Question bank
Chapter-1 Rational Numbers
Q-1 Find the absolute value of the following :
(a) − 13/ 15
(b) − 13/ 18
Q-2 Arrange the following rational numbers in ascending order:
(a) 1/ 2, 2 /3, -1 /4, -3/ 5
(b) 2 /3, 5/ 6, -8/ 3, 6 /-9
Q-3 Find the sum of the following :
(a) − 3 /4 and 4 /5
(b) −2 /15 and 3 /4
(c) − 5/ 6 and 7 /15
Q-4 Find the product of the following :
(a) 3/ 10× -19 /2× 10/19
(b) 9 /2× -7 /5
Q-5 Divide the following :
(a) (− 4) ÷ 2 /3
(b) 2 /3÷ 5 /11
(c) − 4/ 5÷ 12
Q-6 Answer the following questions.
5. The sum of two rational numbers is 1/ 2 . If one of them is 3 /4 , find the other.
6. The product of two rational numbers is (− 15/ 7) . If one of them is (− 10 /21) , find the other number.
Q-7 Verify that [−(− x)] = x, for a each of the following :
(a) x = 2/ 3
(b) x = − 5/ 7
Q-8 Verify that x + y = y + x, for each of the following :
(a) x = −2 /3 and y = 1/ 3
(b) x = 4 /5 and y = − 7/ 2
Q-9 Find the multiplicative inverse of each of the following :
(a) − 1
(b) 5
(c) −2 × − 3 /5
Q-10 For each of the following, check that x ÷ y ≠ y ÷ x
(a) x = 1/ 5 and y = 13 /15
(b) x = 20/ 40 and y = 0
Q-11 Answer the following questions.
5. Find three rational numbers between(− 4) and (− 2)
8. Write five rational numbers between 2.5 and 2. 7
Chapter-2 Exponents or Powers
Q-1 Write the base and exponent in each of the following :
(a) (−2) ^3
(b) (3) ^4
(c) (-5/6) ^4
Q-2 Write the following in exponential form
(a) (− 3)× (− 3)× (− 3)
(b) 3/ 8 × 3/8 ×3/8×3/8 ×3/8
(c) 81 /625
Q-3 Simplify and express the following in exponential form :
(a) 5^3 × 5^2
(c) 2^4× 2^ 4
Q-4 Simplify the following and write in exponential form :
(a) 2^3 × 4^3
(b) y^x*x^x*z^x
Q-5 Find the value of :
(a) (2/3)^3*(3/5)^2
(b) (-2)^4÷(-2/3)^5
(c) (1/2)^4 ÷ (1/3)^4
Q-6 For any non-zero rational number x, which of the following statements are true?
(a) x×^-m x^-n = x ^-m+n
(b) (X^M) ^-N =X^mn
(c) x^m÷ x^n = x^n-m
(d) (x^n)^0= x^0
Chapter-3 Square and Square Root: Cube and Cube Root
Q-1 Using the prime factorisation method, find which of the following numbers are perfect squares.
(a) 225
(b) 189
(c) 441
(d) 729
(e) 1575
Q-2 Which of the following are the squares of even numbers?
(a) 196
(b) 441
(c) 400
(d) 324
Q-3 Which of the following are the squares of odd numbers?
(a) 121
(b) 225
(c) 196
(d) 484
Q-4 Without adding find the sum :
(a) (1 + 3 + 5 + 7 + 9 + 11)
(b) (1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19)
(c) (1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 + 21 + 23)
Q-5 Answer the following questions.
(a) Express 64 as the sum of eight odd numbers.
(b) Express 121 as the sum of eleven odd numbers.
Q-6 Find the square root of the following by prime factorisation method :
(a) 1521
(b) 1600
(c) 1764
Q-7 Which of the following numbers are cubes of even numbers ?
(a) 512
(b) 729
(c) 3375
Q-8 Answer the following questions.
