10th Class Mathematics Real Numbers Question Bank

done Real Numbers Total Questions - 47

• question_answer1)
  The L.C.M. and H.C.F. of marks scored by Ajit and Amar in a math test are 5040 and 12 respectively. If Amar's score is 144, what is Ajit's score?
  A)
   288                                        done clear
  B)
   132 done clear
  C)
   564                        done clear
  D)
          420 done clear
  View Solution play_arrow

• question_answer2)
  '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] nor [b]. done clear
  View Solution play_arrow

• question_answer3)
  The factor tree shows the prime factorization of 1314. Find the respective values of 'a' and 'b'.
  A)
   3, 37                      done clear
  B)
          3, 73 done clear
  C)
   73, 3                      done clear
  D)
          9, 73 done clear
  View Solution play_arrow

• question_answer4)
  The following are the first and last steps in finding the H.C.F. of 408 and 1032 using Euclid's algorithm.

  Step 1: \[\text{1}0\text{32}=\text{4}0\text{8}\times \text{2}+\text{216}\]

  Step 2: ___________

  Step 3: ___________

  Step 4: \[\text{192 }=\text{24}\times \text{8}+0\]

  Choose the steps 2 and 3.

  (i) 408=2161+1921

  (ii) 408=216+180+12

  (iii) 216 =192 1 + 24

  (iv) 192 = 24 8 + 0

  A)
   (i) and (ii)            done clear
  B)
   (i) and (iii) done clear
  C)
   (ii) and (iii)      done clear
  D)
          (iii) and (iv) done clear
  View Solution play_arrow

• question_answer5)
  For what value of 'x' does 6x end with 5?
  A)
   0 done clear
  B)
   1 done clear
  C)
   5 done clear
  D)
   Never ends with 5. done clear
  View Solution play_arrow

• question_answer6)
  If 4 divides 1728, which of the following statements is true?
  A)
   4 divides 12.   done clear
  B)
          6 divides 1728. done clear
  C)
   2 divides 1728. done clear
  D)
          4 divides 144. done clear
  View Solution play_arrow

• question_answer7)
  Dimensions of a rectangle are\[({{2}^{5}}\times 7)cm\]and\[(\text{2}\times {{\text{5}}^{\text{2}}}\times {{\text{7}}^{\text{3}}})cm\]. Express the area of the rectangle in prime factorization form.
  A)
   \[\text{2}\times \text{5}\times \text{7c}{{\text{m}}^{\text{2}}}\]  done clear
  B)
          \[2\times 73c{{m}^{2}}\] done clear
  C)
   \[\text{26}\times \text{52}\times \text{74 c}{{\text{m}}^{\text{2}}}\] done clear
  D)
         \[\text{25}\times \text{52}\times \text{73c}{{\text{m}}^{\text{2}}}\] done clear
  View Solution play_arrow

• question_answer8)
  Choose the irrational number.
  A)
   \[2-\sqrt{4}\]                    done clear
  B)
          \[{{(\sqrt{5})}^{2}}\] done clear
  C)
   \[\sqrt{9}-\sqrt{4}\]      done clear
  D)
          \[\sqrt{2}-\sqrt{3}\] done clear
  View Solution play_arrow

• question_answer9)
  Given\[a=3-\sqrt{2}\]. and\[b=3+\sqrt{2}\], which of the following is correct?
  A)
   a + b is irrational. done clear
  B)
   a - b is rational. done clear
  C)
   ab is rational. done clear
  D)
   \[\frac{a}{b}\]is rational. done clear
  View Solution play_arrow

• question_answer10)
  Euclid's division lemma: For any two positive integers 'a' and 'b', there exist unique integers 'q' and 'r' such that\[\text{a}=\text{bq}+\text{r}\]. 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
  View Solution play_arrow

• question_answer11)
  Which of the following is a non-terminating repeating decimal?
  A)
   \[\frac{24}{1600}\]                         done clear
  B)
   \[\frac{171}{800}\] done clear
  C)
   \[\frac{123}{{{2}^{2}}\times {{5}^{3}}}\]               done clear
  D)
          \[\frac{145}{{{2}^{3}}\times {{5}^{2}}\times {{7}^{2}}}\] done clear
  View Solution play_arrow

