10th Class Mathematics Real Numbers Question Bank

done Real Number Total Questions - 40

• question_answer1)
  The L.C.M. and H.C. F. of marks scored by Supravin & Kumar in a test are 1489645 and 1 respectively. If Supravin's score is 1145, what is Kumar's score?
  A)
   68                                done clear
  B)
   666           done clear
  C)
   1295                done clear
  D)
   1301 done clear
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• question_answer2)
  \[\mathbf{5}\mathbf{.67}\overline{\mathbf{23}}\]
  A)
   An integer                     done clear
  B)
   A rational number done clear
  C)
   An irrational number      done clear
  D)
   A natural number. done clear
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• question_answer3)
  The value of\[\frac{\mathbf{1}}{\mathbf{1+}\sqrt{\mathbf{2}}}\mathbf{+}\frac{\mathbf{1}}{\sqrt{\mathbf{2}}\mathbf{+}\sqrt{\mathbf{3}}}\mathbf{+}\frac{\mathbf{1}}{\sqrt{\mathbf{3}}\mathbf{+}\sqrt{\mathbf{4}}}\mathbf{is}\]
  A)
   0                                 done clear
  B)
   1         done clear
  C)
   2                                 done clear
  D)
   4 done clear
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• question_answer4)
  The value of \[\frac{\mathbf{1}}{\mathbf{1+}\sqrt{\mathbf{2}}}\mathbf{+}\frac{\mathbf{1}}{\sqrt{\mathbf{2}}\mathbf{+}\sqrt{\mathbf{3}}}\mathbf{+}\frac{\mathbf{1}}{\sqrt{\mathbf{3}}\mathbf{+}\sqrt{\mathbf{4}}}\mathbf{+}.......\]\[\frac{\mathbf{1}}{\sqrt{\mathbf{34}}\mathbf{+}\sqrt{\mathbf{35}}}\mathbf{+}\frac{\mathbf{1}}{\sqrt{\mathbf{35}}\mathbf{+}\sqrt{\mathbf{36}}}\] is
  A)
   0                                 done clear
  B)
   2            done clear
  C)
   3                                 done clear
  D)
   5 done clear
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• question_answer5)
  'P' is the remainder obtained when a perfect square is divided by 3. What is the value of 'p'?
  A)
   1                                 done clear
  B)
   0              done clear
  C)
   Either (a) or (b)   done clear
  D)
   Neither (a) or (b) done clear
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• question_answer6)
  If \[\sqrt{\mathbf{p}}\mathbf{<}\sqrt{\mathbf{q}}\mathbf{<}\sqrt{\mathbf{r}}\mathbf{<}\sqrt{\mathbf{s}}\]where p, q, r, s are consecutive natural numbers, then
  A)
   \[\sqrt{s}-\sqrt{r}>\sqrt{q}-\sqrt{p}\]       done clear
  B)
   \[\sqrt{q}-\sqrt{p}>\sqrt{s}-\sqrt{r}\] done clear
  C)
   \[\sqrt{s}-\sqrt{q}>\sqrt{r}-\sqrt{p}\]       done clear
  D)
   \[\sqrt{s}-\sqrt{r}=\sqrt{q}-\sqrt{p}\] done clear
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• question_answer7)
  The factor tree shows the prime factorization of 1020. Then (a, b) is
  A)
   2, 17                            done clear
  B)
   3, 34         done clear
  C)
   34, 3                done clear
  D)
   5, 17 done clear
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• question_answer8)
  If \[\mathbf{m=}{{\left( \mathbf{1}-{{\mathbf{2}}^{\frac{\mathbf{1}}{\mathbf{4}}}} \right)}^{-\,\mathbf{1}}}\mathbf{,}\]then m can also be written as,
  A)
   \[\left( 1-\sqrt[4]{2} \right)\left( 2-\sqrt{2} \right)\]   done clear
  B)
   \[\left( 1-\sqrt[4]{2} \right)\left( 2+\sqrt{2} \right)\] done clear
  C)
   \[-\left( 1+\sqrt[4]{2} \right)\left( 1+\sqrt{2} \right)\] done clear
  D)
   \[\left( 1+\sqrt[4]{2} \right)\left( 2+\sqrt{2} \right)\] done clear
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• question_answer9)
  Euclid's division lemma: For any two positive integers 'a' and 'b', there exist unique integers 'q' and 'r' such that a = bq + r. What is the condition that 'r' must satisfy?
  A)
   \[0\le r\le b\]                  done clear
  B)
   \[0<r\le b\] done clear
  C)
   \[0\le r<b\] done clear
  D)
   \[0<r<b\] done clear
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• question_answer10)
  The 1000th  root of \[\mathbf{1}{{\mathbf{0}}^{\left( \mathbf{1}{{\mathbf{0}}^{\mathbf{10}}} \right)}}\] is
  A)
   \[{{10}^{77}}\]                                  done clear
  B)
   \[{{10}^{\left( {{10}^{7}} \right)}}\]   done clear
  C)
   \[{{\left( \sqrt[3]{10} \right)}^{{{10}^{5}}}}\]            done clear
  D)
   \[{{10}^{{{\left( \sqrt[3]{10} \right)}^{10}}}}\] done clear
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• question_answer11)