5. Find the volume of a cube, each of whose edge measure 5.3 cm.
6. Find the smallest number by which 2560 must be multiplied so that the product becomes a perfect cube.
7. Find the side of a cube whose volume is 820.025 cubic metres
Chapter-4 Algebraic Expressions and Factorisation
Q-1 Classify the following algebraic expressions as monomials, binomials or trinomials :
(a) 2/ 3 ab^2
(b) x^2- xy + 15
(c) 6pq + 3
(d) x^2+ y^ 2
Q-2 Write the degree of the following polynomials :
(a) 3+ 7x^2 -4x+x^3
(b) 6xy -7x^2 + 8x^ 2y ^2
(c) 4x^5 -3x^3y+3xy^3 +8y^5
(d) x^3y^3 -8x^2y^ 217xy+8
Q-3 Subtract the following :
(a) 6y^2 from -lly^2
(b) l0x+ 7y from-15x+6y
(c) 20-3x+ 4x^2 -x^3 from x^3 -x^2 + 2x-19
Q-4 . Multiply :
(a) 2xx7x
(b) 3x^2 x6x^3
Q-5 Find the following products :
(a) (2x - y) (3x - 5y)
(b) (3a+2)(2a- 5)
(c) (p + q)(p - q)
Q-6 Expand each of the following by using a suitable identity :
(a) (x+ 3)^2
(b) (x-7)^2
(c) (2m+ 5)^2
Q-7 Find the following products using an identity :
(a) (2m+ 3) (2m - 3)
(b) (5x-7y) (5x+7y)
Q-8 Evaluate without actual multiplication :
(a) (98)^ 2
(b) (107)^ 2
(c) 88x92
(d) 198 x 202
Q-9 Find all possible factors of the following :
(a) 12p^2q
(b) 16xy^2z
(c) 20a^2b^2c^2
Q-10 Factorise using suitable groupings :
(a) abc − ab − c + 1
(b) p^2q- pr^2 - pq+ r^2
(c) 4x^2 +2y^2 +x^2y ^2 +8
Chapter-5 Linear Equations in One Variable
Q-1 Solve the following equations and verify the solution :
(a) 8x + 3 = 27
(b) 5x − 7 = 2x + 8
(c) 3(x −1) = 8
(d) 5x −(3x − 1) = x − 4
Q-2 Answer the following questions.
1. Two numbers are in the ratio 8 : 3. If the sum of the numbers is 143, find the numbers.
2. 2 /3 of a number is 20 less than the original number. Find the number.
3. Four-fifths of a number is 10 more than two-thirds of the number. Find the number.
4. Twenty-four is divided into two parts such that 7 times the first part added to 5 times the second part makes 146. Find each part.
5. Find the number whose fifth part increased by 5 is equal to its fourth part diminished by 5.
Chapter-6 Commercial Method
Q-1 Answer the following questions.
3. The variable x varies directly as y. When y is 10, x is 3 /2 . Find y when x is 9.
4. Sumita bought 12 notebooks for Rs 168. Find the cost of 9 notebooks.
5. A car is running at an average speed of 50 km/h. How much distance will it cover in 12 minutes?
6. A worker is paid Rs 210 for 6 days work. If he gets Rs 875 in a certain month, for how many days did he work in that month ?
7. Five typists can type 100 pages in a day. How many pages can 8 typists type in a day ?
Q-2 Answer the following questions.
2. If 6 men can whitewash a building in 5 days, find the number of days in which the building will be white washed by 15 men.
3. If 40 cows can graze a field in 10 days, how many cows will graze the same field in 25 days ?
4. A garrison of 400 men had food for 35 days, however, 50 men went away. How many days will the food last now.
5. A person has enough money to buy 25 cycles worth ` 500 each. How many cycles will the person be able to buy if each cycle now cost ` 125 more ?
6. A car covers a certain distance in 10 hours at a speed of 48 km/hr. By how much should its speed be increased so that it takes only 8 hours to cover the same distance?
7. A contractor employed 560 men to complete a project in 7 months. If he wishes to complete the same project in 5 months. How many more men should be employ ?
8. At a scout camp, there is sufficient food for 64 scouts to last for 7 days. If 8 scouts leave the camp. How long will the food last now?