• question_answer12)
  Choose the terminating decimal.
  A)
   \[\frac{141}{1000}\]       done clear
  B)
          \[\frac{17}{30}\] done clear
  C)
   \[\frac{271}{90}\]                            done clear
  D)
          \[\frac{53}{343}\] done clear
  View Solution play_arrow

• question_answer13)
  Find the number which when divided by 43 leaves a remainder 32 and gives a quotient 25.
  A)
   1045                                      done clear
  B)
   1107 done clear
  C)
   1150                                      done clear
  D)
   1105 done clear
  View Solution play_arrow

• question_answer14)
  By what number must 1789 be divided to get a quotient 29 and remainder 49?
  A)
   60                          done clear
  B)
          61 done clear
  C)
   59                                          done clear
  D)
   52 done clear
  View Solution play_arrow

• question_answer15)
  What is the L.C.M. of 140 and 605 if their H.CF. is H?
  A)
   8000                      done clear
  B)
          5500 done clear
  C)
   8400                                      done clear
  D)
   7700 done clear
  View Solution play_arrow

• question_answer16)
  910 blue pens and 1001 red pens are distributed to students of class X so that each student gets the same number of pens of each kind. What is the maximum strength of the class?
  A)
   91                          done clear
  B)
          80 done clear
  C)
   94                          done clear
  D)
          86 done clear
  View Solution play_arrow

• question_answer17)
  Books in a library are stacked in such a way that they are stored subject wise and the stacks are of the same size. If there are 144 Geography books, 384 History books and 240 Economics books, in the library, in how many stacks can the books be arranged?
  A)
   18                          done clear
  B)
          14 done clear
  C)
   16                          done clear
  D)
          12 done clear
  View Solution play_arrow

• question_answer18)
  What is the L.C.M. of\[\frac{6}{14}\]and\[\frac{2}{7}\]?
  A)
   \[\frac{3}{7}\]                   done clear
  B)
          \[\frac{6}{7}\] done clear
  C)
   \[\frac{4}{7}\]                   done clear
  D)
          \[\frac{5}{7}\] done clear
  View Solution play_arrow

• question_answer19)
  Which of the following is an incorrect statement?                           
  A)
   If\[\sqrt{a}+\sqrt{b}\]is an irrational number, then\[\sqrt{ab}\]is also an irrational number. done clear
  B)
   The reciprocal of an irrational number is always an irrational number. done clear
  C)
   There are infinitely many rational numbers between any two irrational numbers. done clear
  D)
   \[\text{7}\times \text{13}+\text{13}\]is a prime number. done clear
  View Solution play_arrow

• question_answer20)
  Which of the following is true for two co- prime numbers?
  A)
   Their H.C.F. is 1. done clear
  B)
   Their L.CM. 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
  View Solution play_arrow

• question_answer21)
  The difference of the L.C.M. and H.C.F. of 210 and 55 is expressed as 210 x 6 + 55y. What is the value of\[{{\text{y}}^{\text{3}}}\]?
  A)
   361                        done clear
  B)
          19 done clear
  C)
   55                          done clear
  D)
          6859              done clear
  View Solution play_arrow

• question_answer22)
  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
  View Solution play_arrow

• question_answer23)
                           A positive number 'n' when divided by 8 leaves a remainder 5. What is the     remainder when\[\text{2n}+\text{4}\]is divided by 8?    
  A)
   8                             done clear
  B)
          1                    done clear
  C)
   6            done clear
  D)
          0 done clear
  View Solution play_arrow

• question_answer24)
  The remainder when a number is divided by 143 is 31.What is the remainder when the same number is divided by 11?
  A)
   5                             done clear
  B)
          7 done clear
  C)
   6                             done clear
  D)
          9 done clear
  View Solution play_arrow

