Download Assignment CBSE Class VIII Maths

Assignment on Maths class 8th. Prepared by Jsunil tutorial

1. An underground water tank is in the shape of cube of side 7 m. What will be its volume?

2. What will be volume of a box whose length 16 m, breadth 8 m and height is 5 m?

3. The length, breadth and height of a room are 12 m, 10 m, and 9m respectively. Find the area of  our walls of room?

4. The volume of a cube is 27a³ . Find the length of its edge?

5. How much Aluminium sheet will be required to make a container with lid whose length is 13 m, breadth is 8 m and height is 4 m?

6. The volume of a cube is 1331 cm3 . Find the length of its edge?

7. The length of diagonal of a cube is 17.32 cm. Find the volume of that cube?

8. Three cubes whose sides are 6 cm, 8 cm and 10 cm. They are melted and form a cube. Find the volume of that cube?

9. Two cubes have edge 10 m. Their edges have been joined and form a cuboid. What will be the surface area of cuboid thus formed?

10. The total volume of a cube is 512 cubic cm. Find the side of a cube?

11. A rectangular box 14 cm long, 10 cm wide and 5 cm high is to be made with card-board. Find the area of card-board to make that box?

12. What will be the volume of a cylindrical tank whose radius is 7 cm and height is 5 cm?

13. How many solid spheres of  2/3 cm radius can be made from a solid sphere of 2 cm radius?

14. If the volume and surface area of a sphere is numerically same then what will be its radius?

15. The volume of a right circular cylinder is 392 π cm3 and its height is 8 cm. Find the radius?

AREA 
1. Verify Euler’s formula for a) Square pyramid b) Pentagonal prism c) tetrahedron 
2. The area of a rhombus is equal to the area of a triangle whose base and the corresponding altitude 
are 24.8 cm and 16.5 cm respectively. If one of the diagonal of the rhombus is 22 cm, find the length of the other diagonal.
3. The floor of a rectangular hall has a perimeter 250m. If the cost of paining the four walls at the 
rate of Rs 10 per m2 is Rs 1500. Find the height of the hall. Ans: 3/5 m = 0.6m
4. A room is half as long again as it is broad. The cost of carpeting the room at Rs 3.25 per m2 is Rs 175.50 and the cost of papering the walls at Rs 1.40 per m2 is Rs 240.80. If 1 door and 2 windows occupy 8m2, find the dimensions of the room. 
5. A river 2m deep and 45m wide is flowing at the rate of 3 km per hour. Find the volume of water that runs into the sea per minute. 
6. A closed cylinder has diameter 8cm and height 10cm. Find its total surface area and volume. 
7. The volume of a metallic cylinder pipe is 748cm3 . Its length is 14 cm and external diameter 18cm. Find its thickness. 
8. A cylindrical bucket, 28cm in diameter 72cm high is full of water. The water is emptied into a rectangular tank, 66cm long and 28cm wide. Find the height of the water level in the tank. 
9. A cylindrical tube, open at both ends, is made of metal. The internal diameter of the tube is 10.4cm and its length is 25cm. The thickness of the metal is 8mm everywhere. Calculate the volume of the metal. 
10. The difference between outside and inside surface of a cylindrical metallic pipe 14cm long is 44cm2 . If the pipe is made of 99 cm3 . Find the outside and inner radii of the pipe. 
Volume and surface area. 
1. A hollow cylindrical pipe is 21 dm long. Its outer and inner diameters are 10cm and 6cm respectively. Find the volume of copper used in making the pipe. 
2. The height of a right circular cylinder is 10.5m. Three times the sum of the areas of its two circular faces is twice the area of the curved surface. Find the volume of the cylinder. 
3. The circumference of the base of a 10m high conical tent is 44m. Calculate the length of canvas used in making the tent if width of canvas is 2m. 
4. The radius and height of a cone are in the ratio 4:3 the area of the base is 154cm2. find the area of 
the curved surface.
5. The volume of a metallic cylindrical pipe is 748cm3 . Its length is 14 cm and its external radius is 9 cm. Find its thickness.
6. A well of inner diameter 14m is dug to a depth of 15m. Earth taken out of it has been evenly spread all around it to a width of 7m to form an embankment. Find the height of the embankment. 
7. A cloth having an area of 165m is shaped into a cylindrical tent of radius 5m. How many students can sit in the tent if a student occupies 5/7 m2 ? Find the volume of air for each student. 
8. The difference between inside and outside surfaces of cylindrical tube 14cm long is 88 sq.cm. If the volume of the tube is 176 cubic cm. find the inner and outer radii of the tube.
9. The area of three adjacent faces of a cuboidal box are 120cm2, 72cm2 and 60cm2 respectively. Find the volume of the box.
10. The total surface area of a hollow cylinder which is open from both sides is 4620cm2, area of base ring is 15.5cm2 and height 7cm. Find the thickness of the cylinder.

