Question bank
Chapter-1 Integers
Q-1 Arrange the following integers in as cending order :
(a) 7, − 5, 1, − 12, 0, 6, − 3
(b) −18, 7, 5, −10, 12, −21
Q-2 Write the ab solute value of the following :
(a) |− 6 − 3 |
(b) |0 −12|
(c) |−21 + 3|
(d) |−12 −7|
Q-3 Which temperature is higher ?
(a) −7°C or + 7°C
(b) −3°C or 12°C
(c) 0°C or − 30°C
(d) − 14°C or 22°C
Q-4 Multiply the following :
(a) 0 and 30
(b) (− 12) and 0
(c) 8 and (− 7)
(d) (−25) and 8
(e) 32 and − 9
Q-5 Fill in the blanks :
(a) (− 9)× 0 × (12) =________
(b) (−1)× (−1)× (+1) =_____________
(c) (121) ÷(− 11) =_____________
(d) ____________ ÷ (-13) = 13
Q-6 Simplify and find the absolute value of the following :
(a) 20 ÷(− 5)
(b) 6 × (− 3)
(c) (− 10) −(− 15) ÷ 5 −(−2)
(d) 6 × (− 5) −(− 3)
Q-7 State true or false :
(a) 0 × (− 4) = 0
(b) (− 3) − 1 = (−2)
(c) (− 16) − 0 = 0
(d) (− 12) + 12 = 0
(e) (− 16) ÷ 4 = − 4
(f) (− 8)× (− 1) = (− 8)
Q-8 Calculate the following using suitable arrangements :
(a) (− 142) + (− 58) + 200
(b) 123× 7 + 123× 3
(c) (− 50)× 125× (− 6)× 8
Q-9 Answer the following questions.
4. An integer divided by (− 7) gives 9. Find the integer.
5. Give one example of the distributive property of multiplication over subtraction
6. Find the integer which when multiplied by (− 1) gives (−25)
7. Determine the integer which when divided by (− 1) gives (− 47).
Chapter-2 Fractions
Q-1 Which of the following fractions are unit fractions?
3 /7, 6 /3, 1 /5, 9 /17, 1/ 20, 1 /2, 7/ 31, 1 /7
Q-2 Write the following fractions in ascending or der :
(a) 6 /11, 9 /11, 1 /11, 3/ 11
(b) 1, 2 /5, 1, 1 /2, 2, 1/ 4
Q-3 Add the following:
(a) 1 /9 and 2 /9
(b) 6 /13 and 7 /13
(c) 3/ 7 and 5 /28
(d) 13 /25 and 9/ 5
Q-4 Find the difference:
(a) 3 /8 -1 /8
(b) 7 /12- 3 /12
(c) 47 /11- 25 /11
(d) 7, 1 /6, 2, 3/ 42
Q-5 Find the product :
(a) 1, 1/ 3 × 0
(b) 4, 3 /4 × 2
(c) 3/ 7 × 9
(d) 2, 5/ 4 × 8
(e) 3, 1/ 9 × 21
Q-6 Find the product :
(a) 1/ 2* 1/ 3* 1/ 4
(b) 2/ 3 *3 /4 *4/ 5
(c) 1 /4 *2, 1/ 2* 4 /5
Q-7 Divide the following :
(a) 1 /7 ÷2
(c) 9 ÷ 3 /4
(d) 3 ÷ 2 /21
Chapter-3 Rational Numbers
Q-1 Answer the following questions.
Do both −5 /7 and 5/ − 7 represent the same negative rational number?
Q-2 Answer the following questions.
(a) -5/-3
(b) − 9 /17
(c) − 6 /-15
(d) 7/ − 13
Q-3 Find the absolute value of the following :
(a) 7 /10
(b) 3 /8
(c) − 3 /-5
Q-4 Find the value of w in the following :
(a) -2 /3= 6/ w
(b) 6/-7=42/w
(c) 9 /− 5= w/ 25
Q-5 . Find the sum :
(a) −3/4+ 4/5
(b) −2/15+3/4
(c) − 5 /6+ 7 /15
Q-6 Find the product of the following :
(a) 3/ 10 * -19/ 2 *10 /19
(b) 9 /2 × -7 /5
Chapter-4 Decimals
Q-1 Convert the following decimals into fractions :
(a) 2.25
(b) 6.50
(c) 10.75
(d) 120.125
Q-2 Convert the following unlike decimals into like decimals :
(a) 1.2, 2.25, 3.175, 5.2
(b) 20.5, 28.235, 120.6, 385.55
Q-3 Convert the following like decimals into unlike decimals :
(a) 63.500, 265.250, 50.626
(b) 72.250, 165.300, 275.35
Q-4 Find the difference :
(a) 300 − 126.75
(b) 623.123 − 172.256
(c) 1987.5 − 928.62
(d) 3485.26 −2123.135
Q-5 Find the product of the following:
(a) 73.92 × 10
(b) 7.54 × 10
(c) 84.003× 10
(d) 0.83× 10
Q-6 Find the product of the following :
(a) 1.3× 1.3× 0.13
(b) 2.4 × 1.5× 2.5
(c) 0.8 × 3.5× 0.05
(d) 0.2 × 0.02 × 0.002
Q-7 Divide the following :
(a) 131.6 by 10
(b) 32.56 by 10
(c) 0.34 by 10
Q-8 Answer the following questions.
