance of 13 cm from the centre O of a circle of radius 5 cm, the pair of tangents PQ and PR to the circle are drawn. Then the area of the quadrilateral PQOR is
(a) 60 cm²
(b) 65 cm²
(c) 30 cm²
(d) 32.5 cm²
Answer: a
Explaination:
Reason: OP² = OQ² + PQ²
169 = 25 + PQ²
PQ² = 144
PQ = 12
Area PQOR = ar (AOPQ) + ar (AOPR)
= 12 × 12 × 5 + 12 × 12 × 5 = 60 cm²
MCQ Questions for Class 10 Maths Question 11. In the given figure, AB and AC are tangents to the circle with centre O such that ∠BAC = 40°, then ∠BOC is equal to [AI2011]
(a) 40°
(b) 50°
(c) 140°
(d) 150°
Answer: c
Explaination:
(c) In quadrilateral ABOC
∠ABO + ∠BOC + ∠OCA + ∠BAC = 360°
⇒ 90° + ∠BOC + 90° + 40° = 360°
⇒ ∠BOC = 360° – 220° = 140°
12. In the given figure, point P is 26 cm away from the centre O of a circle and the length PT of the tangent drawn from P to the circle is 24 cm. Then the radius of the circle is [Foreign 2011]
(a) 25 cm
(b) 26 cm
(c) 24 cm
(d) 10 cm
Answer: d
Explaination: (d) v OT is radius and PT is tangent
∴ OT ⊥ PT
Now, in AOTP,
⇒ OP² = PT² + OT²
⇒ 26² = 24² + OT²
⇒ 676 – 576 = OT²
⇒ 100 = OT²
⇒ 10 cm = OT
13. A line through point of contact and passing through centre of circle is known as
(a) tangent
(b) chord
(c) normal
(d) segment
Answer: c
Explaination: (c) normal
Maths MCQ for Class 10 Cbse With Answers Pdf Question 14. C (O, r1) and C(O, r2) are two concentric circles with r1 > r2 AB is a chord of C(O, r1) touching C(O, r,2) at C then
(a) AB = r1
(b) AB = r2
(c) AC = BC
(d) AB = r1 + r2
Answer: c
Explaination:
(c) ∵ AB touches
C(0, r<sub>2</sub>)
∴ OC ⊥ AB
Also, perpendicular from the centre to a chord bisects the chord.
∴ AC = BC
15. Two parallel lines touch the circle at
points A and B respectively. If area of the circle is 25 n cm2, then AB is equal to
(a) 5 cm
(b) 8 cm
(c) 10 cm
(d) 25 cm
Answer: c
Explaination:
(c) Let radius of circle = R
∴ πR² = 25π
⇒ R = 5 cm
∴ Distance between two parallel tangents = diameter = 2 × 5 = 10 cm.
MCQ Questions for Class 10 Maths Circles Question 16. From a point P which is at a distance of 13 cm from the centre O of a circle of radius 5 cm, the pair of tangents PQ and PR to the circle are drawn. Then the area of the quadrilateral PQOR is [NCERT Exemplar Problems]
(a) 60 cm²
(b) 65 cm²
(c) 30 cm²
(d) 32.5 cm²
Answer: a
Explaination:
17. In figure AT is a tangent to the circle with centre O such that OT = 4 cm and ∠OTA = 30°. Then AT is equal to [NCERT Exemplar Problems]
(a) 4 cm
(b) 2 cm
(c) 2√3 cm
(d) 4√3 cm
Answer: c
Explaination:
18. In figure if O is centre of a circle, PQ is a chord and the tangent PR at P makes an angle of 50° with PQ, then ∠POQ is equal to [NCERT Exemplar Problems]
(a) 100°
(b) 80°
(c) 90°
(d) 75°
Answer: a
Explaination:
(a) OP ⊥ PR [Y Tangent and radius are ⊥ to each other at the point of contact]
∠OPQ = 90° – 50° = 40°
OP = OQ [Radii]
∴ ∠OPQ = ∠OQP = 40°
In ∆OPQ,
⇒ ∠POQ + ∠OPQ + ∠OQP = 180°
⇒ ∠POQ + 40° + 40° = 180°
∠POQ = 180° – 80° = 100°.