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ASSIGNMENT FOR THE SESSION 2011-2012 Class: VIII Mathematics Term -II

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ASSIGNMENT FOR THE SESSION 2011-2012 Class: VIII Subject : Mathematics Term -IITrapezium
1. The parallel sides of a trapezium are 25 cm and 11 cm, while its non parallel sides are 15cm and
13cm. find the area of the trapezium.

2. The parallel sides of a trapezium are 78 cm and 52 cm, while its non parallel sides are 28cm and
30cm. find the area of the trapezium.

3. The parallel sides of a trapezium are 12cm and 36cm respectively. Its non parallel sides are each equal to 15cm. Find the area of the trapezium.

AREA

1. Verify Euler’s formula for a) Square pyramid b) Pentagonal prism c) tetrahedron

2. The area of a rhombus is equal to the area of a triangle whose base and the corresponding altitude
are 24.8 cm and 16.5 cm respectively. If one of the diagonal of the rhombus is 22 cm, find the length of the other diagonal.

3. The floor of a rectangular hall has a perimeter 250m. If the cost of paining the four walls at the
rate of Rs 10 per m2 is Rs 1500. Find the height of the hall. Ans: 3/5 m = 0.6m

4. A room is half as long again as it is broad. The cost of carpeting the room at Rs 3.25 per m2 is Rs 175.50 and the cost of papering the walls at Rs 1.40 per m2 is Rs 240.80. If 1 door and 2 windows occupy 8m2, find the dimensions of the room.

5. A river 2m deep and 45m wide is flowing at the rate of 3 km per hour. Find the volume of water that runs into the sea per minute. Ans: 4500m3

6. A closed cylinder has diameter 8cm and height 10cm. Find its total surface area and volume.

7. The volume of a metallic cylinder pipe is 748cm3 . Its length is 14 cm and external diameter 18cm. Find its thickness.

8. A cylindrical bucket, 28cm in diameter 72cm high is full of water. The water is emptied into a rectangular tank, 66cm long and 28cm wide. Find the height of the water level in the tank. Ans: 24cm

9. A cylindrical tube, open at both ends, is made of metal. The internal diameter of the tube is 10.4cm and its length is 25cm. The thickness of the metal is 8mm everywhere. Calculate the volume of the metal.

10. The difference between outside and inside surface of a cylindrical metallic pipe 14cm long is 44cm2 . If the pipe is made of 99 cm3 . Find the outside and inner radii of the pipe.

Volume and surface area.

1. A hollow cylindrical pipe is 21 dm long. Its outer and inner diameters are 10cm and 6cm respectively. Find the volume of copper used in making the pipe.

2. The height of a right circular cylinder is 10.5m. Three times the sum of the areas of its two circular faces is twice the area of the curved surface. Find the volume of the cylinder.

3. The circumference of the base of a 10m high conical tent is 44m. Calculate the length of canvas used in making the tent if width of canvas is 2m.

4. The radius and height of a cone are in the ratio 4:3 the area of the base is 154cm2. find the area of
the curved surface.

5. The volume of a metallic cylindrical pipe is 748cm3 . Its length is 14 cm and its external radius is 9 cm. Find its thickness.

6. A well of inner diameter 14m is dug to a depth of 15m. Earth taken out of it has been evenly spread all around it to a width of 7m to form an embankment. Find the height of the embankment.

7. A cloth having an area of 165m is shaped into a cylindrical tent of radius 5m. How many students can sit in the tent if a student occupies 5/7 m2 ? Find the volume of air for each student.

8. The difference between inside and outside surfaces of cylindrical tube 14cm long is 88 sq.cm. If the volume of the tube is 176 cubic cm. find the inner and outer radii of the tube.

9. The area of three adjacent faces of a cuboidal box are 120cm2, 72cm2 and 60cm2 respectively. Find the volume of the box.

10. The total surface area of a hollow cylinder which is open from both sides is 4620cm2, area of base ring is 15.5cm2 and height 7cm. Find the thickness of the cylinder.
RATIO AND PROPOTION
1. The extension in an elastic string varies directly as the weight hung on it. If a weight of 150g produces an extension of 2.8cm, what weight would produce an extension of 19.6cm?

