class 6 True or False

 Class 6  Maths 

True or False & Fillups

 I.TRUE OR FALSE

            1. 100 lakhs make a million.  ---  false

            2. The estimated value of 46530 to the nearest hundred is 46500. --- true

            3. The successor of the greatest 5 digit number is 100000. --- true

            4. In Roman numerals V, L and D are never repeated. --- true

            5. The difference in the face and the place value of 5 in 85419 is 85414. --- false

            6. The natural number 1 has no predecessor. --- true

            7. If a and b are whole numbers and a < b, then a+1 < b+1. --- true

            8. Every whole number has its predecessor. --- false 

            9. In rectangle diagonal bisect at 90 degree. --- false 

          10. An equilateral triangle is acute angled triangle. --- true

          11.  A number and its successor are always co-primes. --- true

          12. Two consecutive numbers cannot be both primes. --- false

          13. If a number is divisible by 3, it must be divisible by 9. --- false

          14. The sum of the two consecutive odd numbers is always divisible by 4. --- true

          15. A number is divisible by 18, if it is divisible by both 3 and 6. ---false

          16. Point has a size because we can see it as a thick dot on paper. --- false

          17. Two lines in a plane always intersect at a point. --- false

          18. All radii of a circle are equal. --- true

          19. Diameter is a chord of a circle. --- true

          20. The distance between parallel lines is same throughout. --- true

          21. Four points are collinear if any three of them lie on the same line. --- false

          22. The line segments forming letter T form perpendicular lines. --- true

          23. An obtuse angled triangle can be isosceles. --- true

          24. The point at which two adjacent sides of a polygon meet is called its vertex. --- true

          25. Every negative integer is less than every natural number. --- true

          26. The additive inverse of zero is zero. --- true

          27. Greatest negative integer is zero. --- false

          28. -5 < -4 => | -5 | < | -4 |. --- false

          29. The sum of three different integers can never be negative. --- false

          30. Zero is not an integer. --- false

          31. The successor of - 25 is - 24. --- true

          32. The multiplicative inverse of 7 is -7 --- false

I. FILL IN THE BLANKS

       1. 564 when estimated to the nearest hundred is 600.

       2. The smallest digit number with four different digits is 1023.

       3. Face value of 2 in 54321 is 2.

       4. Place value of 2 in 12345 is 2000.

       5. Example of palindromic number is 323.

       6. Dividend = division x Quotient + remainder.

       7. Whole numbers are represented by W and natural numbers are

            Represented by N.

       8. Zero is the additive identity of the whole numbers.

       9. Product of even number is always even.

     10. Natural number 1 has no predecessor.

     11. The smallest composite number is 4.  

     12. The smallest prime number is 2.

     13. The HCF of two consecutive odds numbers is 1.

     14. 1 is neither prime nor composite.

     15. A number having only two factors is called a prime number.

     16. Centroid is the point, where three medians of a triangle meet.

     17. All radii/diameters of a circle are equal.

     18. A figure which begins and ends at the same point is called a closed curve.

     19. A median of a triangle is the line segment that joins a vertex to

           the mid-point of opposite sides.

     20. A line has no end points.

     21. Measure of an acute angle is less than 90.

     22. Measure of an obtuse angle is greater than 90 but less than 180.

     23. Complement of an angle of 45 is 45.

     24. Angles are measured in degrees.

     25. A square is a rectangle with a pair of adjacent sides equal.

     26. Triangle is classified in terms of sides as well as angles.

     27. A complete angle = 360.

     28. Sum of all angles of a pentagon is 540.

     29. The sum of an integer and its opposite is zero.

     30. Farther a number from zero on the left smaller is its value.

     31. Farther a number from zero on the right larger is its value.

     32. Zero is an integer which is neither positive nor negative.

     33. If x and y are two integers, then (x - y) is also an integer.

     34. a + 0 = a = 0 + a, here 0 is called additive identity.

     35. 2/3 + _______ = 19

     36. 7- 2/3 =________.

     37. 42/54 = ________.

     38. 6 1/6- ________ = 29/30

     39. 72/90 reduced to simplest form is _________.