19. Match the column:
| (1) The tangent at any point of a circle is … | (A) known as tangent to the circle |
| (2) The line containing the radius through the point of contact is … | (B) to the radius through the point of |
| (3) The lengths of tangents drawn from an external point to a circle are… | (C) called the ‘normal’ to circle |
| (4) When two end points of the corresponding chord of a secant coincide, it is … | (D) equal |
(a) 1 → A, 2 → B, 3 → C, 4 → D
(b) 1 → B, 2 → A, 3 → D, 4 → C
(c) 1 → D, 2 → A, 3 → C, 4 → B
(d) 1 → B, 2 → C, 3 → D, 4 → A
Answer:
Explaination: Properties of circle.
Questions on Circles for Class 10 Question 20. In figure, O is the centre of a circle, AB is a chord and AT is the tangent at A. If ∠AOB = 100°, then ∠BAT is equal to [Delhi 2011]
(a) 100°
(b) 40°
(c) 50°
(d) 90°
Answer: c
Explaination:
(c) ∠AOB = 100°
∠OAB = ∠OBA (∵ OA and OB are radii)
Now, in ∆AOB,
∠AOB + ∠OAB + ∠OBA = 180°
(Angle sum property of A)
⇒ 100° + x + x = 180° [Let ∠OAB = ∠OBA = x]
⇒ 2x = 180° – 100°
⇒ 2x = 80°
⇒ x = 40°
Also, ∠OAB + ∠BAT = 90°
[∵ OA is radius and TA is tangent at A]
⇒ 40° + ZBAT = 90°
⇒ ∠BAT = 50°
21. In the figure PA and PB are tangents to the circle with centre O. If ∠APB = 60°, then ∠OAB is [Delhi 2011]
(a) 30°
(b) 60°
(c) 90°
(d) 15°
Maths Multiple Choice Questions With Answers for Class 10 Question 22. In the given figure, TP and TQ are two tangents to a circle with centre O, such that ∠POQ = 110°. Then ∠PTQ is equal to [Foreign 2011]
(a) 55°
(b) 70°
(c) 110°
(d) 90°
Answer: b
Explaination:
(b) In quadrilateral POQT,
∠PTQ + ∠TPO + ∠TQO + ∠POQ
= 360°
⇒ ∠PTQ + 90° + 90° + 110° = 360°
⇒ ∠PTQ + 290° = 360°
⇒ ∠PTQ = 360° – 290° = 70°
23. Infigure,PQandPRaretangentstoacirclewith centreA. If ∠QPA=27°, then ∠QAR equals to [Foreign 2012]
(a) 63°
(b) 153°
(c) 110°
(d) 90°
Answer: c
Explaination:
(c) ∠QPA = ∠RPA
[∵ ∆AQP ≅ ∆ARP (RHS congruence rule)]
⇒ ∠RPA = 27°
∴ ∠QPR = ∠QPA + ∠RPA
= 27° + 27° = 54°
Now,
∠QAR + ∠AQP + ∠ARP + ∠QPR = 360°
⇒ ∠QAR = 90° + 90° + 54° = 360°
⇒ ∠QAR = 360° – 234° = 126°
Circles MCQ Class 10 Question 24. In figure if PQR is the tangent to a circle at Q whose centre is O, AB is a chord parallel to PR and ∠BQR = 70°, then ∠AQB is equal to [NCERT Exemplar Problems]
(a) 20°
(b) 40°
(c) 35°
(d) 45°
Answer:
Explaination:
(b) AB || PR
∴ ∠ABQ =∠BQR
[Alternate interior angles]
⇒ ∠ABQ = 70°
Also, ∠BQR = ∠BAQ [Angles in alternate segment]
⇒ ∠BAQ = 70°
In ∆AQB,
∠BAQ + ∠ABQ + ∠AQB = 180°
⇒ 70° + 70° + ∠AQB = 180°
⇒ ∠AQB = 180° – 140° = 40°.
25. The common point of the tangent and the circle is called _____ .
Answer:
Explaination: point of contact
26. Two concentric circles are of radii 13 cm and 5 cm. The length of the chord of larger circle which touches the smaller circle is _____ .
Answer:
Explaination: 24 cm. Hint: ∵ AB touches the smaller circle
∴ OC ⊥ AB and hence AC = BC
In right ∆OCA,
OA² = OC² + AC²
⇒ AC²= 13² – 5²
⇒ AC = 12
∴ AB = 2 × 12 = 24 cm.
MCQ on Circles Class 10 Question 27. A quadrilateral ABCD is drawn to circumscribe a circle. If AB =12 cm, BC = 15 cm and CD = 14 cm, then AD is equal to _____ .