2. A group of 120 men had provisions for 200 days. After 5 days, 30 men died due to an epidemic. How long will the remaining food lost?

3. 1200 soldiers in a fort had enough food for 28 days. After 4 days. Some soldiers were transferred to another fort and thus the food lasts for an extra 32 days. How many soldiers left the fort?

4. If 12 men or 15 woman can finish a piece of work in 66 days. How long will 2 men and 3 woman take to finish the work?

5. If 5 men or 7 women earn Rs 525 per day, how much would 7 men and 13 women earn per day?

6. In an army camp of 1400 men, these is enough food to last for 18 days if each man consumes 396g per day. How many men should leave the camp so that the same food may last for 21 days with each man having 432g per day?

Bar Graph

1. The following table shows that the favorite sports of 250 students of a school. Represent the data
by a bar graph.
Sports                  Cricket Foot ball Tennis Badminton Swimming
No of students         75   35  50 25 65

2. Given below is a table which shows the year wise strength of a school. Represent this data by a
bar graph.

Year 2001 -02 2002 -03 2003 -04 2004 -05 2006 -07
No of students 800 975 1100 1400 1625

3. The air distances of four cities from Delhi ( in km) are given below. Represent the data by a bar graph.

City Kolkata Mumbai Chennai Hyderabad
Distance from Delhi in Km 1340 1100 1700 1220

4. The following is the distribution of weights in kg of 52 persons:
Weight in kg 30 – 40 40 – 50 50 – 60 60 – 70 70 – 80
Persons 10 15 17 6 4

5. What is the lower limit of class 50 – 60? 6. Find the class mark of the classes 40 – 50, 50 – 60

7. What is the class size?

Pie Chart
1. The number of students in a school speaking different languages is given below. Present the data
in a pie chart
Language Hindi English Marathi Bengali Tamil
No of students 40 12 9 7 4

2. The number of hours spend by a school boy on various activities on a working day are given below.

Activity School Homework Play Sleep Others

No of hours 8 4 3 7 3

3. Draw a pie chart for the following data of the investment pattern in a five year plan:

Agriculture Irrigation Small industries Transport Power Social service
14% 16% 29% 17% 16% 8%

Probability
1. A coin is tossed 500 times and we get head;285times, tail;215 times, when a coin is tossed at random, what is the probability of getting i) a head ii) a tail?

2. Two coins are tossed 400 times and we get two heads ; 112 times, one head : 160 times, zero head : 128 times when two coins are tossed at random, what is the probability of getting i) 2 heads ii) 0ne head iii) 0 head.

3. Three coins are tossed 200 times and we get three heads: 39 times , two heads 58 times , one head; 67 times, 0 head ;36 times. When three coins are tossed at random what is the probability of getting i) 3 heads ii ) 1 head iii) 0 head iv) 2 heads.

4. Two coins are tossed simultaneously 500 times, we get two heads 105 times, one head 275 times and no head 120 times. Find the probability of getting i) 2 tails ii) one tails iii) 2 heads.

5. All kings, jacks and diamonds have been removed from a pack of cards and the remaining cards are well shuffled. A card is drawn at random. Find the probability that it is (i) a red queen (ii) a face card (iii) a diamond (iv) a black card.

6. The shoppers who come to a departmental store are marked as : man(M), woman(W), boy (B)or girl ( G). The following list gives the shoppers who came during the first hour in the morning:

W W M W G W M W B W G M W M B G B W G W M G W M W G M W B W M W G W MW G M W B G W M W W M W G W M W G W M W G W M W W .
Make a frequency distribution table using tally marks.

7. A box contains 17 cards numbered 1,2,3,4,……17. A card is drawn at random from the box. Find the probability that the number on the card is
i) odd ii) even iii) prime iv) divisible by 3
v) divisible by 2 and 3 both vi) divisible by 4 or 7 vii) divisible by 2 or 3.

8. Numbers 2 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 onto it. What is the probability of.

i) getting a number 6? ii) getting a prime number iii) getting a number greater than 5?
Graph
1. Plot the following points on the graph paper and name the quadrant in which it lies
(4, -2 ) (-1 ,3) ( 0, -1 ) ( 5, -2) ( 2, 1 ) ( -5, -3 ) and (-2, 0)

2. Draw the graph of the following equations.
i) 3x +2y =5 ii) y – 3x =2

3. Solve the following system of linear equations graphically.
a) 4x – 5y – 20 and 3x + 5y – 15 = 0
b) x + 2y = 3 and 4x = 3Y = 2.

