CBSE Class 10 Mathematics Number Systems Assignment Set 02

School Assignments for Class 10 Mathematics: Number System

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Number System MCQ Questions with Answers Class 10 

Question- π is
(1) Rational
(2) Irrational
(3) Imaginary
(4) An integer
Ans-2
 
Question- An irrational number is
(1) A terminating and nonrepeating decimal
(2) A nonterminating and nonrepeating decimal
(3) A terminating and repeating decimal
(4) A nonterminating and repeating decimal
Ans-2
 
Question- Which of the following statement is true ?
(1) Every point on the number line represents a rational number
(2) Irrational numbers cannot be represented by points on the number line
(3) 22/7 is a rational number
(4) None of these
Ans- 2
 
Question- The sum of rational and irrational number is always
(1) Rational
(2) Irrational
(3) Both
(4) Can't say
Ans- 2
 
Question- The product of rational and irrational number is always
(1) Rational
(2) Irrational
(3) Both
(4) Can't say
Ans-2 
 
Question- 961/625 is a
(1) Terminating decimal
(2) Nonterminating decimal
(3) Cannot be determined
(4) None of these
Ans- 1
 
Question- Which of the following has most number of divisors ?
(1) 99
(2) 101
(3) 176
(4) 182
Ans-3 
 
Question-A number n is said to be perfect if the sum of all its divisors (excluding n itself) is equal to n. An example of perfect number is
(1) 6
(2) 9
(3) 15
(4) 21
Ans-1 
 
Question-The least number which should be added to 2497 so that the sum is exactly divisible by 5, 6, 4 and 3 is
(1) 3
(2) 13
(3) 23
(4) 33
Ans-3 
 
Question-The least number which is a perfect square and is divisible by each of the numbers 16, 20 and 24, is
(1) 1600
(2) 3600
(3) 6400
(4) 14400
Ans-2 
 
Question-The smallest number which when diminished by 7,is divisible by 12, 16, 18, 21 and 28 is
(1) 1008
(2) 1015
(3) 1022
(4) 1032
Ans-2 
 
Question-The least number which when increased by 5 is divisible by each one of 24, 32, 36 and 54, is
(1) 427
(2) 859
(3) 869
(4) 4320
Ans-2 
 
Question-The least number, which when divided by 12, 15, 20 and 54 leaves in each case a remainder of 8, is
(1) 504
(2) 536
(3) 544
(4) 548
Ans-4 
 
Question-The largest four-digit number which when divided by 4, 7 or 13 leaves a remainder of 3 in each case, is
(1) 8739
(2) 9831
(3) 9834
(4) 9893
Ans-2 
 
Question-The least multiple of 7, which leaves a remainder of 4, when divided by 6, 9, 15 and 18 is
(1) 74
(2) 94
(3) 184
(4) 364
Ans-4 
 
Question-The least number, which when divided by 48, 60,72, 108 and 140 leaves 38, 50, 62, 98 and 130 as remainders respectively, is
(1) 11115
(2) 15110
(3) 15120
(4) 15210
Ans-2 
 
Question-Find the least multiple of 23, which when divided by 18, 21 and 24 leaves remainders 7, 10 and 13 respectively.
(1) 3002
(2) 3013
(3) 3024
(4) 3036
Ans- 2
 
Question- The least number which when divided by 5, 6, 7 and 8 leaves a remainder 3, but when divided by 9 leaves no remainder, is
(1) 1677
(2) 1683
(3) 2523
(4) 3363
Ans-2 
 
Question- The product of two numbers is 960. If H.C.F. is 8, then the numbers are
(1) 24,40
(2) 8, 120 or 24, 40
(3) 8, 140
(4) none of these
Ans-2 
 
Question- The least number divisible by 12, 15, 20, and is perfect square is
(1) 900
(2) 400
(3) 36
(4) 256
Ans- 1
 
Question- The largest number which divides 133 and 245 leaving a remainder 5 is
(1) 17
(2) 15
(3) 8
(4) 16
Ans-4 
 
Question- The H.C.F,. of two numbers is 1/5 of their L.C.M. If the product of two number is 720, then the H.C.F. of the numbers is
(1) 13
(2) 12
(3) 14
(4) 18
Ans-2 
 
Question- The L.C.M. of two numbers is 39780 and their ratio is 13 : 15 then the numbers are
(1) 273,315
(2) 2652,3060
(3) 516, 685
(4) none
Ans-2 
 
