1. Find perimeter of rectangle whose length =6m8dm and breadth = 4m 6dm
2. Find the cost of fencing rectangle field 24n long and 18m wide at Rs. 6.25 per meter.
3. The length and breadth of rectangle field are in ratio 5:3. If its perimeter is 64m. Find the dimensions.
4. The cost of fencing a rectangle field at Rs. 14.60 per m is 1606. If the width of the field is 23m find its length.
5. The length and breadth of rectangle field are in ratio 3:2. The cost of fencing the field at Rs. 6.50 per m is Rs. 520. Find the dimensions of the field.
6. The cost of putting fence around a square field at Rs. 15 per m is Rs. 432. Find the length of each side of the field.
7. Each side of square is of 21m. Adjacent to this field, there is a rectangular field having its side in ratio 4:3. If perimeters of both fields are equal find the dimensions of the rectangular field.
8.Find the circumference of circle if r =14cm
9. Find the diameter of circle if circumference is 66cm
10. Find the diameter of circle if circumference is 75 3/7 cm
11. The diameter of wheel of a car is 70cm. Find the distance travel by wheel of car in 1000 revolutions.
12. Find the circumference of circle if diameter of circle is 10m.
13. The diameter of wheel of a car is 70cm. How many revolutions will it take to make to travel 1.65 km.
14. The diameter of wheel of a car is 70cm. Find the distance travel by wheel of car in 50 revolutions.
15. Find the diameter of circle if circumference is 88 cm.
16. The diameter of wheel of a car is 77cm. How many revolutions will it take to make to travel 1210km.
17. Find the radius of circle if circumference is 66cm
18. Find the area of a rectangle whose length and breadth 45cm and 16cm respectively. Also find perimeter of rectangle
19. A room is 5m 40cm long and 3m 75cm wide. Find the area of the carpet needed to cover the floor.
20. Find the cost of cultivating a rectangular field 34m long and 18m wide at Rs. 4.50 per sq metre. Also find the cost of fencing the field at Rs. 2.25 per metre.
6th Area and Perimeter -2
1. A room is 9.68m long and 6.3m wide. Its floor is to be covered with rectangular tiles of size 22cm by 10cm. Find the total cost of the tiles at Rs. 5 per tiles.
2. The area of rectangle is 650 sq cm and one of its side is 13cm. Find the perimeter of rectangle.
3. The total cost of flooring a room at Rs. 8.50 per sq metre is Rs. 510. If the length of the room is 8m. Find its breadth.
4. Find perimeter of square field whose side is 6.3m
5. The top of the table measure 2m 25 cm by 1m 20 cm .Find its area in square metre.
6. How many envelop can be made from a sheet of paper 324cm by 172cm . if envelop require a piece of paper of size 18cm by 12cm.
7. A room is 12.5m by 8m .A square carpet of side 8m is laid on the floor .Find the area of carpet that is not carpeted.
8. A garden is 120 m by 96 m . Two cross road each 5 m wide are laid in the middle parallel to length and breadth. find the area of cross road .
6. How many envelop can be made from a sheet of paper 324cm by 172cm . if envelop require a piece of paper of size 18cm by 12cm.
7. A room is 12.5m by 8m .A square carpet of side 8m is laid on the floor .Find the area of carpet that is not carpeted.
8. A garden is 120 m by 96 m . Two cross road each 5 m wide are laid in the middle parallel to length and breadth. find the area of cross road .
9. Find the area of path running outside if the dimension of field is 15m by 10m and breadth of path is 0.5 m .
10 Find the area of path running inside if the square field of 10 m and width of path is 2 m . Find cost of leveling at Rs 2.50 per sq.m
11. (i) How many sq.cm in a square meter.
11. (i) How many sq.cm in a square meter.
(ii) What is the difference between 3 square meter and 3 meter square
12. A lane, 150m by 9m is paved with bricks of length 22.5cm and breadth 7.5cm. Find the number of bricks required.
133. A room is 13m long and 9m broad. Find the cost of carpeting the room with a carpet 75cm broad at the rate of Rs. 6.50 per metre.
14. The length and breadth of rectangular park are in ratio 5:3 and its perimeter is 128 m. find the area of the park.
15. Two plots have same perimeter. One is a square of side 64m and other is rectangle of length 70m and breadth 58m which field has greater area and by how much.
16. Find the cost of cultivating a rectangular field at Rs. 1.50 per sq metre is Rs. 1833. If breadth of field is 26 m . Find the cost of fencing at Rs. 7.50 per metre.
17. The length and breadth of a play ground are 62m60cm and 25m40cm respectively. Find the cost of turfing at Rs. 2.50 per square meter .How long man take to go three times around the field if he walks at the rate of 2 metre per second.