  The following are the first and last step in finding the H.C.F. of 36 and 56 using Euclid?s algorithm.

  Step 1:\[\mathbf{56= 36\times 1+20}\]

  Step 2: ____________

  Step 3: ____________

  Step 4:\[\mathbf{16=4\times 4+0}\]

  Choose the steps 2 and 3.

  (i)\[36=20\times 1+16\]

  (ii)\[24=20\times 1+4\]

  (iii)\[20\text{ }=16\times 1+4\]

  (iv)\[~56=18\times 2+20\]

  A)
   (i) and (ii)                      done clear
  B)
   (i) and (iii)     done clear
  C)
   (ii) and (iii)                    done clear
  D)
   (iii) and (iv) done clear
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• question_answer12)
  The difference between \[\mathbf{1}{{\mathbf{0}}^{{{\mathbf{(10)}}^{\mathbf{2}}}}}\] and \[{{\left( \mathbf{1}{{\mathbf{0}}^{\mathbf{10}}} \right)}^{\mathbf{2}}}\] is the order of
  A)
   0                                 done clear
  B)
   \[{{10}^{80}}\]           done clear
  C)
  \[{{10}^{20}}\]                       done clear
  D)
   None of these done clear
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• question_answer13)
  For what value of 'x' does \[{{\mathbf{3}}^{\mathbf{x}}}\] end with 5?
  A)
   0                                 done clear
  B)
   5              done clear
  C)
   500                              done clear
  D)
   Never ends with 5 done clear
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• question_answer14)
  When a number is divided by 19, its remainder is always
  A)
   Greater than 19 done clear
  B)
   Lies between 19 and 57 done clear
  C)
   Greater or equal to zero but less than 19  done clear
  D)
   Less than zero done clear
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• question_answer15)
  If 9 divides 6561, which of the following statements is true?
  A)
   9 divides 81    done clear
  B)
   7 divides 243    done clear
  C)
   7 divides 2178               done clear
  D)
   9 divides 2189 done clear
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• question_answer16)
  \[{{\mathbf{X}}_{\mathbf{1}}}\mathbf{,}{{\mathbf{X}}_{\mathbf{2}}}\mathbf{,}{{\mathbf{X}}_{\mathbf{3}}}....\mathbf{,}{{\mathbf{X}}_{\mathbf{12}}}\] are integers none of which are divisible by 3. The remainder when\[\mathbf{X}_{\mathbf{1}}^{\mathbf{2}}\mathbf{,X}_{\mathbf{2}}^{\mathbf{2}}\mathbf{,X}_{\mathbf{3}}^{\mathbf{2}}\mathbf{+}....\mathbf{+X}_{\mathbf{12}}^{\mathbf{2}}\] is divided by 3 is
  A)
   0    done clear
  B)
   0 or 2         done clear
  C)
   1 or 2                           done clear
  D)
   1 done clear
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• question_answer17)
  Diagonals of a rhombus are \[\left( {{\mathbf{2}}^{\mathbf{5}}}\mathbf{\times 7} \right)\] cm and \[\left( \mathbf{2\times }{{\mathbf{5}}^{\mathbf{2}}}\mathbf{\times }{{\mathbf{7}}^{\mathbf{3}}} \right)\] cm. Express the area of the rhombus in prime factorization form.
  A)
   \[2\times 5\times 7\text{ }c{{m}^{2}}\]             done clear
  B)
   \[{{2}^{2}}\times {{5}^{2}}\times {{7}^{2}}c{{m}^{2}}\]   done clear
  C)
   \[{{2}^{5}}\times {{5}^{2}}\times {{7}^{4}}c{{m}^{2}}\]    done clear
  D)
   \[~{{2}^{6}}\times {{5}^{2}}\times {{7}^{4}}c{{m}^{2}}\] done clear
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• question_answer18)
  Set of natural number is a subset of
  A)
   Set of even numbers       done clear
  B)
   Set of odd numbers done clear
  C)
   Set of composite numbers          done clear
  D)
   Set of real numbers. done clear
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• question_answer19)
  Choose the irrational number.
  A)
   \[3-\sqrt{9}\]                 done clear
  B)
   \[{{\left( \sqrt{12} \right)}^{2}}\]        done clear
  C)
   \[\sqrt{625}-\sqrt{576}\]             done clear
  D)
   \[\sqrt{125}-\sqrt{64}\] done clear
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• question_answer20)
  \[\mathbf{1/}\left( \sqrt{\mathbf{3}}\mathbf{-}\sqrt{\mathbf{2}} \right)\]is not equal to
