10th Class Mathematics Real Numbers Question Bank

done Case Based (MCQs) - Real Numbers Total Questions - 40

• question_answer1)

  Direction: Q. 1 to 5

  To enhance the reading skills of grade X students, the school nominates you and two of your friends to set up a class library. There are two sections-section A and section B of grade X. There are 32 students in section A and 36 students in section B.

  Read carefully the given paragraph and answer the following questions:

  The product of the powers of each prime factors of 36 is:
  A)
  2 done clear
  B)
  4 done clear
  C)
  3 done clear
  D)
  5 done clear
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• question_answer2)
  If p and q are positive integers such that \[p=a{{b}^{2}}\] and \[q={{a}^{2}}b,\] where a, b are prime numbers, then the \[LCM\,(p,q)\] is:
  A)
  \[ab\] done clear
  B)
  \[{{a}^{2}}{{b}^{2}}\] done clear
  C)
  \[{{a}^{3}}{{b}^{2}}\] done clear
  D)
  \[{{a}^{3}}{{b}^{3}}\] done clear
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• question_answer3)
       What is the minimum number of books you will acquire for the class library, so that they can be distributed equally among students of Section A or Section B?                      
  A)
  144 done clear
  B)
  128 done clear
  C)
  288 done clear
  D)
  272 done clear
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• question_answer4)
  If the product of two positive integers is equal to the product of their HCF and LCM is true, then the HCF (32,36) is:
  A)
  2 done clear
  B)
  4 done clear
  C)
  6 done clear
  D)
  8 done clear
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• question_answer5)
  If 288 books are distributed among the students of section B, how many will each get?                                   
  A)
  9 done clear
  B)
  8 done clear
  C)
  6 done clear
  D)
  7 done clear
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• question_answer6)
                                 

  Direction: Q. 6 to 10

  A seminar is being conducted by an educational organization, where the participants will be educators of different subjects. The number of participants in Hindi, English and Mathematics are 60, 84 and 108 respectively.

  Subjectwise details is given in the paragraph, read carefully and answer the following questions:

  The sum of the powers of each prime factor of 108 is:   
  A)
  2 done clear
  B)
  3 done clear
  C)
  4 done clear
  D)
  5 done clear
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• question_answer7)
  In each room the same number of participants are to be seated and all of them being in the same subject, hence maximum number of participants that can accommodated in each room are:
  A)
  14 done clear
  B)
  12 done clear
  C)
  16 done clear
  D)
  18   done clear
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• question_answer8)
  What is the minimum number of rooms required during the event?
  A)
  11 done clear
  B)
  31 done clear
  C)
  41 done clear
  D)
  21 done clear
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• question_answer9)
  The LCM of 60. 84 and 108 is:
  A)
  3780 done clear
  B)
  3680 done clear
  C)
  4780 done clear
  D)
  4680 done clear
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• question_answer10)
  The product of HCF and LCM of 60, 84 and 108 is:      
  A)
  55360 done clear
  B)
  35360 done clear
  C)
  45500 done clear
  D)
  45360 done clear
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• question_answer11)

  Direction: Q. 11 to 15

  A mathematics exhibition is being conducted in a reputed school and one of your mathematics teacher is making model of a factor tree. He has some difficulty and asks for your help in completing a quiz for the viewers.

  Observe the above factor tree and answer the following questions.