6th Ratio and Proportional – 2
21. If 36 , x , x , 16 are in proportional Find value of x
22. Find value of x if 25, 35, x are in proportional
23. An electrical pole cast shadow length 20 m at a time when a tree of 6 cm cast shadow of 8 m. Find the height of pole.
24. The length of the sides of a triangle are in ratio 1: 3: 5 .If perimeter of triangle is 90 cm find its largest side
25. Rohit earns Rs. 7650 and saves Rs. 918 per month Find ratio of
(I) his income to his saving (II) His income to his expenditure (III) his expenditure to his saving
26. Find the ratio of the price of pencil to that of ball pen if pencil cost Rs 96 per score and ball pen cost Rs. 50.40 per dozen
27. (i)Find the ratio of 75 paisa and Rs 3 (i)Find the ratio of 125 gm to 2 kg. ?
28. Neha got 850 marks out of 1000 marks and Sazia got 375 in 500.Express their marks in ratio?
29. The number of boys in school is 500 and that of girls 275. Find the Ratio of
(i) Boys to that of girls (ii) Boys to total num of students (iii) Total number to that of girls.
30. The ratio of the height of Mohit and Rohit is 4 : 3 . if Rihit is 1.5 m tall . Find the height of Mohit 31. Jaya is 1.30m tall and Shakshi is 1m25 cm tall . Find the ratio of their height ?
32 Are 5 : 6 : : 10 : 12 and 12 : 18 : : 14 : 24 equivalent ?
33. Find the value of x : (i) X/5 = 6/15 (ii) 7/8 = 21 /X (iii) 44 : X : : 11 : 4 (iv) 7 : X = 21 : X
34. The ratio of income to expenditure 9 : 8 Find saving, if total income is Rs. 2700
35. Two numb. are in ratio 2 : 7 . If the sum of the num is 81 .Find the numbers?
36.The ratio of boys to girls in a school is 8 : 3 if the num. of boys are 400 find the number of girls.
38. Is 3 : 5 equivalent to 4: 6 ? Why or why not ?
39. The 1st 2nd and 4th term of a proportion al is 6 ,10 ,15 . Find the third term ?
40. First ,third, fourth term of a proportional are 45,25,35, Find third term.
41. If 36 , x , x , 16 are in proportional Find value of x
42. Find value of x if 25,35, x are in proportional
43. An electrical pole cast shadow length 20 m at a time when a tree of 6 cm cast shadow of 8 m. Find the height of pole.
44. The length of the side of a triangle are in ratio 1 : 3 : 5 .If perimeter of triangle is 90 cm find its largest side.
45. Rohit earns Rs. 7650 and saves Rs. 918 per month Find ratio of
(I) his income to his saving (II) His income to his expenditure (III) his expenditure to his saving
46. Find the ratio of the price of pencil to that of ball pen if pencil cost Rs 96 per score and ball pen cost Rs. 50.40 per dozen.
6th Unitary methods
1. A truck runs 495 km on 36 liter petrol. How many km can it run on 35 liter petrol?
2.12 men can reap a field in 25 days. in how many days can 20 man reap field ?
3. In a camp, there were provisions for 425 men for 30 days. However, 375 men attend the camp. How many provision last?
4. If 48 boxes are needed for 6000 pens. How many boxes will be needed for 1875 pens?
5. A bus travel 36 km in 2/3hr. If it maintains a uniform speed, how long will it takes to cover162 km? How for does it travel in 8 hrs. ?
6.25 bags each weighting 40 kg, cost Rs 2750. Find the cost of 35 bags of wheat if each weighting 50 kg?