     40. The additive inverse of 3 is ________.

 Class 10 QUIZ REAL NUMBERS

 The prime factorisation of  120 is

  2^2×5 

   2^2×5×3

   2^2×5^2×3

  3^2×5^2×2^2

Answer : B  

The prime factorisation of 375 is

  5^2×3^2×2^2

  5×3×2

  5^2×2^2×3

  5^2×3^2×2

Answer : C  5^2×2^2×3  

If the prime factorization of 1440 is 2^5×6^2×5, then the value of b is

  3

  3^2

  3^3

  +5

Answer : A  3

If the prime factorization of 380 is a^2 bc then the value of a^2,b,c is

  2,5,19

  2,5,9

  12,5,9

  2,15,19

Answer : A 

If the prime factorization of 22275 is 3^a×5^b×〖11〗^c, then the value of a,b,c is

  a=5, b=2, c=1

   a=+3, b=2, c=1

  a=5, b=2, c=4

  a=4, b=2, c=1

Answer : D  a=4, b=2, c=1

The prime factorization of 12716 is

  2×11×17

  2^2×〖11〗^2×〖17〗^2

  2^2×11×〖17〗^2

  2×〖11〗^2×〖17〗^2

      Answer : C  2^2×11×〖17〗^2

The prime factorization of 3690 is

  5×3×2×41

  5^2×3^2×2×41

  5×3^2×2×41

  5×3^2×2^2×41

      Answer : C  5×3^2×2×41

If HCF (33,45) is 3, then the LCM (33,45) is

  459

  495

  49

  45

Answer : B  495

If the LCM of (64,40) is 320, then the HCF (64,40) is

  8

  9

  10

  5

Answer : A  8

If the LCM (a,b) is 36 and HCF (a,b) is 6 then (a×b) is

  217

  271

  216

  261

Answer : C  216

      

QUESTION BANK CLASS 8 SQUARE AND SQUARE ROOTS

   QUESTION BANK  CLASS 8 SQUARE AND SQUARE ROOTS

 the area of a square = side × side (where ‘side’ means ‘the length of a side’)

Such numbers like 1, 4, 9, 16, 25, ... are known as square numbers.

 In general, if a natural number m can be expressed as n² , where n is also a natural number, then m is a square number.

The numbers 1, 4, 9, 16 ... are square numbers. These numbers are also called perfect squares.

All these numbers end with 0, 1, 4, 5, 6 or 9 at units place. None of these end with 2, 3, 7 or 8 at unit’s place. 

If a number ends in 0, 1, 4, 5, 6 or 9, then it must be a square number.

if a number has 1 or 9 in the units place, then it’s square ends in 1.

when a square number ends in 6, the number whose square it is, will have either 4 or 6 in unit’s place.

in general we can say that there are 2n non perfect square numbers between the squares of the numbers n and (n + 1).

the sum of first n odd natural numbers is n²

‘If the number is a square number, it has to be the sum of successive odd numbers starting from 1 . 

t if a natural number cannot be expressed as a sum of successive odd natural numbers starting with 1, then it is not a perfect square.

For any natural number m > 1, we have (2m)²  + (m² – 1)² = (m² + 1)² . So, 2m, m² – 1 and m² + 1 forms a Pythagorean triplet.

finding the square root is the inverse operation of squaring. 

t there are two integral square roots of a perfect square number. In this chapter, we shall take up only positive square root of a natural number. Positive square root of a number is denoted by the symbol.$\sqrt{}$

every square number can be expressed as a sum of successive odd natural numbers starting from 1.

each prime factor in the prime factorisation of the square of a number, occurs twice the number of times it occurs in the prime factorisation of the number itself.

t if a perfect square is of n-digits, then its square root will have n/2 digits if n is even or  (n +1)/2  if n is odd.