Q-3 Find the gain or loss percent when :
(a) C.P = Rs 620 and S.P = RS 713
(b) C.P = Rs 675 and S.P = Rs 630
(c) C.P = Rs 345 and S.P = Rs 372.60
(d) C.P = Rs 80 and S.P = Rs 76.80
Q-4 Find the selling price when :
(a) C.P = Rs 1650 and Gain % = 4%
(b) C.P = Rs 875 and loss % = 12%
(c) C.P = Rs 915 and Gain % = 6, 2/ 3 %
(d) C.P = Rs 645 and loss % = 13, 1/ 3 %
Q-5 Find the discount per cent when :
(a) M.P = Rs 650 and S.P = Rs 585
(b) M.P = Rs 1600 and S.P = Rs 1200
Q-6 Answer the following questions.
2. At a clearance sale, all goods are on sale at a 45% discount. If the marked price of a skirt is Rs 600, find its selling price
3. A discount of 12% is given on the marked price of an article, and it is sold for Rs 880. Find its market price.
4. A refrigerator is available for Rs 14,500, including sales tax. If the rate of sales tax is 10%, find the price of the refrigerator without tax
5. The marked price for a medicine is Rs 155.50. If the rate of sales tax is 6%, calculate the amount the man has to pay for the medicine.
Chapter-7 Simple Interest and Compound Interest
Q-1 Answer the following questions.
1. Find the amount and compound interest on ` 2500 for 2 years at 10% per annum, compound annually.
2. Find the amount and compound interest on Rs 16000 for 3 years at 5% per annum, compound annually
3. Find the difference between the simple interest and the compound interest on Rs 5000 for 2 years at 6% per annum
4. Ratna obtained a loan of Rs 25000 from the Syndicate bank to renovate her house. If the rate of interest is 8% per annum. What amount will she have to pay to the bank after 2 years to discharge her debt ?
5. Harpreet borrowed Rs 20000 from her friend at 12% per annum simple interest. She lent it to Alam at the same rate but compounded annually. Find her gain after 2 years.
6. Manoj deposited a sum of Rs 64000 in a post office for 3 years, compounded annually at 7, 1 /2 % per
Q-2 Find the amount and the compound interest by using the formula in each of the following :
1. Principal = Rs 6000, rate = 5% p.a,, Time = 2 years
2. Principal = Rs 10,000, rate = 11% p.a,, time = 2 years
4. Principal = Rs 31250, rate = 8% p.a,, time = 3 years.
5. Principal = Rs 6750, rate = 6, 2 /3 % p.a,, time = 3 years.
6. Principal = Rs 62500, rate = 12% p.a,, time =2, 1 /2 years
7. Principal = Rs 15000, rate = 10% p.a,, time =2, 1/ 5 years.
8. Principal = Rs 8000, time = 2 years and the rates being 9% per annum during the first year and 10% per annum during the second year
Q-3 Answer the following questions.
1. What sum will become Rs 2025 in 2 years at 12.5% per annum compound interest?
2. What sum will become Rs 9261 after 3 years at 5% per annum compound interest?
3. In how much time would Rs 5000 amount to ` 6655 at 10% per annum compound interest
Chapter-8 Quadrilaterals
Q-1 Answer the following questions.
2. In a parallelogram ABCD,∠D = 140° . Find the measures of ∠ A and ∠B.
3. The sum of two opposite angles of a parallelogram is 160°. Find all the angles of the parallelogram
4. Two opposite angles of a parallelogram are (3x −2)° and (50 − x)°. Find the measure of each angle of the parallelogram.
5. Find the length of the diagonal of a rectangle whose sides are 12 cm and 5 cm.
6. ABCD is a parallelogram in which ∠DAB = 75° and ∠DBC = 60°. Calculate the measure of ∠CDB and ∠ ADB.
Q-2 Answer the following questions.
