10th Class Mathematics Real Numbers Question Bank

done Assertion And Reason (MCQs) - Real Numbers Total Questions - 20

• question_answer1)

  Directions (Q. Nos. 1 - 20): In the following questions, a statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choce as:

  Assertion (A): \[11\times 4\times 3\times 2+4\] is a composite number.

  Reason (R): Every composite number can be expressed as product of primes.

  A)
  Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A) done clear
  B)
  Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A) done clear
  C)
  Assertion (A) is true but reason (R) is false done clear
  D)
  Assertion (A) is false but reason (R) is true done clear
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• question_answer2)

  Assertion (A): For no value of n. where n is a natural number, the number \[{{8}^{n}}\] ends with the digit zero.

  Reason (R): The prime factorisation of a natural number is unique, except for the order of its factors.

  A)
  Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A) done clear
  B)
  Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A) done clear
  C)
  Assertion (A) is true but reason (R) is false done clear
  D)
  Assertion (A) is false but reason (R) is true done clear
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• question_answer3)

  Assertion (A): If LCM = 350, product of two numbers is \[25\times 70,\] then their HCF = 5.

  Reason (R): LCM x Product of numbers = HCF.

  A)
  Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A) done clear
  B)
  Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A) done clear
  C)
  Assertion (A) is true but reason (R) is false done clear
  D)
  Assertion (A) is false but reason (R) is true done clear
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• question_answer4)
                     

  Assertion (A): HCF of \[(23, 53)\] is 1.

  Reason (R): If p and q are primes, then HCF \[(p,q)=1\]

  A)
  Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A) done clear
  B)
  Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A) done clear
  C)
  Assertion (A) is true but reason (R) is false done clear
  D)
  Assertion (A) is false but reason (R) is true done clear
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• question_answer5)

  Assertion (A): If HCF \[(209,737)=11\] and LCM \[(209,737)=209\times R,\] then the value of R is 68.

  Reason (R): For any two positive numbers a and b, HCF \[(a,b)\times LCM\,(a,b)=a\times b.\]

  A)
  Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A) done clear
  B)
  Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A) done clear
  C)
  Assertion (A) is true but reason (R) is false done clear
  D)
  Assertion (A) is false but reason (R) is true done clear
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• question_answer6)

  Assertion (A): \[\frac{1242}{49}\]is a non-terminating repeating decimal.

  Reason (R): The rational number \[\frac{p}{q}\] is a terminating decimal, if \[q=({{2}^{m}}\times {{5}^{n}})\]for some whole numbers m and n.

  A)
  Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A) done clear
  B)
  Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A) done clear
  C)
  Assertion (A) is true but reason (R) is false done clear
  D)
  Assertion (A) is false but reason (R) is true done clear
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• question_answer7)

  Assertion (A): \[\sqrt{2}\]is an irrational number.

  Reason (R): If p be a prime, then \[\sqrt{p}\] is an irrational number.

  A)
  Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A) done clear
  B)
  Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A) done clear
  C)
  Assertion (A) is true but reason (R) is false done clear
  D)
  Assertion (A) is false but reason (R) is true done clear
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• question_answer8)

  Assertion (A): The rational number \[\frac{117}{819}\]has a terminating decimal expansion.

  Reason (R): Let \[x=p/q\] be a rational number, such that the crime factorisation of q is not of the form \[{{2}^{n}}\times {{5}^{m}},\]decimal expansion, which is non-terminating repeating (recurring).

   
  A)
  Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A) done clear
  B)
  Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A) done clear
  C)
  Assertion (A) is true but reason (R) is false done clear
  D)
  Assertion (A) is false but reason (R) is true done clear
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• question_answer9)

  Assertion (A): \[\sqrt{5}\] is an irrational number.

  Reason (R): If m is a natural number which is not a perfect square, then \[\sqrt{m}\] is irrational

  A)
  Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A) done clear
  B)
  Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A) done clear
  C)
  Assertion (A) is true but reason (R) is false done clear
  D)
  Assertion (A) is false but reason (R) is true done clear
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• question_answer10)
                                    

  Assertion (A): \[\frac{13}{3125}\]is a terminating decimal fraction.

  Reason (R): If \[q={{2}^{n}}\cdot {{5}^{m}}\] where n, m are non-negative integers, then \[\frac{p}{q}\] is a terminating decimal fraction.