                                 The value of A is:
  A)
  20825 done clear
  B)
  15005     done clear
  C)
  56920 done clear
  D)
  17429 done clear
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• question_answer12)
  The value of B is:
  A)
  23 done clear
  B)
  17 done clear
  C)
  11 done clear
  D)
  19 done clear
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• question_answer13)
  The value of C is:
  A)
  22 done clear
  B)
  23 done clear
  C)
  35 done clear
  D)
  19 done clear
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• question_answer14)
  The prime factorisation of 20825 is:
  A)
  \[{{5}^{2}}\times {{7}^{2}}\times 17\] done clear
  B)
  \[{{5}^{2}}\times {{7}^{2}}\times 13\] done clear
  C)
  \[5\times {{7}^{2}}\times {{11}^{2}}\] done clear
  D)
  \[{{5}^{2}}\times 7\times 17\] done clear
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• question_answer15)
  According to Fundamental Theorem of Arithmetic, 20825 is a:
  A)
  even number  done clear
  B)
  prime number done clear
  C)
  neither prime nor composite done clear
  D)
  composite number done clear
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• question_answer16)

  Direction: Q. 16 to 20

  A sweetseller has 420 kaju barfis and 130 gola barfis. He wants to stack them in such a way that each stack has same number, and they take up the least area of the tray.

  Based on the above details of a sweet shop answer the  following questions:

  The total number of sweets are:
  A)
  420 done clear
  B)
  130 done clear
  C)
  550 done clear
  D)
  290 done clear
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• question_answer17)
  The product of exponents of the prime factors of total number of sweets is:
  A)
  2 done clear
  B)
  3 done clear
  C)
  5 done clear
  D)
  6 done clear
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• question_answer18)
  What is the number of sweets that can be placed in each stack for this purpose?                              
  A)
  45 done clear
  B)
  40 done clear
  C)
  10 done clear
  D)
  35 done clear
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• question_answer19)
  The sum of exponents of the prime factors of the number of sweets that can be placed in each stack for this purpose, is:
  A)
  5 done clear
  B)
  2 done clear
  C)
  4 done clear
  D)
  6 done clear
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• question_answer20)
  What is the total number of rows in which they can be placed?
  A)
  15 done clear
  B)
  25 done clear
  C)
  35 done clear
  D)
  55 done clear
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• question_answer21)

  Direction: Q. 21 to 25

  Old age homes are mean for senior citizens who are unable to stay with their families or destitute. These old age homes have special medical facilities for senior citizens such as mobile health care systems, ambulances nurses and provision of well balanced meals.

  Himanshu, Gaurav and Gagan start preparing cards for greeting each person of an old age home on new year. In order to complete one card, they take 10, 16 and 20 min respectively.

  Based on the given time, answer the following questions:

  If all of them started together, after what time will they start preparing a new card together.
  A)
  85 min done clear
  B)
  80 min done clear
  C)
  60 min done clear
  D)
  90 min done clear
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• question_answer22)
  What is the common time to make one card?
  A)
  1 min done clear
  B)
  2 min done clear
  C)
  4 min done clear
  D)
  None of these done clear
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• question_answer23)
  The smallest prime even number is:
  A)
  1 done clear
  B)
  3 done clear
  C)
  2 done clear
  D)
  4 done clear
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• question_answer24)
  A largest positive integer that divides given two positive integers is called the:
  A)
  LCM done clear
  B)
  HCF done clear
  C)
  do not say anything done clear
  D)
  None of these   done clear
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• question_answer25)
  Co-prime number are those numbers which do not have any common factor other than:
  A)
  0 done clear
  B)
  1 done clear
  C)
  2 done clear
  D)
  None of these done clear
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• question_answer26)

  Direction: Q. 26 to 30

  In a morning walk, Naveeka, Arjun and Vedant step off together, their steps measuring 240 cm, 90 cm, 120 cm respectively. They want to go for a juice shop for a health issue, which is situated near by them.

  Read the above paragraph and answer the following questions.