1. ABCD is a rhombus whose diagonals intersect at 0. If AB = 10 cm andBD = 16 cm, find the length of the diagonal AC.
2. The diagonals of a rhombus are 6 cm and 8 cm. Find the length of each side of the rhombus.
3. In the figure given below, ABCD is a trapezium with AB ||DC. If ∠ A = 50° and ∠B = 70°, find the measures of ∠ ADC and ∠DCB.
Chapter-9 Constructions of Quadrilaterals
Q-1 Answer the following questions.
1. Construct a parallelogram ABCD in which AB = 5.5 cm, AD = 4 cm and diagonal BD = 6.5 cm
2. Construct a parallelogram ABCD in which AB = 4.2 cm, BC = 5.5 cm and ∠B = 70°.
3. Construct a square with a diagonal of length 8 cm.
4. Construct a rectangle ABCD in which AB = 5 cm and diagonal AC = 7cm
5. Construct a rhombus whose diagonals are 6 cm and 4 cm.
Chapter-10 Representing 3D and 2D
Q-1 How many faces and edges do each of the following solids have ?
(a) Triangular prism
(b) Hexagonal pyramid
(c) Tetrahedron
(d) Octahedron
Q-2 . Write down the number of edges of each of the following figures :
(a) Tetrahedron
(b) Rectangular pyramid
(c) Cube
(d) Triangular prism
Q-3 Write down the number of vertices of each of the following figures :
(a) Cuboid
(b) Square pyramid
(c) Tetrahedron
(d) Triangular prism
Chapter-11 Area of Polygons
Q-1 Answer the following questions.
1. Find the area of a trapezium whose parallel sides are 24 cm and 20 cm and the distance between them is 15 cm
2. Find the area of a trapezium whose parallel sides are 38.7 cm and 22.3 cm and the distance between them is 16 cm
3. The area of a trapezium is 1080 cm^ 2 . If the lengths of its parallel sides are 55.6 cm and 34.4 cm, find the distance between them.
4. The area of a rhombus is 560 cm^ 2 . If one of its diagonals is 28 cm, find the length of the other diagonal
5. Find the area of a rhombus where each side measures 20 cm and one of its diagonals is 32 cm
6. If the area of a rhombus is 48 cm ^2 and one of its diagonals is 12 cm, find the side of the rhombus.
Q-2 Answer the following questions.
Find the area of the field ABCDEF as shown below :
. Find the area of the polygon PQRSTUV as shown in figure :
Chapter-12 Volume and Surface Area
Q-1 Answer the following questions.
2. The volume of a cube is 27,000 cm 3 . Find the side of the cube.
3. A rectangular container of oil is 20 cm long and 12 cm wide. It contains 1.680 litres of oil. What is the depth of the oil in the container.
4. What will happen to the volume of a cube if its edge is (a) doubled, (b) halved?
5. Three cubes, each measuring 6 cm, are joined end to end. Find the volume of the resulting cuboid
6. A wall of length 25 m, width 64 cm, and height 2m is to be constructed by using bricks, each of dimension 20 cm × 10 cm × 8 cm. How many bricks will be needed to construct the wall?
7. How many wooden cubical blocks of side 25 cm can be cut from a cuboidal block of wood of size 3 m × 75 cm × 50 cm, assuming that there is no wastage of wood?
8. The length, breadth and height of a cuboidal water tank are 7m, 6 m and 15 m respectively. If 8400 litres of water is pumped out of the water tank, find the fall in the water level in the water tank.
9. A cuboidal block of silver is 9 cm long, 4 cm wide, and 3.5 cm high. If beads of volume 1.5 cm^ 3 each are made from it, find the number of beads that can be made from the block.
Q-2 Answer the following questions.
1. Find the volume of a right circular cylinder of radius 2.8m and height 15 m
2. The area of the base of a right circular cylinder is 616 cm 2 and its height is 2.5 cm. Find the volume of the cylinder
3. A hollow cylindrical pipe is 21 m long. Its inner and outer diameters are 6 cm and 10 cm respectively. Find the volume of the metal used in making the pipe.
4. Two cylindrical cans have the same bases of diameter 14 cm. One of the cans is 10 cm high and the other is 20 cm high. Find the ratio of their volumes.