• question_answer25)
  Three ropes are 7 m, 12 m 95 cm and 3 m 85 cm long. What is the greatest possible length which can be used to measure these ropes?
  A)
   35 cm                   done clear
  B)
          55 cm done clear
  C)
   1 m                        done clear
  D)
          65 cm done clear
  View Solution play_arrow

• question_answer26)
  Three bulbs are connected in such a manner that they glow for every 24 seconds, 36 seconds and 54 seconds respectively. All of them glow at once at 8 a.m. When will they again glow simultaneously?
  A)
   8:30:36 a.m. done clear
  B)
          8:03:36 a.m. done clear
  C)
   8:36:03 a.m. done clear
  D)
          8:36:30 a.m. done clear
  View Solution play_arrow

• question_answer27)
  Find The largest number which divides the numbers 120, 224 and 256.
  A)
   8            done clear
  B)
          6 done clear
  C)
   4            done clear
  D)
          5 done clear
  View Solution play_arrow

• question_answer28)
  A book seller purchased 117 books out of which 45 books are of mathematics and the remaining 72 books are of physics. Each book has the same size. Mathematics and physics books are to be packed in separate bundles and each bundle must contain the same number of books. Find the least number of bundles which can be made of these 117 books.
  A)
   8                             done clear
  B)
          11 done clear
  C)
   13                                          done clear
  D)
   9 done clear
  View Solution play_arrow

• question_answer29)
  Sandeep donated 75 glucose biscuits and 45 monaco biscuits to the students of a class. These are to be packed in identical packets. The two type of biscuits are to be packed separately and each containing the equal number of biscuits. Find the least number of glucose and monaco biscuit packets respectively.
  A)
   5, 15                      done clear
  B)
          5, 3 done clear
  C)
   2, 3                                        done clear
  D)
   3, 2 done clear
  View Solution play_arrow

• question_answer30)
  An army contingent of 616 members is to march behind an army band of 32 members in a parade. The two groups are to march in the same number of columns. What is the maximum number of columns in which they can march?
  A)
   3                             done clear
  B)
          8 done clear
  C)
   12                          done clear
  D)
          4 done clear
  View Solution play_arrow

• question_answer31)
  96 books of English, 240 books of hindi and 336 books of mathematics have to be packed in bundles with each bundle containing equal number of books of each of the subjects. What is the difference of the largest number of books which can be packed in each bundle and the least number of bundles which can be made?
  A)
   1                             done clear
  B)
          3 done clear
  C)
   34                          done clear
  D)
          48 done clear
  View Solution play_arrow

• question_answer32)
  Which of the following is true about \[\text{17}\times \text{41}\times \text{43}\times \text{61}+\text{43}\]?
  A)
   It is a prime number. done clear
  B)
   It is a composite number. done clear
  C)
   It is an odd number. done clear
  D)
   Both [a] and [b] done clear
  View Solution play_arrow

• question_answer33)
  A circular field has a circumference of 360 km. Two cyclists Sumeet and John start together and cycle at speeds of 12 km/hr and 15 km/hr respectively, a round the circular field. After how many hours will they meet again at the starting point?
  A)
   100 hours           done clear
  B)
          171 hours done clear
  C)
   120 hours                           done clear
  D)
   140 hours done clear
  View Solution play_arrow

• question_answer34)
  Find the H.C.F. of 6930 and 8085.
  A)
   1155                      done clear
  B)
          2205 done clear
  C)
   1515                      done clear
  D)
          2025 done clear
  View Solution play_arrow

• question_answer35)
  If 0.2317 is expressed in the form of\[\frac{p}{q}\] where 'p' and 'q' are co-prime and also 'q' is in the form\[{{2}^{n}}\times {{5}^{m}}\]what are the values of 'm' and 'n' respectively?
  A)
   4 and 3                 done clear
  B)
          4 and 5 done clear
  C)
   4 and 4                 done clear
  D)
          3 and 4 done clear
  View Solution play_arrow