Construction of Quadrilaterals.

1. Construct a quadrilateral ABCD given that AB = 3.7cm, BC = 3.8 cm, CD = 4.3 cm, DA = 4.6 cm and ∠ D =75

2. Construct a quadrilateral ABCD given that BC=4.5 cm, AB=4cm, ∠ B=75 ∠ A=90 and ∠ C=120

3. Construct a quadrilateral ABCD in which AB=BC=5.5cm, CD=4cm, DA=6.3cm and AC=9.4cm. Measure BD.

4. Construct a quadrilateral ABCD, where A=65, B=105, C=75, BC=5.7 cm and CD=6.8 cm.

5. Construct a quadrilateral PQRS in which PQ=6 cm, QR=5.6 cm, RS=2.7 cm, ∠ Q=45 and ∠ R= 90

6. Construct a parallelogram with diagonals 5.4 cm and 6.2 cm and the angle included by the two diagonals is 45

7. Construct a parallelogram ABCD using only ruler and compass, such that AB=6cm, BC=3cm and angle B=45. Write the steps of construction in brief.

8. Construct a rhombus ABCD using only ruler and compass, such that the side of the rhombus is 4 cm and one of its angles is 30. Write the steps of construction in brief.

9. Construct a trapezium ABCD in which AB=6 cm, BC= 4 cm, CD=3.2 cm ∠ B=75 and DC||AB.

10. Draw a trapezium ABCD in which AB//DC, AB = 7 cm, BC = 5cm, AD = 6.5 cm and ∠ B = 60
PARALLELOGRAM
1. Two adjacent angles of a parallelogram are as 2:3. Find the angles

2. Prove that the opposite sides of a parallelogram are equal.

3. Prove that in a parallelogram diagonals bisect each other.

4. In the adjacent figure, ABCD is a parallelogram and line segments AE and CF bisect the angles A and C respectively. Show that AE // CF.

5. Two lines AC and BD, 5cm each bisect each other. If A,B,C,D are joined what type of quadrilateral is formed. Justify your answer.

6. ABCD is a parallelogram in which AB= 2AD and p is the midpoint of AB, then Find ∠CPD.

7. In a parallelogram ABCD, if AB= 2x+5, CD= y+1 AD=y+5 and BC=3x-4, then find the ratio of AB:BC.

8. ABCD is a parallelogram whose diagonals intersect each other at O. A line segment EOF is drawn to meet AB at E and DC at F. Prove that OE = OF.

9. ABCD is a parallelogram in which AB is produced to E so that BE=AB. Prove that ED bisects BC.

10. PQRS is a rectangle. PR is a diagonal. QM & SN are perpendiculars drawn from Q & S on PR. Prove that QM = SN.

Quadrilateral

1. ABCD is a quadrilateral in which AB=AD and BC=DC. Prove that AC bisects ∠A and ∠C.

2. If angles P, Q, R and S of the quadrilateral PQRS taken in order and in the ratio 3:7:6:4 then show that PQRS is a trapezium.

3. In a quadrilateral ABCD, the line segments bisecting∠ C and ∠D meet at E. Prove that ∠A+∠B =2∠CED

4. If bisectors of ∠A and ∠B of a quadrilateral ABCD intersect each other at P , of ∠B and ∠ C at Q, of ∠C and ∠D at R and ∠ D and ∠A at S, then show that PQRS is a quadrilateral whose opposite angles are supplementary.

5. In a quadrilateral ABCD, the bisectors of < A and < B meet in a point P. If ∠ C = 100 and ∠ D = 60, find the measure of ∠ APB

CBSE 7th Maths Question Papers |Sample Papers | Test papers

7th Ratio and Proportion

Complete the following statements using the help box:

1. The comparison of two quantities of the same kind by means of division is termed as ___.

2. The two quantities to be compared are called the ________ of the ratio.

3. The first term of the ratio is called the _________ and the second term is called the ___.

4. In a ratio, only two quantities of the __________ unit can be compared.

5. If the terms of the ratio have common factors, we can reduce it to its lowest terms by 
cancelling the _____.

6. When both the terms of a ratio are multiplied or divided by the same number (other than 
zero) the ratio remains _________ .The obtained ratios are  called__________.