1. If a natural number m can be expressed as n 2 , where n is also a natural number, then m is a square number. 

2. All square numbers end with 0, 1, 4, 5, 6 or 9 at units place. 

3. Square numbers can only have even number of zeros at the end. 

4. Square root is the inverse operation of square. 

5. There are two integral square roots of a perfect square number. Positive square root of a number is denoted by the symbol . For example, 32 = 9 gives 9 3 

EXAMPLE:

Find the perfect square numbers between (i) 30 and 40 (ii) 50 and 60

Which of the following numbers would have digit 6 at unit place. (i) 19² (ii) 24² (iii) 26² (iv) 36² (v) 34²  

What will be the “one’s digit” in the square of the following numbers? (i) 1234 (ii) 26387 (iii) 52698 (iv) 99880 (v) 21222 (vi) 9106

1. How many natural numbers lie between 9² and 10² ? Between 11² and 12² ? 

2. How many non square numbers lie between the following pairs of numbers (i) 100² and 101² (ii) 90² and 91² (iii) 1000² and 1001²

The square of which of the following numbers would be an odd number/an even number? Why? (i) 727 (ii) 158 (iii) 269 (iv) 1980 

2. What will be the number of zeros in the square of the following numbers? (i) 60 (ii) 400  

Find whether each of the following numbers is a perfect square or not? (i) 121 (ii) 55 (iii) 81 (iv) 49 (v) 69

Express the following as the sum of two consecutive integers. (i) 21² (ii) 13² (iii) 11² (iv) 19²

 2. Do you think the reverse is also true, i.e., is the sum of any two consecutive positive integers is perfect square of a number? Give example to support your answer.

Write the square, making use of the above pattern. (i) 111111² (ii) 1111111²

Can you find the square of the following numbers using the above pattern? (i) 6666667² (ii) 66666667²

Find the square of the following numbers without actual multiplication. (i) 39 (ii) 42

Find the squares of the following numbers containing 5 in unit’s place. (i) 15 (ii) 95 (iii) 105 (iv) 205 

 Write a Pythagorean triplet whose smallest member is 8.

Find a Pythagorean triplet in which one member is 12.

Find the square root of 6400

Is 90 a perfect square?

Is 2352 a perfect square? If not, find the smallest multiple of 2352 which is a perfect square. Find the square root of the new number.

Find the smallest number by which 9408 must be divided so that the quotient is a perfect square. Find the square root of the quotient.

Find the smallest square number which is divisible by each of the numbers 6, 9 and 15.

 Find the square root of : (i) 729 (ii) 1296

: Find the least number that must be subtracted from 5607 so as to get a perfect square. Also find the square root of the perfect square.

: Find the greatest 4-digit number which is a perfect square. 

Find the least number that must be added to 1300 so as to get a perfect square. Also find the square root of the perfect square. 

Find the square root of 12.25.

Area of a square plot is 2304 m2 . Find the side of the square plot.

There are 2401 students in a school. P.T. teacher wants them to stand in rows and columns such that the number of rows is equal to the number of columns. Find the number of rows. 

EXERCISE 5.1 

1. What will be the unit digit of the squares of the following numbers? (i) 81 (ii) 272 (iii) 799 (iv) 3853 (v) 1234 (vi) 26387 (vii) 52698 (viii) 99880 (ix) 12796 (x) 55555 

2. The following numbers are obviously not perfect squares. Give reason. (i) 1057 (ii) 23453 (iii) 7928 (iv) 222222 (v) 64000 (vi) 89722 (vii) 222000 (viii) 505050 

3. The squares of which of the following would be odd numbers? (i) 431 (ii) 2826 (iii) 7779 (iv) 82004 

4. Observe the following pattern and find the missing digits. 

11² = 121 

101² = 10201 

1001² = 1002001 

100001² = 1 ......... 2 ......... 1 

10000001² = ........................... 

5. Observe the following pattern and supply the missing numbers. 

11² = 1 2 1 

101² = 1 0 2 0 1 

10101² = 102030201 

1010101² = ........................... 

............ ² = 10203040504030201 

6. Using the given pattern, find the missing numbers. 

1² + 2² + 2² = 3²

 2² + 3² + 6² = 7² 

3² + 4² + 12² = 13²

 4² + 5²+ _² = 21²

 5² + _² + 30² = 31² 

6² + 7² + _² = __²

7. Without adding, find the sum. 

(i) 1 + 3 + 5 + 7 + 9 

(ii) 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 +19 

(iii) 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 + 21 + 23 

8. (i) Express 49 as the sum of 7 odd numbers. 

(ii) Express 121 as the sum of 11 odd numbers. 