7. 24 workers can build a wall in 15 days. How many days will 9 workers take to build a similar wall
6th Algebraic equations
1. Write each in product form:- (a) 4a3 (b) 10x3y3z2 (c) 7p2q2
2. Write in exponential form:-
(a) 17 X b X b X c X c X c (b) 13 X p X q X q X q X r X r c) 7 X a X a X a X – - – - – - – - 17 times
3. Add: – (a) 17×2 + 2y2 + 3xy, -9×2 + 11y2 – 3xy and 12×2 – 7y2 + 6xy
(b) –a2 + b2 – 2abc, -3a2 – 2b2 + 4abc and 4a2 + 3b2 – 4abc
4. Subtract
(a) 6×2 – 6y2 + 7xy from 0
(b) 7x – 3y from 7x + 3y
(c) -6×2 + 7y2 + 2xy from 6×2 – 7y2 – 3xy
5. Identify the like terms in x2y3z; xyz; -y3zx2; -2xyz
6. If A=-2l+6m-3p; B=l-m+2p then find 2B-3A
7. Subtract 7x+2y-7z from -1
8. From the sum of 4x-3y+z ; -5x subtract 3y-4z
9. Subtract the sum of 3l +2m – p; 2l – 4m + p ; – 6l + m from 0
10. From the sum of -a+b-3c; 2a+b-c; 1a-4b+5c; 2a-6b+c subtract –a-b-c
11. Write the following statement algebraically:
(a)Product of 4 and a divided by the difference of 5 and a
(b)Two – third of x subtracted from 5 less than x
(c) 15 less the quotient of x by 3
12. Simplify the expressions (i) 3y (2y – 7) – 3 (y – 4) -63 (ii) 5y (3y 2 + 5y- 11) + 3(y3 – 4y2 + 6)
13. Add the following. (i) ab – bc, bc – ca, ca – ab (ii) a – b + ab , b – c + bc , c – a + ac
Linear Equation
1. The present age of Sahil’s mother is three times the present age of Sahil. .After 5 years their ages will add to 66 years. Find their present ages.
2. Bansi has 3 times as many two-rupee coins as he has five-rupee coins. If he has in all a sum of Rs 77, how many coins of each denomination does he have?
3. The difference between two whole numbers is 66. The ratio of the two numbers is 2 : 5. What are the two numbers?
4. Aman’s age is three times his son’s age. Ten years ago he was five times his son’sage. Find their present ages.
Understanding Elementary Shapes
(I) Fill in the blanks :
a) Some acute angles.
b) Some obtuse angles.
c) What is the measure of a straight angle?
III) What shape is
a) A brick.
b) A match box
c) A sweet laddu
d) A ball
e) A die
f) A road roller
(IV) Fill in the blanks
1. A cuboid has __________ faces.
2. Each face has _______ edges.
3. Each face has _________________ vertices.
12. A lane, 150m by 9m is paved with bricks of length 22.5cm and breadth 7.5cm. Find the number of bricks required.
133. A room is 13m long and 9m broad. Find the cost of carpeting the room with a carpet 75cm broad at the rate of Rs. 6.50 per metre.
14. The length and breadth of rectangular park are in ratio 5:3 and its perimeter is 128 m. find the area of the park.
15. Two plots have same perimeter. One is a square of side 64m and other is rectangle of length 70m and breadth 58m which field has greater area and by how much.
16. Find the cost of cultivating a rectangular field at Rs. 1.50 per sq metre is Rs. 1833. If breadth of field is 26 m . Find the cost of fencing at Rs. 7.50 per metre.
17. The length and breadth of a play ground are 62m60cm and 25m40cm respectively. Find the cost of turfing at Rs. 2.50 per square meter .How long man take to go three times around the field if he walks at the rate of 2 metre per second.
6th Ratio and Proportional-1
1. Find the ratio of
(i)40 paisa to Rs 4 (II) 24 min. to an hr (III) 125 ml to 2 litres (IV) 4m to 36 cm (V) Dozen to Score
2. Find the ratio the price of coffee to that of tea, when coffee cost rupees 24 per100 gm and tea Rs 80 per kg?
3. Two numbers are in ratio 2:7. If the sum of the numbers are 81. Find the numbers?
4. Divide the number 642 in ratio 1: 2: 3 among A, B, C
5. The ratio of Length and breadth of rectangle is 5:3. Find l and b if perimeter is 256?
6. Which ratio is larger (I) 5:12 or 17:30 (ii) 2:3 or 16:24
7. A bus travel 126 km in 3hrs.and a train travel 315 km in 5 hrs. Find ratio of their speed?
8. Are (I) 7,42,13,78 in proportional? (ii) Find x if 48, 36, x are in proportional?
9. First, second, fourth term of a proportional are 45, 25, 35, Find third term.
10. If 36 , x , x , 16 are in proportional Find value of x
11. Find value of x if 25,35, x are in proportional
12. An electrical pole cast shadow length 20 m at a time when a tree of 6 cm cast shadow of 8 m. Find the height of pole.
13. The length of the side of a triangle are in ratio 1: 3 : 5 .If perimeter of triangle is 90 cm find its largest side .
14. Rohit earns Rs. 7650 and saves Rs. 918 per month Find ratio of
(I) his income to his saving (II) His income to his expenditure (III) his expenditure to his saving
15. Find the ratio of the price of pencil to that of ball pen if pencil cost Rs 96 per score and ball pen cost Rs. 50.40 per dozen.