Answer:
Explaination: 11 cm. Hint: AB + CD = BC + AD
⇒ 12+ 14= 15+ AD
⇒ AD =11 cm.
28. Number of tangents to a circle which are parallel to a secant is ____ .
Answer:
Explaination: 2
Circle Objective Question 29. A tangent PQ at a point P of a circle of radius 7 cm meets a line through centre O at a point Q so that OQ = 25 cm length PQ is ____ .
Answer: 24 cm
Explaination:
24 cm.
Hint: PQ² = OQ² – OP² = 252²- 7²
⇒ PQ = 24 cm.
30. If the angle between two tangents drawn from an external point P to a circle of radius a and centre O, is 60°, then find the length of OP. [Delhi 2017]
Answer:
Explaination:
31. In the given fig., there are two concentric circles with centre O. PRT and PQS are tangents to the inner circle from a point P lying on the outer circle. If PR = 5 cm, find the length of PS. [Delhi 2017 (C)]
∴ PR = PQ
∴ PQ = 5 cm (∵ PR = 5 cm)
PS = 2PQ (∵ OQ ⊥ PS)
= 2 × 5 = 10 cm
Circle MCQ Pdf Question 32. In the given Fig., O is the centre of the circle, PQ is a chord and PT is tangent to the circle at P. If ∠POQ = 70°, find ∠TPQ. [AI 2017 (C)]
MCQ on Circles With Answer:
Explanation:
Given: O is centre of the circle, PQ is chord and PT is tangent at P.
To find: ∠TPQ
Solution: In ∆OPQ
∠POQ + ∠OPQ + ∠OQP = 180°
⇒ 70° + ∠OPQ + ∠OPQ = 180°
(∵ OP = OQ, radii of the circle)
⇒ 70° + 2∠OPQ = 180°
⇒ 2∠OPQ = 110°
⇒ ∠OPQ = 55°
OP is perpendicular to the tangent at P.
∴ ∠OPT = 90°
⇒ ∠OPQ + ∠TPQ = 90°
⇒ 55° + ∠TPQ = 90°
⇒ ∠TPQ = 90° – 55°
∠TPQ = 35°
33. What is the distance between two parallel tangents of a circle of radius 7 cm?
Answer:
Explaination:
Two parallel tangents of a circle can be drawn only at the end points of the diameter
⇒ l<sub>1</sub> || l<sub>2</sub>
⇒ Distance between l<sub>1</sub> and l<sub>2</sub> = AB
= Diameter of the circle
= 2 × r = 2 × 7 cm = 14 cm
MCQ on Circle Question 34. In the given figure, find ∠QSR.
Answer:
Explaination:
Given: PQ and PR are tangents to a circle with centre O and ∠QPR = 50°.
To find: ∠QSR
∠QOR + ∠QPR =180°
⇒ ∠QOR +50° = 180°
⇒ ∠QOR = 130°
⇒ ∠QSR = 12 ∠QOR [Degree measure theorem]
⇒ ∠QSR =12 × 130° = 65°
Circle MCQ Question 35. In the given figure, AB, AC and AD are tangents. If AB = 5 cm, find AD.
Answer:
Explaination:
Given: AB, AC and AD are tangents. AB = 5 cm.
To find: AD
Sol. AB and AC are tangents from the same point to the circle with centre O.
⇒ AB = AC …(i)
(Length of the tangents from the same external point are equal).
AC and AD are tangents from the same point to the circle with centre O.
⇒ AC = AD …(ii)
(Length of the tangents from the same external point are equal)
From (i) and (ii)
∵ AB = AC = AD = 5 cm
We hope the given MCQ Questions for Class 10 Maths Circles with Answers will help you. If you have any query regarding CBSE Class 10 Maths Chapter 10 Circles Multiple Choice Questions with Answers, drop a comment below and we will get back to you at the earliest.
Free PDF Download of CBSE Class 10 Maths Chapter 9 Application of Trigonometry Multiple Choice Questions with Answers. MCQ Questions for Class 10 Maths with Answers was Prepared Based on Latest Exam Pattern. Students can solve NCERT Class 10 Maths Application of Trigonometry MCQs with Answers to know their preparation level.