9. How many numbers lie between squares of the following numbers?
(i) 12 and 13 

(ii) 25 and 26 

(iii) 99 and 100

EXERCISE 5.2 

1. Find the square of the following numbers. (i) 32 (ii) 35 (iii) 86 (iv) 93 (v) 71 (vi) 46 

2. Write a Pythagorean triplet whose one member is. (i) 6 (ii) 14 (iii) 16 (iv) 18

EXERCISE 5.3 

1. What could be the possible ‘one’s’ digits of the square root of each of the following numbers? (i) 9801 (ii) 99856 (iii) 998001 (iv) 657666025 

2. Without doing any calculation, find the numbers which are surely not perfect squares. (i) 153 (ii) 257 (iii) 408 (iv) 441 

3. Find the square roots of 100 and 169 by the method of repeated subtraction. 

4. Find the square roots of the following numbers by the Prime Factorisation Method. (i) 729 (ii) 400 (iii) 1764 (iv) 4096 (v) 7744 (vi) 9604 (vii) 5929 (viii) 9216 (ix) 529 (x) 8100 

5. For each of the following numbers, find the smallest whole number by which it should be multiplied so as to get a perfect square number. Also find the square root of the square number so obtained. (i) 252 (ii) 180 (iii) 1008 (iv) 2028 (v) 1458 (vi) 768 

6. For each of the following numbers, find the smallest whole number by which it should be divided so as to get a perfect square. Also find the square root of the square number so obtained. (i) 252 (ii) 2925 (iii) 396 (iv) 2645 (v) 2800 (vi) 1620 

7. The students of Class VIII of a school donated ` 2401 in all, for Prime Minister’s National Relief Fund. Each student donated as many rupees as the number of students in the class. Find the number of students in the class. 

8. 2025 plants are to be planted in a garden in such a way that each row contains as many plants as the number of rows. Find the number of rows and the number of plants in each row. 

9. Find the smallest square number that is divisible by each of the numbers 4, 9 and 10. 

10. Find the smallest square number that is divisible by each of the numbers 8, 15 and 20. 

EXERCISE 5.4 

1. Find the square root of each of the following numbers by Division method. (i) 2304 (ii) 4489 (iii) 3481 (iv) 529 (v) 3249 (vi) 1369 (vii) 5776 (viii) 7921 (ix) 576 (x) 1024 (xi) 3136 (xii) 900 

2. Find the number of digits in the square root of each of the following numbers (without any calculation). (i) 64 (ii) 144 (iii) 4489 (iv) 27225 (v) 390625 

3. Find the square root of the following decimal numbers. (i) 2.56 (ii) 7.29 (iii) 51.84 (iv) 42.25 (v) 31.36 

4. Find the least number which must be subtracted from each of the following numbers so as to get a perfect square. Also find the square root of the perfect square so obtained. (i) 402 (ii) 1989 (iii) 3250 (iv) 825 (v) 4000 

5. Find the least number which must be added to each of the following numbers so as to get a perfect square. Also find the square root of the perfect square so obtained. (i) 525 (ii) 1750 (iii) 252 (iv) 1825 (v) 6412 

6. Find the length of the side of a square whose area is 441 m2 . 

7. In a right triangle ABC, ∠B = 90°. (a) If AB = 6 cm, BC = 8 cm, find AC (b) If AC = 13 cm, BC = 5 cm, find AB 

8. A gardener has 1000 plants. He wants to plant these in such a way that the number of rows and the number of columns remain same. Find the minimum number of plants he needs more for this. 

9. There are 500 children in a school. For a P.T. drill they have to stand in such a manner that the number of rows is equal to number of columns. How many children would be left out in this arrangement

QUESTION BANK CLASS 8 DATA HANDLING

  QUESTION BANK  CLASS 8 DATA HANDLING

The information collected in all such cases is called data.

A Pictograph: Pictorial representation of data using symbols.

A bar graph: A display of information using bars of uniform width, their heights being proportional to the respective values.

Double Bar Graph: A bar graph showing two sets of data simultaneously. It is useful for the comparison of the data. 

A circle graph shows the relationship between a whole and its parts. Here, the whole circle is divided into sectors. The size of each sector is proportional to the activity or information it represents.

A circle graph is also called a pie chart. 