  Find the minimum distance of shop from where they start to walk together, so that one can cover the distance in complete steps?
  A)
  720 cm done clear
  B)
  700 cm   done clear
  C)
  620 cm done clear
  D)
  740 cm     done clear
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• question_answer27)
  Find the number of common steps covered by all of them to reach the juice shop.
  A)
  20 done clear
  B)
  30 done clear
  C)
  35 done clear
  D)
  40 done clear
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• question_answer28)
  If a and b are two numbers, then find the relation between LCM and HCF.
  A)
  \[\frac{a}{b}=LCM\,\,(a,b)\,HCF\,\,(a,b)\] done clear
  B)
  \[a\times b=LCM(a,b)\times HCF(a,b)\] done clear
  C)
  \[a\times LCM(a,b)=b\times HCF(a,b)\] done clear
  D)
  \[None\,\, of\,\, the\,\,above\] done clear
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• question_answer29)
  A largest positive integer that divides given two positive integers is called:
  A)
  HCF done clear
  B)
  LCM done clear
  C)
  co-prime done clear
  D)
  None of these done clear
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• question_answer30)
  Factor tree is a chain of factors, which is represented in the form of a:
  A)
  tree done clear
  B)
  division done clear
  C)
  flower done clear
  D)
  None of these done clear
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• question_answer31)

  Direction: Q. 31 to 35

  A shopkeeper has 420 science stream books and 130 arts stream books. He wants to stack them in such a way that each stack has the same number and they take up the least area of the surface.

  Read the above paragraph and answer the following questions.

  If a number has no factors other than 1 and number itself is:
  A)
  composite done clear
  B)
  prime done clear
  C)
  do not say any thing done clear
  D)
  None of these done clear
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• question_answer32)
  What is the maximum number of books that can be placed in each stack for this purpose?
  A)
  10 done clear
  B)
  14 done clear
  C)
  12 done clear
  D)
  15 done clear
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• question_answer33)
  Which mathematical concept is used to solve the problem?
  A)
  Prime factorisation method done clear
  B)
  Area of triangle done clear
  C)
  Arithmetic progression done clear
  D)
  None of the above done clear
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• question_answer34)
  If the shopkeeper double the quantity, then the maximum number of books that can be placed in each stack:
  A)
  remain same done clear
  B)
  double done clear
  C)
  triple done clear
  D)
  None of these done clear
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• question_answer35)
  Find the LCM of the given book streams:
  A)
  5450 done clear
  B)
  5460 done clear
  C)
  2730 done clear
  D)
  None of these done clear
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• question_answer36)

  Direction: Q. 36 to 40

  In our daily life we all see traffic lights. A traffic controller set the timmings of traffic lights in such a way that all light are not green at the same time or specially not in the rush hour. It may create problem in an hour because lights are for few minutes only. So, he take the timmings of nearby places in same area and calculate 1 cm of all traffic stops and he easily manage the traffic by increasing the duration set at different times. There are two traffic lights on a particular highway which shows green light at the interval of 90 seconds and 144 seconds respectively.

  Read the above paragraph carefully and answer the question that follows :

  Find the HCF between two green lights.
  A)
  18 done clear
  B)
  20 done clear
  C)
  16 done clear
  D)
  22 done clear
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• question_answer37)
  Find the LCM between two green lights.
  A)
  720 done clear
  B)
  730       done clear
  C)
  710 done clear
  D)
  740       done clear
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• question_answer38)
  Factor tree is used for determining the:
  A)
  HCF done clear
  B)
  LCM     done clear
  C)
  prime factor done clear
  D)
  None of these done clear
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• question_answer39)
  Identify the correct option.
  A)
  \[HCF\,\,(a,b)\times LCM\,(a,b)=\frac{a}{b}\] done clear
  B)
  \[\frac{HCF\,\,(a,b)}{LCM\,(a,b)}=\frac{a}{b}\] done clear
  C)
  \[HCF\,\,(a,b)\times LCM\,(a,b)=a-b\] done clear
  D)
  \[HCF\,\,(a,b)\times LCM\,(a,b)=ab\] done clear
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• question_answer40)
  A number which do not have any factor other than 1, is:
  A)
  coprime number done clear
  B)
  prime number done clear
  C)
  coprime or prime number done clear
  D)
  None of the above done clear
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