10th Class Mathematics Real Numbers Question Bank

done Case Based MCQs - Real Number Total Questions - 30

• question_answer1)

  Direction: Q. 1 to 5

  Divisibility Rules

  HCF and LCM are widely used in number system especially in real numbers in finding relationship between different numbers and their general forms. Also, product of two positive integers is equal to the product of their HCF and LCM.

  {Product of numbers = \[HCF\times LCM\]}

  Based on the above information answer the following questions.

  If two positive integers a and b are expressible in terms of primes as \[a={{p}^{2}}{{q}^{4}}\] and\[b={{p}^{3}}{{q}^{2}}\], then which of the following is true?

  A)
  \[HCF=p{{q}^{2}}\times LCM\] done clear
  B)
  \[LCM=p{{q}^{2}}\times HCF\] done clear
  C)
  \[LCM={{p}^{2}}q\times HCF\] done clear
  D)
  \[HCF={{p}^{2}}q\times LCM\] done clear
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• question_answer2)
  Vishal has a collection of marbles realizes that if he makes a group of 2 or 3 marbles, there are always one marbles left, then which of the following is correct if the number of marbles is p?
  A)
  p is odd done clear
  B)
  p is even done clear
  C)
  can't say done clear
  D)
  Both [a] and [b] done clear
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• question_answer3)
  Given that HCF (306, 657) = 9, find LCM (306, 657).
  A)
  33228 done clear
  B)
  22833 done clear
  C)
  22338 done clear
  D)
  None of these done clear
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• question_answer4)
  The greatest number of 6-digits exactly divisible by 15, 24 and 36 is
  A)
  999998 done clear
  B)
  999999 done clear
  C)
  999720 done clear
  D)
  999724 done clear
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• question_answer5)
  If N is the sum of first 13986 prime numbers, then N is always divisible by
  A)
  6 done clear
  B)
  4 done clear
  C)
  8 done clear
  D)
  None of these done clear
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• question_answer6)

  Directions: Q. 6 to 10

  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.

  Based on the above information answer the following questions.

  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_answer7)
  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_answer8)
  36 can be expressed as a product of its primes as
  A)
  \[{{2}^{2}}\times {{3}^{2}}\] done clear
  B)
  \[{{2}^{1}}\times {{3}^{3}}\] done clear
  C)
  \[{{2}^{3}}\times {{3}^{1}}\] done clear
  D)
  \[{{2}^{0}}\times {{3}^{0}}\] done clear
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• question_answer9)
  \[7\times 11\times 13\times 15+15\] is a
  A)
  Prime number done clear
  B)
  Composite number done clear
  C)
  Neither prime nor composite done clear
  D)
  None of the above done clear
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• question_answer10)
  If p and q are positive integers such that \[p=a{{b}^{2}}\] and \[q={{a}^{2}}b\] , where a and 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_answer11)
   

  Directions: Q. 11 to 15

  Activity on Real Numbers In a classroom (class-X) activity on real numbers, the students have to pick a number card from a box and frame question on it is not a rational number for the rest of the class. The number cards picked up by first 5 students and their questions on the numbers for the rest of the class are as shown below.

  Based on the above information answer the following questions.

  Akshay picked up \[\sqrt{12}\]and his question was-Which of the following is true about \[\sqrt{12}\]
  A)
  It is a natural number done clear
  B)
  It is an irrational number done clear
  C)
  It is a rational number done clear
  D)
  None of the above done clear
  View Solution play_arrow

• question_answer12)
  Shallu picked up 'BONUS' and her question was-Which of the following is not irrational?
  A)
  \[5-3\sqrt{2}\] done clear
  B)
  \[\sqrt{5}-2\] done clear
  C)
  \[2+2\sqrt{9}\] done clear
  D)
  \[3\sqrt{5}-6\] done clear
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• question_answer13)
  Charu picked up \[\sqrt{3}-\sqrt{2}\]and her question was \[\sqrt{3}-\sqrt{2}\]is ____ number.
  A)
  a natural done clear
  B)
  an irrational done clear
  C)
  a whole done clear
  D)
  a rational done clear
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• question_answer14)
  Bhoomika picked up \[\frac{1}{\sqrt{8}}\]and her question was \[\frac{1}{\sqrt{8}}\]is ____ number.
  A)
  a whole done clear
  B)
  a rational done clear
  C)
  an irrational done clear
  D)
  a natural done clear
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• question_answer15)
  Malika picked up \[\sqrt{5}\]and her question was - Which of the following is not irrational?
  A)
  \[15+3\sqrt{5}\] done clear
  B)
  \[\sqrt{20}-9\] done clear
  C)
  \[4\sqrt{129}\] done clear
  D)
  \[\sqrt{16}\] done clear
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• question_answer16)
   

  Directions: Q. 16 to 20

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

  Based am die above information answer the following questions.

