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

Error in Mathematics - K . Bhanumoorthy

Analyzing the common errors made in Mathematics

Analyzing the common errors will lead us to identify the cause when it happens consistently. Here we discuss about some types of common errors.

Types of Errors: Careless Errors, Computational Errors, and Conceptual Errors.

Careless Errors

These errors occur on account of lack of attention or working too fast. Here are some examples: Copying the problem wrongly, posting a wrong number from the question, Sign, negative / positive. No clear handwriting, on some occasions even over writing.

Remedial ways: First and foremost is to slow down, pay attention what is given, what is asked. Either circling or under lining important information, what to do especially in word problems.

Computational Errors

Mistakes are committed in the process; mistakes are done on the incorrect operation (addition, subtraction, multiplication, division). Making one computational mistakes lead to further mistakes.

Remedial ways: A teacher has to tell the correct procedure. All required steps are to be written by the students. Conceptual learning is more important, small computational error may be avoided. Final solution is not important than understanding the Concept. One has to work carefully with given data. Check the answer step by step after solving, in order to have accuracy and correct solution.

Conceptual Errors

If students have not understood the concepts, these kinds of mistakes occur. We can say either incorrect logic or incorrect method. Preventing conceptual errors are not as easy as other errors.

Examples: Jim has a bag of 24 chocolates. He decided to share equally with 6 of his friends, how many each friend gets? Solution is  24 / 6=4 is the correct  answer, instead if they have multiplied 24 X 6 ,there we do understand ,the concept is not understood properly ,though the multiplication result may be correct . Student go wrong while calculating surface Area, Total Surface area, care to be taken when one side is closed, both sides are closed, hollow cylinder, especially in semi-sphere, etc. Same is applicable while calculating Volume. Area and volume to be defined clearly of 3 dimensional figures.

Remedial ways: Introduce concepts in hands-on, conceptual ways using teaching aids. Teach a concept more than one way (Open ended approach). Have Math talks. Use math journals.

- K. Bhanu Moorthy