16. The ratio of the height of Mohit and Rohit is 4: 3 if Rohit is 1.5 m tall. Find the height of Mohit?
17. Neha got 850 marks out of 1000 marks and Suzie got 375 in 500. Express their marks in ratio?
18. The ratio of income to expenditure 9: 8 Find saving, if total income is Rs. 2700
19. Jaya is 1.30m tall and Shakshi is 1m25 cm tall. Find the ratio of their height
20. First ,third, fourth term of a proportional are 45,25,35, Find third term.
1. Find the ratio of
(i)40 paisa to Rs 4 (II) 24 min. to an hr (III) 125 ml to 2 litres (IV) 4m to 36 cm (V) Dozen to Score
2. Find the ratio the price of coffee to that of tea, when coffee cost rupees 24 per100 gm and tea Rs 80 per kg?
3. Two numbers are in ratio 2:7. If the sum of the numbers are 81. Find the numbers?
4. Divide the number 642 in ratio 1: 2: 3 among A, B, C
5. The ratio of Length and breadth of rectangle is 5:3. Find l and b if perimeter is 256?
6. Which ratio is larger (I) 5:12 or 17:30 (ii) 2:3 or 16:24
7. A bus travel 126 km in 3hrs.and a train travel 315 km in 5 hrs. Find ratio of their speed?
8. Are (I) 7,42,13,78 in proportional? (ii) Find x if 48, 36, x are in proportional?
9. First, second, fourth term of a proportional are 45, 25, 35, Find third term.
10. If 36 , x , x , 16 are in proportional Find value of x
11. Find value of x if 25,35, x are in proportional
12. An electrical pole cast shadow length 20 m at a time when a tree of 6 cm cast shadow of 8 m. Find the height of pole.
13. The length of the side of a triangle are in ratio 1: 3 : 5 .If perimeter of triangle is 90 cm find its largest side .
14. Rohit earns Rs. 7650 and saves Rs. 918 per month Find ratio of
(I) his income to his saving (II) His income to his expenditure (III) his expenditure to his saving
15. Find the ratio of the price of pencil to that of ball pen if pencil cost Rs 96 per score and ball pen cost Rs. 50.40 per dozen.
16. The ratio of the height of Mohit and Rohit is 4: 3 if Rohit is 1.5 m tall. Find the height of Mohit?
17. Neha got 850 marks out of 1000 marks and Suzie got 375 in 500. Express their marks in ratio?
18. The ratio of income to expenditure 9: 8 Find saving, if total income is Rs. 2700
19. Jaya is 1.30m tall and Shakshi is 1m25 cm tall. Find the ratio of their height
20. First ,third, fourth term of a proportional are 45,25,35, Find third term.
6th Ratio and Proportional – 2
21. If 36 , x , x , 16 are in proportional Find value of x
22. Find value of x if 25, 35, x are in proportional
23. An electrical pole cast shadow length 20 m at a time when a tree of 6 cm cast shadow of 8 m. Find the height of pole.
24. The length of the sides of a triangle are in ratio 1: 3: 5 .If perimeter of triangle is 90 cm find its largest side
25. Rohit earns Rs. 7650 and saves Rs. 918 per month Find ratio of
(I) his income to his saving (II) His income to his expenditure (III) his expenditure to his saving
26. Find the ratio of the price of pencil to that of ball pen if pencil cost Rs 96 per score and ball pen cost Rs. 50.40 per dozen
27. (i)Find the ratio of 75 paisa and Rs 3 (i)Find the ratio of 125 gm to 2 kg. ?
28. Neha got 850 marks out of 1000 marks and Sazia got 375 in 500.Express their marks in ratio?
29. The number of boys in school is 500 and that of girls 275. Find the Ratio of
(i) Boys to that of girls (ii) Boys to total num of students (iii) Total number to that of girls.
30. The ratio of the height of Mohit and Rohit is 4 : 3 . if Rihit is 1.5 m tall . Find the height of Mohit 31. Jaya is 1.30m tall and Shakshi is 1m25 cm tall . Find the ratio of their height ?
32 Are 5 : 6 : : 10 : 12 and 12 : 18 : : 14 : 24 equivalent ?
33. Find the value of x : (i) X/5 = 6/15 (ii) 7/8 = 21 /X (iii) 44 : X : : 11 : 4 (iv) 7 : X = 21 : X
34. The ratio of income to expenditure 9 : 8 Find saving, if total income is Rs. 2700
35. Two numb. are in ratio 2 : 7 . If the sum of the num is 81 .Find the numbers?
36.The ratio of boys to girls in a school is 8 : 3 if the num. of boys are 400 find the number of girls.