  A)
  Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A) done clear
  B)
  Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A) done clear
  C)
  Assertion (A) is true but reason (R) is false done clear
  D)
  Assertion (A) is false but reason (R) is true done clear
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• question_answer11)

  Assertion (A): A number N when divided by 15 gives the remainder 2. Then the remainder is same when N is divided by 5.

  Reason (R): \[\sqrt{3}\] is an irrational number.

  A)
  Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A) done clear
  B)
  Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A) done clear
  C)
  Assertion (A) is true but reason (R) is false done clear
  D)
  Assertion (A) is false but reason (R) is true done clear
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• question_answer12)

  Assertion (A): Denominator of\[\text{34}.\text{12545}\]. When expressed in the form \[\frac{p}{q},\]\[q\ne 0,\] is of the form \[{{2}^{m}}\times {{5}^{n}},\]where m, n are                                    non-negative integers.

  Reason (R): \[\text{34}.\text{12545}\] is a terminating decimal fraction.

  A)
  Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A) done clear
  B)
  Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A) done clear
  C)
  Assertion (A) is true but reason (R) is false done clear
  D)
  Assertion (A) is false but reason (R) is true done clear
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• question_answer13)

  Assertion (A): The HCF of two numbers is 16 and their product is 3072. Then their \[\text{LCM}=\text{162}\].

  Reason (R): If a, b are two positive integers, then \[HCF\times LCM=a\times b.\].

  A)
  Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A) done clear
  B)
  Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A) done clear
  C)
  Assertion (A) is true but reason (R) is false done clear
  D)
  Assertion (A) is false but reason (R) is true done clear
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• question_answer14)

  Assertion (A): \[{{6}^{n}}\] ends with the digit zero, where n is natural number.

  Reason (R): Any number ends with digit zero. if its prime factor is of the form \[{{2}^{m}}\times {{5}^{n}},\] where m, n are natural

  A)
  Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A) done clear
  B)
  Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A) done clear
  C)
  Assertion (A) is true but reason (R) is false done clear
  D)
  Assertion (A) is false but reason (R) is true done clear
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• question_answer15)

  Assertion (A): 2 is a rational number.

  Reason (R): The square roots of all positive integers are irrationals.

  A)
  Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A) done clear
  B)
  Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A) done clear
  C)
  Assertion (A) is true but reason (R) is false done clear
  D)
  Assertion (A) is false but reason (R) is true done clear
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• question_answer16)

  Assertion (A): \[\sqrt{a}\] is an irrational number, where a is a prime number.

  Reason (R): Square root of any prime number is an irrational number.

  A)
  Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A) done clear
  B)
  Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A) done clear
  C)
  Assertion (A) is true but reason (R) is false done clear
  D)
  Assertion (A) is false but reason (R) is true done clear
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• question_answer17)

  Assertion (A): If \[LCM\,\,\{p,q\}=30\]and \[HCF\,\,\{p,q\}=5,\]then \[p\cdot q=150.\]

  Reason (R): LCM of \[(a,b)\times HCF\]of\[(a,b)=a\cdot b\].

  A)
  Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A) done clear
  B)
  Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A) done clear
  C)
  Assertion (A) is true but reason (R) is false done clear
  D)
  Assertion (A) is false but reason (R) is true   done clear
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• question_answer18)

  Assertion (A): For any two positive integers a and b, \[HCF(a,b)\times LCM(a,b)=a\times b.\]

  Reason (R): The HCF of two numbers is 5 and their product is 150. Then their LCM is 40.

  A)
  Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A) done clear
  B)
  Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A) done clear
  C)
  Assertion (A) is true but reason (R) is false done clear
  D)
  Assertion (A) is false but reason (R) is true done clear
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• question_answer19)

  Assertion (A): \[{{n}^{2}}-n\] is divisible by 2 for every positive integer.

  Reason (R): \[\sqrt{2}\] is not a rational number.

  A)
  Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A) done clear
  B)
  Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A) done clear
  C)
  Assertion (A) is true but reason (R) is false done clear
  D)
  Assertion (A) is false but reason (R) is true done clear
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• question_answer20)

  Assertion (A): \[{{n}^{2}}+n\] is divisible by 2 for every positive integer n.

  Reason (R): If x and y are odd positive integers, from \[{{x}^{2}}+{{y}^{2}}\] is divisible by 4.

  A)
  Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A) done clear
  B)
  Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A) done clear
  C)
  Assertion (A) is true but reason (R) is false done clear
  D)
  Assertion (A) is false but reason (R) is true done clear
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