7. In a ratio the order of the terms is very important. (Say True or False)

8. Ratios are mere numbers. Hence units are not needed. (Say True or False)

9. Equality of two ratios is called a __________. If a,b;c,d are in proportion, then a:b::c:d .

10. In a proportion, the product of extremes =___________

Help Box:

1) Ratio 2) terms 3) antecedent, consequent  4) same 5) common terms 6) unchanged, equivalent ratios 7) True 8) True 9) proportion 10) product of means

1. Find 5 equivalent ratios of 2:7

2. Reduce 270 : 378 to its lowest term.

3. Find the ratio of 9 months to 1 year

4. If a class has 60 students and the ratio of boys to girls is 2:1, find the number of boys and 
girls.

5. A ribbon is cut into 3 pieces in the ratio 3: 2: 7. If the total length of the ribbon is 24 m, find 
the length of each piece.

6. The ratio of boys to girls in a class is 4 : 5. If the number of boys is 20, find the number of 
girls.

7. If A : B = 4 : 6, B : C = 18 : 5, find the ratio of A : B : C.

8. A bronze statue is made of copper, tin and lead metals. It has1/10 of  tin , 1/4of  lead and 
the rest copper. Find the part of copper in the bronze statue.

                7th Direct variation and indirect variation

In direct variation, when a given quantity (x) is changed in some ratio then the other quantity(y) is also changed in the same ratio. Then x/ y = constant

In Indirect variation, when a given quantity (x) is changed in some ratio then the other quantity(y) is do not changed in the same ratio. Then xy = constant

Þ It can be stated that if two quantities vary inversely, their product is a constant

1. Choose the correct answer

i) If the cost of 8 kgs of rice is Rs 160, then the cost of 18 kgs of rice is

(A) Rs.480 (B) Rs 180 (C) Rs 360 (D) Rs 1280

ii) If the cost of 7 mangoes is `35, then the cost of 15 mangoes is

(A) Rs 75 (B) Rs 25 (C) Rs 35 (D) Rs 50

iii) A train covers a distance of 195 km in 3 hrs. At the same speed, the distance travelled in 5  hours is

(A) 195 km. (B) 325 km. (C) 390 km. (D) 975 km.

iv) If 8 workers can complete a work in 24 days, then 24 workers can complete the same work in 

(A) 8 days (B) 16 days (C) 12 days (D) 24 days

v) If 18 men can do a work in 20 days, then 24 men can do this work in

(A) 20 days (B) 22 days (C) 21 days (D) 15 days

1. If x varies directly as y, complete the given tables:

x	1	1			9	15
y	2		10	16

2. If x varies inversely as y, complete the given tables:

x	20	10	40	50
y			50		250

3. A car travels 360 km in 4 hrs. Find the distance it covers in 6 hours 30 mins at the same speed

4. 7 men can complete a work in 52 days. In how many days will 13 men finish the same work?

5. A book contains 120 pages. Each page has 35 lines . How many pages will the book 
contain if every page has 24 lines per page?

6. A car travels 60 km in 45 minutes. At the same rate, how many kilo metres will it travel in 
one hour?

7. A car takes 5 hours to cover a particular distance at a uniform speed of 60 km / hr. How 
long will it take to cover the same distance at a uniform speed of 40 km / hr?

8. 150 men can finish a piece of work in 12 days. How many days will 120 men take to finish 
the same work?

9. A troop has provisions for 276 soldiers for 20 days. How many soldiers leave the troop so 
that the provisions may last for 46 days?

10. A book has 70 pages with 30 lines of printed matter on each page. If each page is to 
have only 20 lines of printed matter, how many pages will the book have?

11. There are 800 soldiers in an army camp. There is enough provisions for them for 6o 
days. If 400 more soldiers join the camp, for how many days will the provisions last?

12. A wheel makes 48 revolutions in 3 seconds. How many revolutions does it make in 30 
seconds?

                                           7^th Percentage

The word ‘Percent’ is derived from the Latin word ‘Percentum’, which means ‘per hundred’ or ‘hundredth’ or ‘out of 100’.

• Percentage also means ‘percent’.

• Symbol used for percent is %

• Any ratio x : 100 is called ‘Percent’.

1) Write the following as a percent:                  (i) 20:100 (ii) 100:93(iii)100/100 (iv) 0.07

2) Write the following percent as a ratio:          (i) 43% (ii) 17 ¹/₂(iii) 5% (iv) 33 ¹/₃ %

3) Write the following percent as a fraction: (i) 25% (ii) 12 ¹/₂% 2 (iii) 33%

4) 9/10 of your blood is water. What % of your blood is not water.

5) 2/5 of your body weight is muscle. What % of body is muscle?

In a class of 35 students, 7 students were absent on a particular day. What percentages of 
the students were absent?

