MCQ - Real Number - Class 10 - Part 4

31. If a and b are positive integers, then HCF(a,b) x LCM (a,b) =

                a) a x b                  b) a + b                 c) a – b                  d) a/b

32. π is –

                a) a natural number                        b) not a real number

                c) a rational number                       d) an irrational number

33.  The missing number in the factor tree is-

a)       4                                      b) 5                                        c) 6                         d) 8

34. 91/625   , when written in decimal form terminates; as the factor of denominator are in the form of 2^m x 5ⁿ. This number will terminate after how many digits?

                a) 1                         b) 2                        c) 3                         d) 4

35.  Decimal representation of rational number 8/27 is –

                a) 0.                b) 0.29                 c) 0.2                 d) none of these

36. The HCF and LCM of two numbers are 4 and 9696, then the product of two numbers is –

                a) 9696                  b) 24242               c)38784                                 d) 4848

37. A number p/q when expressed in decimal form terminates after 7 digits then factor of q are of the form of x^m × yⁿ; the value of x + y should be –

                a) 7                         b) 14                      c) 9                         d) 26

38. The HCF of two numbers is 8, which one of the following can never be their LCM

                a) 24                      b) 48                      c) 56                       d) 60

39. The LCM of two co-prime number is 638. One number is 29, find the other number

                a) 16                      b) 22                      c) 36                       d) 17

40. IF A, B and C are three numbers such that LCM of A and B is B and the LCM of B and C is C then LCM of A, B and C is

                a) A                        b) B                        c) C                         d)

NB :- Answer is marked with red


DR RAJESH KUMAR THAKUR

MCQ - Real Number - Class 10 - Part 3

21. The rational number that corresponds to 0.6 + 0.  + 0.4  is –

                a) 83/90                b)7/9                                     c) 43/90                                d) 167/90

22.  The HCF of two consecutive rational number p and p + 1 is

                a) p                        b) p+ 1                                  c) 1                                         d) 0

23. If pⁿ = ( a x 5)ⁿ, for pⁿ to end with the digit zero a = ---- for any natural number n is –

                a)  any natural number                  b) any even number                      

                c) any odd number                          d) none

24. 2 -  is –

                a) a rational number                       b) a natural number                       

                c) an irrational number                  d) a whole number

25. The number given below which always ends with the digit 6 for all-natural numbers n is –

                a) 4ⁿ                                                       b) 6ⁿ

                c) 2ⁿ                                                       d) 8ⁿ

26. There is a circular path around a field. Nilabh takes 22 minutes to complete one round while Nishtha takes 20 minutes to complete the same. If they both start at the same time and move in the same direction, after how many minutes will they meet again at the starting point?

                a) 220                    b) 3.4                     c) 440                    d) 4.4

27.  If two positive integers p and q can be expressed as p = ab² and b = xy² ; a, b being prime number then LCM( p ,q) is –

                a) ab                      b) a²b²                  c)a³b²                    d)a²b³

28.  Any one of number m, m + 2 and m + 4 is a multiple of –

                a) 2                         b) 3                        c) 4                         d) 5

29. If p is a prime number and p divides k² , then p divides :-

                a) 2k²                     b) k                        c) 3k                       d) none of these

30. If p = HCF (100, 190) and q = LCM (100,190) then p²q² is

                a)3.61 x 10⁶         b)3.61 x 10³         c) 3.61 x 10⁵        d)3.61 x 10⁸

^{NB :- Answer is marked with red colour}

MCQ - Real Number - Class 10 - Part 2

11. A number which can be expressed in the form of p/q, where q ≠ 0 is a rational number is:-

                a) p and q are co- prime number              

                b) p and q are real numbers

                c) p and q are irrational numbers

                d) p and q are integers

12. n² – 1 is divisible by 8, if n is

                a) an integer                                                      b) a natural number                       

c) an odd number                                            d) an even number

13. If a non- zero rational number is multiplied by an irrational number then we always get –

                a) an irrational number                                 b) a rational number

                c) zero                                                                  d) one

14.  The largest number which divides 70 and 125 leaving remainder 5 and 8 respectively is –

                a) 13                      b) 65                      c) 875                    d) 1750

15. The product of a non-zero rational and an irrational number is –

                a) always irrational                          b) always rational

                c) rational or irrational                   d) one

16. If we write 0  as a rational number, we get

                a) 9/10                  b) 1                        c) 5/10                  d) 0

17. Write an irrational number between 2 and 3 is –

                a) 2.5                     b) 2.001                                c) 2.1333333456…                             d) 2.1

18. The least number that is divisible by all numbers from 1 to 10 (both inclusive) is –

                a) 10                      b) 100                                    c) 504                                    d) 2520

19. if the HCF of 65 and 117 is expressible in the form of 65m – 117 then the value of m is –

                a) 1                         b) 2                                        c) 3                                         d) 4

20. The greatest number that divides 87 and 97 leaving 7 as remainder is –

                a) 10                      b) 1                                        c) 87 x 97                             d) 6300

Dr Rajesh Kumar Thakur

NB :- Answer is written with red colour

MCQ - Class 10 - Real Number - Part 1

1.  For The given positive integers, a and b, there exist unique integer q and r satisfying a = bq + r where  is known as -

a)  Fermat Lemma                                                    

b) Gauss lemma                                                     

c) Euclid division lemma                                      

 d) Poincare Lemma

2.  The sum or difference of a rational and an irrational number will be

    a)  Rational                                     b) Irrational

    c) Natural                                        d) Whole

3. Let x = be a rational number such that the prime factorization of q is not of the form of 2^m. 5ⁿ; where m and n being non – negative integers, then x has a ------------------ decimal expansion.

                   a) non terminating repeating                   b) terminating

                   c) non terminating non repeating          d) none of these

4. “Every composite number can be expressed as a product of primes, and this expression is unique, apart from the order in which the prime factors occur”. This statement is better known as –

                 a) Fundamental Theorem of Algebra      b) Fundamental theorem of Arithmetic

                 c) Fundamental theorem of geometry   d) None of these

 5. For some integer m, every even integer is of the form

                a) m                       b ) m + 1                               c) 2m                     d) 2m + 1

 6. For some integer q, every odd integer is of the form

                a) q                        b) q + 1                                 c) 2q                      d) 2q + 1

 7.  The unit digit obtained on simplifying 207 x 39 x 72 x 94 is:

                a) 2                         b) 3                                        c) 4                         d) 0

8.  Total number of even prime number is: -

                a) 0                         b) 1                        c) 2                                         d) 3

9. How many rational number can be obtained between 2 and 3:-

                a) 2                         b) 5                        c) infinite                             d) 1000

10. If mⁿ = 32, where m and n are positive integers, then the value of n^mn is :-

                a) 234                    b) 2¹⁰                     c) 5¹⁰                                      d) 5²⁴

^{Dr Rajesh Kumar Thakur} 

^{Note : - Answer is marked here with Red colour}