MCQ On Application Of Trigonometry Class 10 Question 1. The shadow of a tower is equal to its height at 10-45 a.m. The sun’s altitude is
(a) 30°
(b) 45°
(c) 60°
(d) 90°
Answer: b
Explaination: Reason: Let the height of tower BC = rm and sun’s altitude = θ
Then Length of its shadow, AB = x m
In rt. ∆ABC, tan θ = BCAB = xx = 1
⇒ tan θ = tan 450
∴ θ = 45°
2. In given figure, the value of CE is
(a) 12 cm
(b) 6 cm
(c) 9 cm
(d) 6√3 cm
Answer: a
Explaination: Reason: In rt. ∆EBC, cos 60° = BCCE
⇒ 12 = 6CE
⇒ CE = 12 cm
MCQ Questions For Class 10 Maths Trigonometry Question 3. In given figure, the value of ZC is
(a) 90°
(b) 45°
(c) 30°
(d) 60°
Answer: d
Explaination: Reason: In rt. ∆ABC, cos C = BCAB = 714 = 12
⇒ cos C = cos 60°
∴ C = 60°
MCQ On Application Of Trigonometry Question 4. In given Fig., the angle of depression from the observing position D and E of the object at A are
(a) 60°, 60°
(b) 30°, 30°
(c) 30°, 60°
(d) 60°, 30°
Answer: c
Explaination:
Reason: ∵ APD, ∠1 = 90° – 60° = 30°
∴ APE, ∠2 = ∠EAB …[alt Zs]
∴ ∠2 = 60°
Hence the angles of depression at D and E are 30° and 60° respectively.
Some Applications Of Trigonometry Class 10 MCQ Question 5. In given figure, the length of AP is
Answer: b
Explaination:
MCQ NCERT Application Of Trigonometry Class 10 Question 6. In given figure, the value of AE is
Answer: a
Explaination: Reason: ∠AED = ∠EAB = 30°
In rt. ∆AED, sin 30° = ADAP
⇒ 12 = 45AE
⇒ AE = 90 cm
Trigonometry MCQ Class 10 Question 7. In given figure, AD = 4 cm, BD = 3 cm and CB = 12 cm. The value of tan θ is
Answer: c
Explaination: Reason: In rt ∆ADB,
AB² = AD² + BD² = (4)² + (3)² = 16 + 9 = 25
∴ AB = √25 = 5
∴ In rt ∆ABC, tan θ ABBC = 512
8. In figure given ABCD is a rectangle, the value of CE is
(a) 1 cm
(b) 2 cm
(c) 3 cm
(d) 4 cm
Answer: d
Explaination: Reason: Since ABCD is a rectangle
∴ BC = AD = 8 cm and B = 90°
In rt ∆CBE, cos 60° = CEBC
⇒ 12 = CE8
∴ CE = 82 = 4 cm
Trigonometry MCQ Questions Question 9. In given figure, ABCD is a || gm. The lenght of AP is
(a) 2 cm
(b) 4 cm
(c) 6 cm
(d) 8 cm
Answer: c
Explaination: Reason: Since ABCD is a || gm
∴ AD = BC = 4√3
In rt ∆APD, sin 60° = APAD
⇒ 3√2=AP43√
⇒ 2AP = 4 × 3 = 12
∴ AP = 6 cm
MCQ On Trigonometry For Class 10 With Solutions Question 10. When the length of shadow of a vertical pole is equal to √3 times of its height, the angle of elevation of the Sun’s altitude is
(a) 30°
(b) 45°
(c) 60°
(d) 15°
Answer: a
Explaination: Reason: Let the height of the vertical pole, BC = h m
∴ Shadow AB = √3 h m and the angle of elevation ZBAC = θ
In rt ∆ABC, tan θ = BCAB=h3√h=13√ = tan 30°
∴ θ = 30°
Hence the Sun’s altitude is 30°
MCQ Trigonometry Class 10 Question 11. The angle of elevation of top of a tower from a point on the ground, which is 30 m away from the foot of the tower is 30°. The length of the tower is
(a) √3 m
(b) 2√3 m
(c) 5√3m
(d) 10√3 m
Answer: d
Explaination:
MCQ Questions On Trigonometry For Class 10 Question 12. A plane is observed to be approaching the airport. It is at a distance of 12 km from the point of observation and makes an angle of elevation of 60°. The height above the ground of the plane is
(a) 6√3 m
(b) 4√3 m
(c) 3√3 m
(d) 2√3 m
Answer: a
Explaination:
Trigonometry Multiple Choice Questions And Answers Pdf Question 13. The upper part of a tree is broken by the wind and makes an angle of 30° with the ground. The distance from the foot of the tree to the point where the top touches the ground is 5 m. The height of the tree is
(a) 10√33 m
(b) 5√33 m
(c) √3 m
(d) √3/5 m
Answer: b
Explaination:
MCQ On Trigonometry 10th Question 14. The angles of elevation of the top of a rock from the top and foot of 100 m high tower are respectively 30° and 45°. The height of the rock is