5. Ram bought 36 mangoes. 5 mangoes were rotten. What percentage of the mangoes was 
rotten?

6. In a class of 50, 23 were girls and the rest were boys. What is the percentage of girls and 
the percentage of boys?

7. Ravi got 66 marks out of 75 in Mathematics and 72 out of 80 in Science. In which subject 
did he score more?

8. Express as a decimal (a) 25.7%    (b) 15%

9. Find the value of (a)% 1/2 of 200.  (b) 0.75% of 40 kg.

10. In 2011, the population of a town is 1,50,000. If it is increased by 10% in the next year, find the population in 2012.

11. The percentage of literacy in a village is 47%. Find the number of illiterates in the village, 
if the population is 7,500.

12. Is it true?  20% of 25 is same as 25% of 20.

13.  The tax in a restaurant is 1.5% of your total bill.

a) Write the tax % as a decimal.  b) A family of 6 members paid a bill of ` 750. What is the tax 
for  their bill amount?  c) What is the total amount that they should pay at the restaurant?

14. 1) Any fraction with its denominator 100 is called __________

2)1/2 = -----------%             3) 35% = ------------ ( in fraction)

4) 0.05 = ----------------%   5)1/4 =  ----- %

                   7^th Profit and Loss

The price at which any one buys goods at the market is called the Cost Price(C.P.).

The price at which one can sell the goods at the market is called the Selling Price (S.P.).

Additional amount given or taken for CP is called the profit.

1. Choose the correct answer:

i) If the cost price of a bag is Rs. 575 and the selling price is Rs.625, then there is a profit of 
Rs.

(A) 50 (B) 575 (C) 625 (D) none of these

ii) If the cost price of the box is Rs.155 and the selling price is Rs.140, then there is a loss of 
Rs.

(A) 155 (B) 140 (C) 15 (D) none of these

iii) If the selling price of a bag is `235 and the cost price is `200, then there is a

(A) profit of Rs.235 (B) loss of Rs.3  (C) profit of Rs.35 (D) loss of Rs.200

iv) Gain or loss percent is always calculated on

(A) cost price (B) selling price (C) gain (D) loss

v) If a man makes a profit of Rs.25 on a purchase of Rs.250, then profit% is 

(A) 25 (B) 10 (C) 250 (D) 225

1. Sanjay bought a bicycle for Rs. 5,000. He sold it for Rs.600 less after two years. Find the selling price and the loss percent.

2. A fruit seller bought 8 boxes of grapes at Rs.150 each. One box was damaged. He sold the remaining boxes at Rs.190 each. Find the profit / loss percent.

3. A shop keeper bought 10 bananas for `100. 2 bananas were rotten. He sold the remaining bananas at the rate of Rs. 11 per banana. Find his gain or loss % 6. A shop keeper purchased 100 ball pens for Rs. 250. He sold each pen for Rs. 4. Find the profit percent.

4. A vegetable vendor bought 40 kg of onions for Rs. 360. He sold 36 kg at Rs. 11 per

kg. The rest were sold at Rs. 4.50 per kg as they were not very good. Find his profit / loss  Percent.

5. A trader mixes two kinds of oil, one costing Rs. 100 per Kg. and the other costing `80 per Kg. in the ratio 3: 2 and sells the mixture at Rs.  101.20 per Kg. find his profit or loss percent.

6. Sathish sold a camera to Rajesh at a profit of 10 %. Rajesh sold it to John at a loss of 12 %. If John paid Rs. 4,840, at what price did Sathish buy the camera?

7. The profit earned by a book seller by selling a book at a profit of 5% is Rs. 15 more than when he sells it at a loss of 5%. Find the Cost Price of the book.

                              7^th Simple Interest

1. Radhika invested Rs.5,000 for 2 years at 11 % per annum. Find the simple interest and the amount received by him at the end of 2 years.

2. Find the simple interest and the amount due on Rs. 7,500 at 8 % per annum for 1 year 6 months.

3. Find the simple interest and the amount due on Rs. 6,750 for 219 days at 10 % per annum.

4. Rahul borrowed Rs. 4,000 on 7th of June 2006 and returned it on 19th August2006. Find the amount he paid, if the interest is calculated at 5 % per annum

5. Find the rate percent per annum when a principal of Rs. 7,000 earns a S.I. of Rs.1, 680 in 16 months.

6. Vijay invested Rs.10, 000 at the rate of 5 % simple interest per annum. He received     Rs.11, 000 after some years. Find the number of years.