5. If the radius of the base of a right circular cylinder is halved, keeping the height the same, what is the ratio of the volume of the reduced cylinder to that of the original cylinder?
6. The diameter and height of a right cylindrical drum are 8.4 m and 3.5 m respectively. How many full bags of wheat can be emptied into the drum if the space required for wheat in each bag is 2.1 cubic metres?
7. A rectangular vessel 25 cm × 8 cm × 11 cm is full of milk. If the milk is poured into an empty cylindrical vessel of diameter 20 cm, what will be the height of milk in the cylindrical vessel?
Q-3 Find the surface area of a cuboid whose :
(a) length = 10 cm; breadth = 12 cm; height = 14 cm
(b) length = 3.2 m, breadth = 30 dm; height = 250 m
Q-4 Answer the following questions.
2. Find the surface area of cube whose volume is 343 cm 2
3. Find the volume of a cube whose surface area is 96 cm^ 2
4. The dimensional of a cuboid are in the ratio 5 : 3 : 1 and its total surface area is 414 m 2 . Find the dimension of the cuboid.
5. The area of four walls of a room is 51 m 2 . If the room is 5 m long and 3.5 m wide, find the height of the room
Q-5 Find the volume, curved surface area and total surface area of each of the cylinders whose dimensions are :
(a) radius of the base = 7 cm and height = 50 cm
(b) radius of the base = 5.6 m and height = 1.25 m
(c) radius of the base = 14 dm and height = 150 m
Q-6 Answer the following questions.
2. A wooden cylindrical pole is 7 m high and its base radius is 10 cm. Find its weight if the wood weights 225 kg per cubic metre
3. The volume of a circulariron rod length 1 metre is 3850 cm ^3 . Find its diameter.
4. The lateral surface area of a cylinder of length 14 metres is 220 cm 2 . Find the volume of the cylinder
Chapter-13 Probability
Q-1 When a dice is thrown, list the outcomes and probability of getting
(a) an even number
(b) a prime number
(c) not a prime number
(d) a number greater than 4.
(e) a number not greater than 4
Q-2 Mark impossible, less likely, equally likely, very likely or certain against each event :
(a) Getting a number more than 6 when a dice is thrown.
(b) The sun will rise from the east.
(c) It will rain when it is cloudy
(d) You will watch TV tonight.
(e) A coin will land on head.
(f) If it rains there are clouds.
(g) Getting a 3 when a dice is thrown.
(h) You will go to school tomorrow because your examinations starts tomorrow.
Q-3 Which of the following is an example of a random experiment ?
(a) Selecting a card from a pack of playing cards
(b) Measuring the weight of a person.
(c) Finding the length of your pencil box.
(d) Throwing two coins together
Q-4 Two dice are thrown simultaneously. Find the probability of :
(a) getting a sum less than 4.
(b) getting a doublet, i.e., [{(1, 1),(2,2),(3, 3)}....(6, 6)]
Q-5 Answer the following questions.
. An integer is chosen at random from the first 50 positive integers. What is the probability that the chosen integer is divisible by 5?
. A dice is thrown 30 times. How many times do you expect the number 6 to appear on the top?
Chapter-14 Data Handling
Q-1 Look at the bar graph and answer the questions that follow :
(a) What information does the bar graph represent ?
(b) In which month was the sale of cars the lowest?
(c) In which month were only 15 cars sold?
(d) How many cars were sold in the last quarter of the year?
Q-2 Look at the bar graph and answer the questions that follow :
(a) What is the title given to the bar graph ?
(b) In which country is the expenditure on health and nutrition the minimum ?
(c) In which country is the expenditure on health and nutrition ten thousand crores ?
(d) What is the ratio of expenditure of India and New york ?
Q-3 Look at the bar graph and answer the questions that follow :
(a) What was the maximum temperature of the day ?
(b) At what time was the temperature recorded as 55°F ?
(c) What was the temperature at 5 am ?
(d) Find the difference between the maximum and the minimum temperatures of the day ?