1. The cost of an umbrella is rs 126.75. What is the cost of 24 such umbrellas?
2. A tin of oil weight 16.8 kg .What is the weight of 45 such tins of oil?
3. Find the weight of 16 bags of sugar, each weighing 48.450 kg.
4. If one drum can hold 16.850 litres of oil, how many litres can 48 such drums hold?
5. A bus can cover 62.5 km in one hour. How much distance can it cover in 18 hours?
Chapter-6 Algebraic Expressions
Q-1 Add the following expressions using horizontal method :
(a) 5x, 7x, − 6x
(e) x − 3y + 4z, y x z − − 2 8 ,5 2 3 x y z
Q-2 Write the numerical coefficient of each term :
(a) − 7y
(b) 3/ 4 ab
(e) xyz
Q-3 Subtract by using the horizontal and column method :
(a) − 8xy from 7xy
(c) (x − y) from (4y − 5x)
Q-4 Answer the following questions.
2. Subtract (2a − 3b + 4c) from the sum of (a + 3b − 4c), ( )4 9 a b c − + and (−2b + 3c − a).
Q-5 Simplify the following:
(a) (5x − 9y) −(− 7x + y)
(c) [7 −2x + 5y −(x − y)] −(5x + 3y − 7)
Chapter-7 Simple Linear Equations
Q-1 Form an equation for each of the following statements :
(a) A number increased by 3 is equal to 5
(b) 3 times a number added to 7 gives 13.
(c) A number is twice the other and their sum is 15.
Q-2 Solve the following equations using the trial and error method :
(a) 2x + 4 = 8
(b) 11 + 2x = 19
Q-3 Solve the following equations and check your answers
(a) 5x −2x + 7 = x + 1
(b) x + (x + 2) = (x + 4) + 31
Q-4 Answer the following questions.
1. Twice a number when decreased by 7 gives 45. Find the number.
2. Thrice a number when increased by 5 gives 44. Find the number.
4. A number when added to its half gives 72. Find the number.
5. A number when added to its half gives two thirds is equal to 55. Find the number.
Chapter-8 Commercial Mathematics
Q-1 Answer the following questions.
1. 10 men can dig a well in 9 days. In how many days can 15 men dig the same well?
2. 10 workers are paid `rs 1680 for one day. How much money will be paid to 28 workers for one day?
3. In a school, the monthly fee collection of 350 students is rs 3,85,000. What will be the collection fee of 58 students for a month?
4. A bag containing 30 apples weight 6 Kg. How much will 1080 such apples weight?
5. The cost of 15 envelopes is rs 37.50. How many envelopes can be bought for rs 300? What will be the cost of 20 envelopes?
6. The total wages of 30 labourers were rs 3450 per day. What would be the total wages if 10 more labourers were added to them ?
7. A car takes 7 hours to cover a certain distance at the speed of 48 Km/hr. If the speed is decreased by 20 Km/ hr. How much time will it take to cover the same distance?
8. A man works 8 hours daily and completes a task in 12 days. If he works 6 hours daily, in how many days will the same work be completed ?
9. Gautam takes 5 hours to paint a wall and Gambhir takes 6 hours to paint the same wall. If they work together, how long will they take to paint the wall ?
Q-2 Express the following fractions as percentages:
(a) 3 / 4
(b) 5 / 8
(c) 1, 7/ 8
(d) 11 / 20
Q-3 Express the following ratios as percent :
(a) 1 : 2
(b) 3 : 4
(c) 5 : 12
(d) 27 : 50
Q-4 Express the following percents as decimals :
(a) 3%
(b) 29%
(c) 25.6%
(d) 212%
Q-5 What percent of
(a) 60 in 600?
(b) rs 50 in rs 250?
(c) 8 hrs in 2 days?
(d) 125 g, in 2.5 kg?
Q-6 Find the number whose :
(a) 12% is 60
(b) 25% is 70
(c) 65% is 221
(d) 12.5% is 1000
Q-7 . Find the S P. when :
(a) C.P = rs 950, Profit = 6%
(b) C.P = rs 380, Profit = 6, 1/ 4 %
Q-8 Find the S P. when
(a) C.P = rs 1540, loss = 5%
(b) C.P = rs 760, loss = 3, 1/ 8 %
Q-9 Answer the following questions.
