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}

Positive Thinking - Part 2 - K Bhanumoorthy

Instead of having expectations with negative thinking, the student should have thought with open mind and positive thinking. Then there would have been every possibility to correct  himself/herself.

Here are Positive ideas /Thinking which would have helped the student

1 .As I am studying well and regular in studies, quarrel between my

    Parents have been getting reduced.

2. As I am being a good student, I get good friends.

3. I am able to achieve the target /aim, by maintaining good health.

4. I do clarify doubts then and there from the subject teachers, so able  

     to  understand  and  learn in a better way.

5. I do respect and love my elder sister and elder brother, so they extend   

    support  and  help  in my studies.

6. I am friendly with my neighbour and have cordial relation with others  

     thereby  I do get help from them.

7. The student who is sitting by the side of me is being corrected then and

     there  when  a mistake is committed; results in, we two learn easily.

8. Since I approach the other people with right attitude, my problems

     are  heard,  I am being helped.

To sum up ,the student might not have lacked behind other students, had he thought with POSITIVE THINKING (note), he /she would have succeeded in studies , why in studies in life too. There ends the discussion.

Conclusion:  In life skills one of the important points is “SELF AWARENESS” which deals with

a)  Areas where strong and weak;

 b) Conscious about health, good character;

c)  Likes and dislikes.

A Chinese proverb to ponder over:

“He who blames others has a long way to go on his journey,

   He who blames himself is half way there

   He who blames no one has arrived.”  

A positive thinking makes any one happier and  more  resilient.

K Bhanumoorthy

Positive Thinking - By K Bhanumoorthy

Reference:  From an article published in Tamil weekly magazine .The contents are very interesting and related to board examination results. I would like to share the matter which is related with academic and progress of students in studies.

This write up is on, the pass percent of a school in board examination. A conversation between a School Head  (SH)  and  another person .The SH was asked ,the pass % of the school,  the answer was “ not bad , though not got 100%  results.“  In continuation, SH presumed and said that there is deterioration, in positive thinking of school students. The reason for such a statement was that the SH has seen the marks obtained by a below average student. The student was asked to give the reasons for the less marks. The SH was shattered and shocked to hear the reasons.  Here were the reasons stated by the student.

·        Had my parents not quarreled while studying, I would have got more Marks.

·        Had I got good friends, I would have clarified doubts with them.

·        Had I acquired good health, still more marks I might have secured.

·        Had my teachers taught much better in an effective way, I might have secured more.

·        Had my elder sister and elder brother helped in my studies, some more marks I would have  scored.

·        Had my neighbor kept TV volume low, I would  have  paid more attention in studies.

·        Had the student who has been sitting by my side, paid due attention, I also would have paid more attention.

·        Had I got opportunities to clarify/speak in class, I would have solved my problems in subjects, attained better position getting some more marks.

These are some of the aspects and reasons listed by the student seem to be correct and justifiable, for his age. Yet! ……

----to be continued

K Bhanumoorthy