Each outcome of an experiment or a collection of outcomes make an event. For example in the experiment of tossing a coin, getting a Head is an event and getting a Tail is also an event.

In case of throwing a die, getting each of the outcomes 1, 2, 3, 4, 5 or 6 is an event.  

1. In order to draw meaningful inferences from any data, we need to organise the data systematically. 

2. Data can also be presented using circle graph or pie chart. A circle graph shows the relationship between a whole and its part

3. There are certain experiments whose outcomes have an equal chance of occurring. 

4. A random experiment is one whose outcome cannot be predicted exactly in advance. 

5. Outcomes of an experiment are equally likely if each has the same chance of occurring. 

6. Probability of an event = $\frac{Number of outcomes that make an event}{Total number of outcomes of the experiment}$ , when the outcomes are equally likely. 

7. One or more outcomes of an experiment make an event. 

8. Chances and probability are related to real life.

EXAMPLE

A bag has 4 red balls and 2 yellow balls. (The balls are identical in all respects other than colour). A ball is drawn from the bag without looking into the bag. What is probability of getting a red ball? Is it more or less than getting a yellow ball?

Adjoining pie chart (Fig 4.4) gives the expenditure (in percentage) on various items and savings of a family during a month. (i) On which item, the expenditure was maximum? (ii) Expenditure on which item is equal to the total savings of the family? (iii) If the monthly savings of the family is ` 3000, what is the monthly expenditure on clothes?

On a particular day, the sales (in rupees) of different items of a baker’s shop are given below. 

ordinary bread : 320 

fruit bread : 80 

cakes and pastries : 160

biscuits : 120 

others : 40 

Total : 720 

Draw a pie chart for this data. 

EXERCISE 4.1 

1. A survey was made to find the type of music that a certain group of young people liked in a city. Adjoining pie chart shows the findings of this survey. From this pie chart answer the following: 

(i) If 20 people liked classical music, how many young people were surveyed? 

(ii) Which type of music is liked by the maximum number of people? 

(iii) If a cassette company were to make 1000 CD’s, how many of each type would they make? 

2. A group of 360 people were asked to vote for their favourite season from the three seasons rainy, winter and summer. 

(i) Which season got the most votes? 

(ii) Find the central angle of each sector. 

(iii) Draw a pie chart to show this information. 

3. Draw a pie chart showing the following information. The table shows the colours preferred by a group of people. 

Colours Number of people 

Blue 18 

Green 9 

Red 6 

Yellow 3 

Total 36 

4. The adjoining pie chart gives the marks scored in an examination by a student in Hindi, English, Mathematics, Social Science and Science. If the total marks obtained by the students were 540, answer the following questions. 

(i) In which subject did the student score 105 marks?
(Hint: for 540 marks, the central angle = 360°. So, for 105 marks, what is the central angle?) 

(ii) How many more marks were obtained by the student in Mathematics than in Hindi? 

(iii) Examine whether the sum of the marks obtained in Social Science and Mathematics is more than that in Science and Hindi. (Hint: Just study the central angles)

5. The number of students in a hostel, speaking different languages is given below. Display the data in a pie chart.

Language Hindi English Marathi Tamil Bengali Total 

Number of students  40 12 9 7 4 72 

EXERCISE 4.2 

1. List the outcomes you can see in these experiments. (a) Spinning a wheel (b) Tossing two coins together 

2. When a die is thrown, list the outcomes of an event of getting (i) (a) a prime number (b) not a prime number. (ii) (a) a number greater than 5 (b) a number not greater than 5. 

3. Find the. (a) Probability of the pointer stopping on D in (Question 1-(a))? 

(b) Probability of getting an ace from a well shuffled deck of 52 playing cards? 

(c) Probability of getting a red apple. (See figure below) 

4. Numbers 1 to 10 are written on ten separate slips (one number on one slip), kept in a box and mixed well. One slip is chosen from the box without looking into it. 

What is the probability of . 

(i) getting a number 6? 

(ii) getting a number less than 6? 

(iii) getting a number greater than 6? 

(iv) getting a 1-digit number? 

5. If you have a spinning wheel with 3 green sectors, 1 blue sector and 1 red sector, what is the probability of getting a green sector? What is the probability of getting a non blue sector? 

6. Find the probabilities of the events given in Question 2.