• question_answer36)
  If 0.737373..... is expressed in the form of\[\frac{p}{q}\], where 'p' and 'q' are co-primes, what are the prime factors of 'q'?
  A)
   4 and 7                 done clear
  B)
          3 and 11 done clear
  C)
   7 and 11              done clear
  D)
          4 and 3 done clear
  View Solution play_arrow

• question_answer37)
  Which of the following is correct about\[\frac{41}{37500}\]
  A)
   It is a non-terminating repeating decimal. done clear
  B)
   It is a terminating repeating decimal. done clear
  C)
   It is a terminating and not repeating decimal. done clear
  D)
   It is a non-terminating and not repeating decimal. done clear
  View Solution play_arrow

• question_answer38)
  Find the L.C.M. of 3465 and 5460.
  A)
   181080                                 done clear
  B)
   180180 done clear
  C)
   108108                 done clear
  D)
          108801 done clear
  View Solution play_arrow

• question_answer39)
  If the LCM Of (480,672) = 3360, find H.C.F. of (480,672).
  A)
   75                                          done clear
  B)
   69 done clear
  C)
   67                                          done clear
  D)
   96 done clear
  View Solution play_arrow

• question_answer40)
  Find the respective values of H.C.F. and L.C.M. of 5474, 9775 and 11730.
  A)
   391 and 410550 done clear
  B)
   319 and 401550 done clear
  C)
   410550 and 319 done clear
  D)
   405150 and 193 done clear
  View Solution play_arrow

• question_answer41)
  The circumferences of the front wheel and the rear wheels of a tricycle are 120 cm and 90 cm respectively. Before beginning to ride the tricycle, Ruth marks the points where the tyres touch the ground as A and B respectively on the front and the rear wheels. How many revolutions do the front and rear wheel make when both A and B touch the ground again simultaneously?
  A)
   6, 8     done clear
  B)
                                          3, 4 done clear
  C)
   9, 12                      done clear
  D)
          1, 4 done clear
  View Solution play_arrow

• question_answer42)
  Which of the following is a correct statement
  A)
   \[\pi \]is a natural number. done clear
  B)
   \[\pi \]is an irrational number. done clear
  C)
   \[\pi \]is not defined. done clear
  D)
   The value of \[\pi \]is \[\frac{22}{7}\]. done clear
  View Solution play_arrow

• question_answer43)
  The product of L.C.M. and H.C.F. of two numbers is 88288. If one of the numbers is 248, find the other number.
  A)
   356                        done clear
  B)
          635 done clear
  C)
   365                        done clear
  D)
          653 done clear
  View Solution play_arrow

• question_answer44)
  The L.C.M. of 318 and 477 is expressed as\[\text{159}\times \text{p}+\text{318}\].What is the value of 'p'?
  A)
   2                             done clear
  B)
          4 done clear
  C)
   3                             done clear
  D)
          0 done clear
  View Solution play_arrow

• question_answer45)
  A rectangular metal piece of dimensions 360 cm by 280 cm is cut into some identical small squares. If the side of each square has the largest possible length, find the number of square pieces formed.
  A)
   126                        done clear
  B)
          20 done clear
  C)
   40                          done clear
  D)
          63 done clear
  View Solution play_arrow

• question_answer46)
  In a school, the duration of a period in junior section is 40 minutes and in senior section is 60 minutes. If the first bell for each section rings at 9 a.m., when will the two bells ring together again?
  A)
   10:45 a.m.     done clear
  B)
          10:15 a.m. done clear
  C)
   12:00 p.m.     done clear
  D)
          11:00 a.m. done clear
  View Solution play_arrow

• question_answer47)
  M The prime factorization of two numbers are \[{{\text{3}}^{\text{2}}}\times {{\text{7}}^{\text{3}}}\times 11\] and\[\text{3}\times {{\text{7}}^{\text{2}}}\times {{11}^{\text{3}}}\times \text{17}\]. Which of the following is a common factor of the numbers?
  A)
   1683                                      done clear
  B)
   5831 done clear
  C)
   1089                      done clear
  D)
          539 done clear
  View Solution play_arrow