Question- The L.C.M. of two numbers is 14 times of their H.C.F. The sum of L.C.M. and H.C.F. is 600. If one of the number is 80, then other is
(1) 280
(2) 218
(3) 25
(4) 45
Ans-1
 
Question- A heap is to be formed with lots of 8, 10 and 15 pebbles of different colours. The smallest number of pebbles in the heap is
(1) 121
(2) 120
(3) 110
(4) 8
Ans-2
 
Question- Three measuring tapes are 64 cm, 72 cm, 96 cm, the shortest length that can measured by any one of the tapes exactly is
(1) 576
(2) 120
(3) 8
(4) 10.
Ans-1

 

More question-

 

1. If the H C F of 657 and 963 is expressible in the form of 657x + 963x - 15 find x.

(Ans:x=22)

Ans:       Using Euclid’s Division Lemma

                      a= bq+r , o ≤ r < b

                     963=657×1+306

                     657=306×2+45

                    306=45×6+36

                   45=36×1+9

                   36=9×4+0

            HCF (657, 963) = 9

         now 9 = 657x + 963× (-15)

              657x=9+963×15

                 =9+14445

              657x=14454

           x=14454/657

              x=22

 

2. Express the GCD of 48 and 18 as a linear combination. (Ans: Not unique)

                        A=bq+r, where o ≤ r < b

                        48=18x2+12                     

                       18=12x1+6

                        12=6x2+0

                     HCF (18,48) = 6

                     now 6= 18-12x1

                    6= 18-(48-18x2)

                    6= 18-48x1+18x2

                   6= 18x3-48x1                  

                   6= 18x3+48x(-1)

                   i.e. 6= 18x +48y 

 6= 18×3 +48×(-1)
 
=18×3 +48×(-1) + 18×48-18×48

=18(3+48)+48(-1-18)

=18×51+48×(-19)

6=18x+48y

Hence, x and y are not unique.
 
3. Prove that one of every three consecutive integers is divisible by 3.

Ans:
n,n+1,n+2 be three consecutive positive integers

We know that n is of the form 3q, 3q +1, 3q + 2

So we have the following cases

Case – I when n = 3q

In the this case, n is divisible by 3 but n + 1 and n + 2 are not divisible by 3

Case - II When n = 3q + 1

Sub n = 2 = 3q +1 +2 = 3(q +1) is divisible by 3. but n and n+1 are not

divisible by 3
 
Case – III When n = 3q +2

Sub n = 2 = 3q +1 +2 = 3(q +1) is divisible by 3. but n and n+1 are not  divisible by 3

Hence one of n, n + 1 and n + 2 is divisible by 3

4. Find the largest possible positive integer that will divide 398, 436, and 542 leaving remainder 7, 11, 15 respectively.
(Ans: 17)

Ans: The required number is the HCF of the numbers

Find the HCF of 391, 425 and 527 by Euclid’s algorithm

 HCF (425, 391) = 17

Now we have to find the HCF of 17 and 527

527 = 17 X 31 +0
 
 
 
Please click the link below to download CBSE Class 10 Mathematics Number Systems Assignment Set B
 

Free study material for Mathematics

Chapter Assignment & Practice Material for Class 10 Mathematics Number System

Chapter Practice Questions for Class 10 Mathematics

Review targeted chapter assignments for Class 10 Mathematics Number System. Built according to official CBSE guidelines, these downloadable problem sets help students build accuracy and prepare effectively for school tests.

Key Advantages of Solving Number System Assignments

  • Exam Alignment: Questions strictly follow contemporary CBSE sample papers and grading schemes.
  • Comprehensive Coverage: Features objective drills, case studies, and structured descriptive problems for Number System.
  • Pacing & Precision: Regular problem-solving builds critical calculation speed and test-taking accuracy.

How to Approach Mathematics Number System Assignments

  1. Textbook Review: Always study the core NCERT book for Class 10 Mathematics prior to beginning the assignment.
  2. Independent Attempt: Solve Number System questions on your own initially before cross-checking with expert solutions.
  3. Error Tracking: Record challenging concepts in a dedicated notebook and practice online MCQ tests for revision.

FAQs

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Are the assignments for Class 10 Mathematics Number System based on the 2026 exam pattern?

Yes. These assignments are designed as per the latest CBSE syllabus for 2026. We have included huge variety of question formats such as MCQs, Case-study based questions and important diagram-based problems found in Number System.

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