7. A sum of money triples itself at 8 % per annum over a certain time. Find the number of years.

8. A certain sum of money amounts to Rs.10, 080 in 5 years at 8 %. Find the principal

9. A certain sum of money amounts to Rs. 8,880 in 6 years and Rs. 7,920 in 4 years 
respectively. Find the principal and rate percent.

10. Find the principal that earns `250 as S.I. in 2¹/₂  years at 10 % per annum.

11. In how many years will a sum of Rs. 5,000 amount to Rs.5,800 at the rate of  8 % per 
annum.

12. A sum of money doubles itself in 10 years. Find the rate of interest.

13. A sum of money doubles itself at 12¹/₂ % per annum over a certain period of time. Find the number of years.

14. A certain sum of money amounts to Rs. 6,372 in 3 years at 6 % Find the principal.

15. A certain sum of money amounts to Rs. 6,500 in 3 years and Rs. 5,750 in 1¹/₂ years respectively. Find the principal and the rate percent?

16. Find the rate per cent at which, a sum of money becomes 9/4 times in 2 years.

17) If Ram needs Rs. 6, 00,000 after 10 years, how much should he invest now in a bank if the bank pays 20 % interest p.a?

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X Maths guess questions for CBSE board exam March 2012

1. If 4a²x² + 4abx + = 0 has equal roots of x, then find the value of k.

2. Two positive numbers differ by 3 and their product is 504.  Find the numbers.

3. The length of a tangent from a point A at a distance 5 cm from the centre of the circle is 4 cm.  Find the diameter of the circle.

4. Two tangents PQ and PR are drawn from an external point P to a circle with centre O. Prove PROQ is a cycle quadrilateral.

5. Determine the ratio in which the point P(x, -2) divides the join of A(-4, 3) and B(2, -4).  Also find the value of x.

6. Area of a sector of a circle of radius 36 cm is 54p cm².  Find the length of corresponding arc of sector.

7. Two cubes each of edge 4 cm are joined face to face.  Find the surface area of the resulting cuboid.

8. A dice is thrown once.  Find the probability of getting:  (a) a prime number (b) a number divisible by 2

Find the sum of all two digit positive numbers divisible by 3.

Question numbers 19 to 28 carry 3 marks each.

9. In an A.P. the first term is 24, the last term is 29 and the sum of all its term is 150.  Find its common difference.

10. For what values of k does (k-12)x ² + 2(k-12)x + 2= 0 has equal roots ?

11. The circumference of the base of a 9 m high wooden solid cone is 44 m.  Find the volume of the cone.

12. A solid metallic sphere of diameter 21 cm is melted and recast into a number of smaller cones each of diameter 7cm and height 3 cm.  Find the number of cones so formed.

13. Find a point on x -axis which is equidistant from the points A(- 5, 4) and B(- 1, 6).

14.Show that the points A (3, 4), B(- 4, 3) and C(5, 0) lie on the circle having centre O(0,0)

15. In what ratio does the x-axis divide the line segment joining the points (- 4, - 6) and (- 1, 7).  Also find the coordinates of the point of division.

16. If all the sides of a parallelogram touch a circle, show that the parallelogram is a rhombus.

17. AB and CD are two parallel tangents to a circle with centre O.  ST is a tangent segment between the parallel tangents touching the circle at Q.  Show that < SOT = 90⁰.

18. An aeroplane flying horizontally 1 km above the ground

is observed at an elevation of 60⁰.  After 10 seconds, its elevation is observed to be 30⁰ Find the speed of the aeroplane in km/hr.

19. A tower is 60 m high.  From the top of it the angles of depression of the top and the bottom of a tree are found to be 30⁰ and 60⁰ respectively.  Find the height of the tree and its distance from the tower.

20. Two dice are thrown simultaneously. Find the probability of getting: 

(a) Same number on both dice.     (b)  Different numbers on both the dice.

21. Two tangents PA and PB are drawn to a circle with centre O from an external point P. Prove that < APB =2 < OAB.

22. In an A.P. the sum of first ten terms is - 80 and the sum of next ten terms is - 280. Find the A.P.

23.The sum of first 7 terms of an A.P. is 49 and that of first 17 terms is 289.  Find the sum of first n terms.

24. Some students planned a picnic.  The budget for food was Rs. 480.  But 8 of them failed to go, the cost of food for each member increased by Rs. 10.  How many students attended the picnic?

25. A fast train takes 3 hours less than a slow train for a journey of 600 km.  If the speed of  the slow train was 10 km/hr less than that of the fast train, find the speeds of the trains.