  In each room the same number of participants are 10 be sealed and all of them being in the sine subject, hence maximum number 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_answer17)
  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_answer18)
  The LCM of 60, 84 and 108 is
  A)
  3780 done clear
  B)
  3680 done clear
  C)
  4780 done clear
  D)
  A680 done clear
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• question_answer19)
  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_answer20)
  108 can be expressed as a product of its primes as
  A)
  \[{{2}^{3}}\times {{3}^{2}}\] done clear
  B)
  \[{{2}^{3}}\times {{3}^{3}}\] done clear
  C)
  \[{{2}^{2}}\times {{3}^{2}}\] done clear
  D)
  \[{{2}^{2}}\times {{3}^{3}}\] done clear
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• question_answer21)
   

  Directions: Q. 21 to 25

  Decimal Expansion

  Decimal form of rational numbers can be classified into two types.

  Let a be a rational number whose decimal expansion terminates. Then a can be expressed in the form \[\frac{p}{q}\], where p and q are co-prime and the prime factorisation of q is of the form \[{{2}^{n}}\,5{{\,}^{m}}\], where n, m are non-negative integers and vice-versa.

  Let \[a=\frac{p}{q}\]be a rational number, such that the prime factorisation of q is not of the form \[{{2}^{n}}{{5}^{m}}\], where n and m are non-negative integers. Then a has a non-terminating repeating decimal expansion.

  Based on the above information answer the following questions.

  Which of the following rational numbers have a terminating decimal expansion?
  A)
  8/15 done clear
  B)
  51/150 done clear
  C)
  \[15/400\] done clear
  D)
    \[129/\left( {{2}^{2}}\times {{5}^{2}}\times {{7}^{2}} \right)\] done clear
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• question_answer22)
  \[23/\left( {{2}^{3}}\times {{5}^{3}} \right)=\]
  A)
  0.575 done clear
  B)
  0.023 done clear
  C)
  0.91 done clear
  D)
  1.15 done clear
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• question_answer23)
  \[686/\left( {{2}^{2}}\times {{5}^{7}}\times {{7}^{3}} \right)\]is a _____ decimal..
  A)
  terminating done clear
  B)
  recurring done clear
  C)
  non-terminating and non-recurring done clear
  D)
  None of the above done clear
  View Solution play_arrow

• question_answer24)
  For which of the following value (s) of \[p,\,251\,\left( {{2}^{3}}\times {{p}^{2}} \right)\] is terminating decimal number?
  A)
  3 done clear
  B)
  7 done clear
  C)
  5 done clear
  D)
  AII of these done clear
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• question_answer25)
  \[61/\left( {{2}^{5}}\times {{5}^{3}} \right)\] is a ______ decimal
  A)
  terminating done clear
  B)
  recurring done clear
  C)
  non-terminating and non-recurring done clear
  D)
  None of the above done clear
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• question_answer26)
   

  Direction: Q. 26 to 30

  A Mathematics Exhibition is being conducted in your School and one of your friends is making a model of a factor tree. He has some difficulty and ask for your help in completing a quiz for the audience. Observe the following factor tree and answer the following:

  Based on the above information answer the following questions.

  What will be the value of x?
  A)
  15005 done clear
  B)
  13915 done clear
  C)
  56920 done clear
  D)
  17429 done clear
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• question_answer27)
  What will be the value of y?
  A)
  23 done clear
  B)
  22 done clear
  C)
  11 done clear
  D)
  19 done clear
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• question_answer28)
  What will be the value of z?
  A)
  22 done clear
  B)
  23 done clear
  C)
  17 done clear
  D)
  19 done clear
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• question_answer29)
  According to Fundamental Theorem of Arithmetic 13915 is a
  A)
  Composite number done clear
  B)
  Prime number done clear
  C)
  Neither prime nor composite done clear
  D)
  Even number done clear
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• question_answer30)
  The prime factorisation of 13915 is
  A)
  \[5\times {{11}^{3}}\times {{13}^{2}}\] done clear
  B)
  \[5\times {{11}^{3}}\times {{23}^{2}}\] done clear
  C)
  \[5\times {{11}^{2}}\times 23\] done clear
  D)
  \[5\times {{11}^{2}}\times {{13}^{2}}\] done clear
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