  A)
   \[\sqrt{3}+\sqrt{2}\]                  done clear
  B)
   \[\frac{\sqrt{3}}{\left( 3-\sqrt{6} \right)}\] done clear
  C)
   \[\left( \sqrt{3}-\sqrt{2} \right)/\left( 5-2\sqrt{6} \right)\]      done clear
  D)
   \[\left( \frac{\sqrt{4}}{\sqrt{10}-\sqrt{8}} \right)\] done clear
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• question_answer21)
    Given \[\mathbf{a=p-}\sqrt{\mathbf{q}}\] and \[\mathbf{b=p+}\sqrt{\mathbf{q}}\] which of the following is correct. Where q is a prime number.
  A)
   a + b is irrational           done clear
  B)
   a - b is rational. done clear
  C)
   2ab is rational done clear
  D)
   \[\frac{a}{b}\] is rational done clear
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• question_answer22)
  According to the fundamental theorem of arithmetic, if p(a prime number) divides \[{{\mathbf{a}}^{\mathbf{2}}}\] and a is positive, then
  A)
   a divides p        done clear
  B)
   \[{{a}^{2}}\] divides p      done clear
  C)
   \[{{p}^{2}}\]divides \[{{a}^{2}}\]                  done clear
  D)
   p divides a done clear
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• question_answer23)
  Which of the following is a non-terminating repeating decimal?
  A)
   \[\frac{72}{6000}\]                               done clear
  B)
   \[\frac{1771}{8000}\] done clear
  C)
   \[\frac{123}{{{4}^{2}}\times {{5}^{4}}}\]                 done clear
  D)
   \[\frac{145}{{{4}^{3}}\times {{5}^{2}}\times {{7}^{2}}}\] done clear
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• question_answer24)
  The number in the form of 4K + 3 where K is whole number, is always;
  A)
   An odd number done clear
  B)
   An even number done clear
  C)
   A perfect square             done clear
  D)
   Divisible by 3 done clear
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• question_answer25)
  Choose the terminating decimal.
  A)
   \[\frac{641}{8000}\]      done clear
  B)
   \[\frac{29}{66}\] done clear
  C)
   \[\frac{283}{120}\]                               done clear
  D)
   \[\frac{617}{81}\] done clear
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• question_answer26)
  The number of subsets of A = {0, 1, 2} will be
  A)
   3                                 done clear
  B)
   5             done clear
  C)
   6                                 done clear
  D)
   8 done clear
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• question_answer27)
  Find the number which when divided by 87 leaves a remainder 49 and gives a quotient 50.
  A)
   3997                            done clear
  B)
   4399     done clear
  C)
   4301                            done clear
  D)
   4019 done clear
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• question_answer28)
  By what number must 1587 be divided to get a quotient 27 and remainder 21?
  A)
   58     done clear
  B)
   57            done clear
  C)
   59                                done clear
  D)
   63 done clear
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• question_answer29)
  At an event on Saraswati Puja for students, 1643 Calendars and 1060 sweets were to be distributed amongst students of class X such that each student gets the same number of calendar and also same number of sweets, what is the maximum number of students in class X?
  A)
   53         done clear
  B)
   93            done clear
  C)
   79                                done clear
  D)
   69 done clear
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• question_answer30)
  Which of the following is true for two co-prime numbers?
  A)
   Then- H.C.F. is 1.          done clear
  B)
   Their L.C.M. is 1. done clear
  C)
   Their H.C.F. is equal to their product. done clear
  D)
   Their L.C.M. is twice their H.C.F. done clear
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• question_answer31)

  Choose the methods that can be used to find the H.C.F. of any two numbers.