(a) 50 m
(b) 150 m
(c) 5o√3m
(d) 50(3 + √3)
Answer: d
Trigonometry MCQs Question 15. The tops of two poles of height 20 m and 14 m are connected by a wire. If the wire makes an angle of 30° with horizontal, the length of the wire is
(a) 6 m
(b) 10 m
(c) 12 m
(d) 20 m
Answer: c
Trigonometry MCQ Questions For 10th Pdf Question 16. The angle of depression of a car, standing on the ground, from the top of a 75 m high tower, is 30°. The distance of the car from the base of the tower (in m) is:
(a) 25√3
(b) 50√3
(c) 75√3
(d) 150
Answer: c
Explaination:
MCQ On Trigonometry Class 10 Question 17. A ladder 15 m long just reaches the top of a vertical wall. If the ladder makes an angle of 60° with the wall, then the height of the wall is
Answer: b
Explaination:
MCQs On Trigonometry Question 18. The line drawn from the eye of an observer to the point in the object viewed by the observer is known as
(a) horizontal line
(b) vertical line
(c) line of sight
(d) transversal line
Answer: c
MCQ On Trigonometry Question Question 19. The tops of two poles of heights 20 m and 14 m are connected by a wire. If the wire makes an angle of 30° with the horizontal, then the length of the wire is
(a) 8 m
(b) 10 m
(c) 12 m
(d) 14 m
Answer: c
Explaination:
Trigonometry MCQs With Answers Question 20. If two towers of heights h1 and h2 subtend angles of 60° and 30° respectively at the mid-point of the line joining their feet, then h1 : h2 =
(a) 1 : 2
(b) 1 : 3
(c) 2 : 1
(d) 3 : 1
Answer: d
Explaination:
MCQ On Trigonometry For Class 10 Question 21. The angle of elevation of the top of a tower from a point 20 metres away from its base is 45°. The height of the tower is
(a) 10 m
(b) 20 m
(c) 30 m
(d) 20√3 m
Answer: b
Explaination:
Maths Application Questions Question Question 22. Two poles are 25 m and 15 m high and the line joining their tops makes an angle of 45° with the horizontal. The distance between these poles is
(a) 5 m
(b) 8 m
(c) 9 m
(d) 10 m
Answer: c
Explaination:
Multiple Choice Questions On Trigonometry Question 23. A portion of a 60 m long tree is broken by tornado and the top struck up the ground making an angle of 30° with the ground level. The height of the point where the tree is broken is equal to
(a) 30 m
(b) 35 m
(c) 40 m
(d) 20 m
Answer:
Explaination:
Trigonometry Objective Questions For Class 10 Question 24. The angle of elevation of the top of a 15m high tower at a point 15m away from the base of the tower is ____ .
Answer:
Explaination:
Hints:
∵ Height of tower = distance of point from the base
∴ Angle of elevation = 45°.
25. The ratio of the height of a tower and the length of its shadow on the ground is √3 : 1. What is the angle of elevation of the sun? [Delhi 2017]
Answer:
Explaination:
26. An observer, 1.5 m tall, is 28.5 m away from a 30 m high tower. Determine the angle of elevation of the top of the tower from the eye of the observer. [Delhi 2017 (C)]
Answer:
Explaination:
Here, AB = DM = 1.5 m
CM = CD – DM
= 30 – 1.5 = 28.5 m
Let 0 be the angle of elevation of the top of the tower from the eye of the observer.
∴ In ∆ACM
tan θ = CMAM=28.528.5
tan θ = 1
tan θ = tan 45°
θ = 45°
27. If a tower 30 m high, casts a shadow 10√3 m long on the ground, then what is the angle of elevation of the sun?
[AI 2017]
Answer:
Explaination:
28. If two towers of height h1 and h2 subtends angles of 60° and 30° respectively at the mid points of line joining their feet, find h1 : h2
Answer:
Explaination:
29. At some time of the day the length of the shadow of a tower is equal to its height. Find the sun’s altitude at that time. [Foreign 2011]
Answer:
Explaination:
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