26. A well of diameter 3 m is dug 14 m deep.  The earth taken out of it has been spread evenly all around it to a width of 4 m to form an embankment.  Find the height of the embankment

27. Draw a pair of tangents to a circle of radius 5 cm which are inclined to each other at an angle of 60⁰.

28. If the radii of the ends of a bucket 45 cm high are 28 cm and 7 cm.  Find its capacity and surface area.

29. The angle of elevation of the top of a building from the foot of a tower is 30⁰ and the angle of elevation of the top of the tower from the foot of the building is 60⁰.  If the tower is 50 m high.  Find the height of the building.

30. Which term of the AP : 6, 13, 20, 27, ....... is 98 more than its 24th term ?

31. Sum of the areas of two squares is 468 m².  If the difference of their perimeters is 24 m, find the sides of the two squares.

32. In Fig.1, two circles touch each other externally at C.  Prove that the common tangent at C bisects the other two common tangents

33. In Fig. 2, a circle touches the side BC of triangle ABC at P and touches AB and AC  produced at Q and R respectively.  Show that   AQ=  1/ 2 (Perimeter of D ABC)

34. If A(1, 2), B(4, y), C(x, 6) and D(3, 5) are the vertices of a parallelogram ABCD taken  in order, find the values of x and y.

35. In what ratio does the y- axis divide the line segment joining the points?

(24, 5) and  (3, 27).

36. Cards marked with numbers 3, 4, 5, ......, 50 are placed in a box and mixed thoroughly.  One card is drawn at random from the box.  Find the probability that the number on the drawn card is (i) divisible by 7.    (ii) Is a perfect square.

37. A toy is in the form of a cone mounted on a hemisphere of common base radius 7 cm.  The total height of the toy is 31 cm.  Find the total surface area of the toy.

38. A horse is tied to a peg at one corner of a square shaped grass field of side 25 m by means of a 14 m long rope.  Find the area of the part of the field in which the horse can graze

Question numbers 19 to 28 carry 3 marks each.

39. Solve the following quadratic equation for x :  p² x ²  +  (p² -  q²)x²  -  q² =0

40. The 4th term of an AP is equal to 3 times the first term and the 7th term exceeds twice the 3rd term by 1.  Find the first term and the common difference.

41. Draw a D ABC with BC= 8 cm,  Ð ABC= 45⁰ and  Ð BAC= 105⁰.  Then construct a triangle whose sides are 2/ 3 times the corresponding sides of the DABC.

42. A circle is inscribed in a triangle ABC having sides AB58 cm, BC= 10 cm and CA = 12 cm as shown in Fig. 3.  Find AD, BE and CF.

43. If the radius of the base of a right circular cylinder is halved, keeping the height same,

find the ratio of the volume of the reduced cylinder to that of the original cylinder.

44. Find the area of the sector of a circle with radius 10 cm and of central angle 60⁰.  Also,

find the area of the corresponding major sector.  OR

A solid metallic sphere of diameter 21 cm is melted and recast into a number of smaller cones, each of diameter 3.5 cm and height 3 cm.  Find the number of cones so formed. 

45. A man standing on the top of a multistory building, which is 30 m high, observes the  angle of elevation of the top of a tower as 60⁰ and the angle of depression of the base of  the tower as 30⁰.  Find the horizontal distance between the building and the tower. Also find the height of the tower.

46. An aeroplane, when 3000 m high, passes vertically above another plane at an instant when the angles of elevation of the two aeroplanes from the same point on the ground  are 60⁰ and 45⁰ respectively.  Find the vertical distance between the two aeroplanes.

47. A box contains 20 balls bearing numbers 1, 2, 3, 4, ........20.  A ball is drawn at random  from the box.  What is the probability that the number on the drawn ball is

(i) An odd number  (ii) Divisible for 2 or 3  (iii) Prime number (iv) Not divisible by 10

48. The mid points of the sides AB, BC and CA of a triangle ABC are D(2, 1), E(1, 0) and  F(21, 3) respectively.  Find the coordinates of the vertices of the triangle ABC.

49. ABCD is a rectangle formed by joining the points A(- 1, - 1), B(- 1, 4), C(5, 4) and D(5, - 1).  P, Q, R and S are the mid points of AB, BC, CD and DA respectively.  Is the  quadrilateral PQRS a square, a rectangle or a rhombus ?  Justify your answer.

50.The line segment joining the points A(2, 1) and B(5, - 8) is trisected at the points P and Q where P is nearer to A.  If point P lies on the line 2x- y+ k = 0, find the value of k.