  (i) Euclid's division lemma

  (ii) Prime factorization

  (iii) Division of the numbers

  (iv) Product of numbers

   
  A)
   (i) and (iv) only  done clear
  B)
   (i), (ii) and (iii) only done clear
  C)
   (i), (iii) and (iv) only       done clear
  D)
   (ii), (iii) and (iv) only done clear
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• question_answer32)
  A positive number 'n' when divided by 9 leaves a remainder 6 what is the remainder when 3n + 2 is divided by 3?
  A)
   0                                 done clear
  B)
   1             done clear
  C)
   2        done clear
  D)
   3 done clear
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• question_answer33)
  The remainder when a number is divided by 165 is 21. What is the remainder, when the same number is divided by 11?
  A)
   4                                 done clear
  B)
   5             done clear
  C)
   11                                done clear
  D)
   10 done clear
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• question_answer34)
  Three distances are 8 m, 9 m 20 cm and 10 m 80 cm long. What is the greatest possible length which can be used to measure these ropes?
  A)
   40 cm    done clear
  B)
   50 cm         done clear
  C)
   60 cm              done clear
  D)
   1 m 20 cm done clear
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• question_answer35)
  Sohan purchased 98 fruits out of which 35 are oranges and the remaining 63 are mangoes. Oranges and mangoes are to be packed in separate bundles and each bundle must contain the same number of fruit. Find the least number of bundles which can be made of these 98 fruit.
  A)
   13                                done clear
  B)
   7             done clear
  C)
   14     done clear
  D)
   9 done clear
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• question_answer36)
  Two candidates during a physical test start running around a circular path. First candidate takes 22 minutes and second candidates takes 24 minutes to complete one round of the path. If both of them start at the same point, then find after how many minutes they will meet again at the same starting point.
  A)
   46 minutes                    done clear
  B)
   1 hour 22 minutes done clear
  C)
   92 minutes                    done clear
  D)
   4 hours 24 minutes done clear
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• question_answer37)
  The sum of \[{{\mathbf{1}}^{\mathbf{2}}}\mathbf{+}{{\mathbf{2}}^{\mathbf{2}}}\mathbf{+}......{{\mathbf{n}}^{\mathbf{2}}}\] is
  A)
   \[\frac{n{{(n+1)}^{3}}}{3}\]               done clear
  B)
   \[\frac{(n+1){{n}^{2}}}{6}\] done clear
  C)
   \[\frac{n(n-1)(2n+1)}{12}\]        done clear
  D)
   \[\frac{n(n+1)(2n+1)}{6}\] done clear
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• question_answer38)
  The sum of \[{{\mathbf{1}}^{\mathbf{3}}}\mathbf{+}{{\mathbf{2}}^{\mathbf{3}}}\mathbf{+}........{{\mathbf{n}}^{\mathbf{3}}}\] is
  A)
   \[\frac{{{n}^{2}}(2n+1)(3n+2)}{6}\]   done clear
  B)
   \[\frac{{{n}^{2}}{{(n+1)}^{2}}}{4}\] done clear
  C)
   \[\frac{{{n}^{3}}(n-1)}{3}\]                done clear
  D)
   \[\frac{{{(n-3)}^{2}}(n+5)}{9}\] done clear
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• question_answer39)
  Find the sum of\[{{\mathbf{2}}^{\mathbf{2}}}\mathbf{+}{{\mathbf{3}}^{\mathbf{2}}}\mathbf{+}........\mathbf{10}{{\mathbf{0}}^{\mathbf{2}}}\].
  A)
   338349       done clear
  B)
   99999         done clear
  C)
   103245            done clear
  D)
   563000 done clear
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• question_answer40)
  Find the sum of \[{{\mathbf{2}}^{\mathbf{2}}}\mathbf{+}{{\mathbf{4}}^{\mathbf{2}}}\mathbf{+}{{\mathbf{6}}^{\mathbf{2}}}........{{\mathbf{(2n)}}^{\mathbf{2}}}\].
  A)
   \[\frac{n{{(n+1)}^{3}}}{3}\]               done clear
  B)
   \[\frac{2n(n+1)(2n+1)}{3}\] done clear
  C)
   \[\frac{n(n-3)(2n+3)}{12}\]        done clear
  D)
   \[\frac{n(n+1)(2n+4)}{6}\] done clear
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