38. Is 3 : 5 equivalent to 4: 6 ? Why or why not ?
39. The 1st 2nd and 4th term of a proportion al is 6 ,10 ,15 . Find the third term ?
40. First ,third, fourth term of a proportional are 45,25,35, Find third term.
41. If 36 , x , x , 16 are in proportional Find value of x
42. Find value of x if 25,35, x are in proportional
43. An electrical pole cast shadow length 20 m at a time when a tree of 6 cm cast shadow of 8 m. Find the height of pole.
44. The length of the side of a triangle are in ratio 1 : 3 : 5 .If perimeter of triangle is 90 cm find its largest side.
45. Rohit earns Rs. 7650 and saves Rs. 918 per month Find ratio of
(I) his income to his saving (II) His income to his expenditure (III) his expenditure to his saving
46. Find the ratio of the price of pencil to that of ball pen if pencil cost Rs 96 per score and ball pen cost Rs. 50.40 per dozen.
6th Unitary methods
1. A truck runs 495 km on 36 liter petrol. How many km can it run on 35 liter petrol?
2.12 men can reap a field in 25 days. in how many days can 20 man reap field ?
3. In a camp, there were provisions for 425 men for 30 days. However, 375 men attend the camp. How many provision last?
4. If 48 boxes are needed for 6000 pens. How many boxes will be needed for 1875 pens?
5. A bus travel 36 km in 2/3hr. If it maintains a uniform speed, how long will it takes to cover162 km? How for does it travel in 8 hrs. ?
6.25 bags each weighting 40 kg, cost Rs 2750. Find the cost of 35 bags of wheat if each weighting 50 kg?
7. 24 workers can build a wall in 15 days. How many days will 9 workers take to build a similar wall
6th Algebraic equations
1. Write each in product form:- (a) 4a3 (b) 10x3y3z2 (c) 7p2q2
2. Write in exponential form:-
(a) 17 X b X b X c X c X c (b) 13 X p X q X q X q X r X r c) 7 X a X a X a X – - – - – - – - 17 times
3. Add: – (a) 17×2 + 2y2 + 3xy, -9×2 + 11y2 – 3xy and 12×2 – 7y2 + 6xy
(b) –a2 + b2 – 2abc, -3a2 – 2b2 + 4abc and 4a2 + 3b2 – 4abc
4. Subtract
(a) 6×2 – 6y2 + 7xy from 0
(b) 7x – 3y from 7x + 3y
(c) -6×2 + 7y2 + 2xy from 6×2 – 7y2 – 3xy
5. Identify the like terms in x2y3z; xyz; -y3zx2; -2xyz
6. If A=-2l+6m-3p; B=l-m+2p then find 2B-3A
7. Subtract 7x+2y-7z from -1
8. From the sum of 4x-3y+z ; -5x subtract 3y-4z
9. Subtract the sum of 3l +2m – p; 2l – 4m + p ; – 6l + m from 0
10. From the sum of -a+b-3c; 2a+b-c; 1a-4b+5c; 2a-6b+c subtract –a-b-c
11. Write the following statement algebraically:
(a)Product of 4 and a divided by the difference of 5 and a
(b)Two – third of x subtracted from 5 less than x
(c) 15 less the quotient of x by 3
12. Simplify the expressions (i) 3y (2y – 7) – 3 (y – 4) -63 (ii) 5y (3y 2 + 5y- 11) + 3(y3 – 4y2 + 6)
13. Add the following. (i) ab – bc, bc – ca, ca – ab (ii) a – b + ab , b – c + bc , c – a + ac
Linear Equation
1. The present age of Sahil’s mother is three times the present age of Sahil. .After 5 years their ages will add to 66 years. Find their present ages.
2. Bansi has 3 times as many two-rupee coins as he has five-rupee coins. If he has in all a sum of Rs 77, how many coins of each denomination does he have?
3. The difference between two whole numbers is 66. The ratio of the two numbers is 2 : 5. What are the two numbers?
4. Aman’s age is three times his son’s age. Ten years ago he was five times his son’sage. Find their present ages.
Understanding Elementary Shapes
(I) Fill in the blanks :
- An angle whose measure is greater than that of a right angle is ___________
- Three edges meet at a point called a ________________________.
- A ___________________________ is larger than a straight angles.
- A Polygon with 5 sides is called a ___________________________.
- A triangle having all three unequal sides is called a ____________________.
a) Some acute angles.
b) Some obtuse angles.
c) What is the measure of a straight angle?
III) What shape is
a) A brick.
b) A match box
c) A sweet laddu
d) A ball
e) A die
f) A road roller
(IV) Fill in the blanks
1. A cuboid has __________ faces.
2. Each face has _______ edges.
3. Each face has _________________ vertices.
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