1. Ritu borrowed some money at 12% per annum. She had to pay rs 180 as interest after 3 years. What sum did she borrow ?
2. What sum of money lent out at 10% per annum would produce rs 150 in 5 years ?
4. In how much time will a certain sum be 1.5 times the principal at 10% per annum ?
5. At what rate per cent per annum will rs 800 amount to rs 1000 in 2 years ?
6. Find the rate of interest by which a sum will triple itself in 16 years ?
7. In how much time will the interest on rs 800 at 12.5% per annum be rs 125?
Chapter-9 Understanding Shapes
Q-1 Find the complement of each of the following :
(a) 32°
(b) 0°
(c) 81°
(d) 63°
(e) 55°
Q-2 Find the supplement of each of the following :
(a) 105°
(b) 99°
(c) 89°
(d) 135°
(e) 12°
Q-3 Answer the following questions.
3. Find the angle which is equal to its complement
4. Which angle is equal to its supplement ?
Q-4 Name the adjacent angles in the following figures :
Q-5 Find the value of x in the following figures :
Q-6 Answer the following questions.
3. In the given figure, l m|| and t is a transversal. Find the measure of all angles, if ∠ = °
5. In the figure, l m|| . Find the value of x
6. In the given figure, AB CD || . Find the value of x.
Chapter-10 Properties of Triangles
Q-1 Answer the following questions.
4. The two interior opposite angles of an exterior angle of a triangle are 65° and 75°. Find the measure of the exterior angle.
5. An exterior angle of a triangle is of measure 95°. One of its interior opposite angles is of measure 38°. Find the measure of the other interior opposite angle.
Q-2 Examine the following sets of number for Pythagorean Triplets :
(a) (6, 8, 10)
(b) (8, 15, 16)
(c) (7, 8, 9)
Q-3 In the following right angled triangles, find the length of the unknown side :
Q-4 Answer the following questions.
5. A man walks 3 km north and then 4 km east. Find how far he is now from the starting position
6. Two towers of heights 28 m and 36 m, respectively are built at a distance of 15 m. Find the distance between their tops.
Chapter-11 Representing 3D In 2D
Q-1 Name the different 2-D figures required to draw the net of :
(a) a square pyramid
(b) a triangular prism
(c) a cone
Q-2 Fill in the blanks :
(a) A cuboid has ................. faces.
(b) A square pyramid has ................. triangular faces.
(c) A cylinder has one ................. face and two ................. faces.
(d) A cone has ................. circular face and ................. curved face.
(e) A tetrahedron has ................. edges and ................. vertices.
(f) A ................. is the solid which has only one curved face
Q-3 What cross section do you get when you give (i) a horizontal cut (ii) a vertical cut to a :
(a) a pineapple
(b) a round apple
(c) an ice-cream cone
(d) a sphere
(e) a cuboid
(f) a tetrahedron
(g) a brick
(h) a die
(i) a circular pipe
Q-4 By which solid objects are the following 2-D figures cast under lamp light?
(a) a circle
(b) a square
(c) a rectangle
(d) a triangle
Q-5 Answer the following questions.
3. Can a cube cast a shadow in the shape of a rectangle?
4. Can a cube cast a shadow in the shape of a hexagon?
Chapter-12 Congruence
Q-1 Answer the following questions.
2. Is ∠ ≅ ∠ POR SOQ if ∠ ≅ ∠ POQ ROS ? If so, why ?
4. Is it correct to say that any two right angles are congruent ? Give reasons.
Q-2 Complete the statements :
(a) Two angles are congruent if ................... .
(b) Two line segments are congruent if ................... .
(c) Two circles are congruent if ................... .
(d) Two squares are congruent if ................... .
(e) Two rectangles are congruent if ................... .
Chapter-13 Construction
Q-1 Some measurements of triangles are given below
(a) ∠A = 85°, ∠ = ° B 115 , AB = 5 cm
(b) ∠Q = 30°,∠R = 60°, QR = 4 7. cm
(c) ∠A = 70°, ∠ = ° B 50 , AC = 3 cm
(d) Sides having length of 2 cm, 2 cm and 5 cm
Q-2 Answer the following questions.
2. Draw a line parallel to a line l through a given point P outside it.
Chapter-14 Perimeter and Area
Q-1 . Find the area of a rectangle ABCD given that :
(a) AB =12 cm, AD =5 cm
(b) BC = 15.5 cm, AB = 23 cm
Q-2 Find the area of ∆ABC given that :
(a) BC =5 cm, CA =7 cm and ∠BCA =90°
(b) ∠ABC =∠CAB =45°, AC =8 cm
Q-3 Answer the following questions.
3. Find the length of the base of a triangle whose area is 220 m2 and altitude is 11m.
4. Find the area of the shaded portion from the measurements given in the figure.
5. Find the area of a parallelogram PQRS if PR =24 cm and QU ST = =6 cm.
7. The base and height of a triangle are in the ratio 4 : 5. If the area of the triangle is 90 m2 , find the measure of its base and height.
8. In a parallelogram ABCD, the length of the altitude corresponding to AB is 8 cm. What is the length of the altitude corresponding to BC ?
Q-4 Find the circumference of a circle whose radius is :
(a) 7 cm
(b) 8.4 cm
Q-5 . Find the circumference of a circle whose diameter is :
(a) 10.5 cm
(b) 21 cm
Q-6 Answer the following questions.
3. The circumference of a circle is 4π . Find the area of the circle.
4. A track is in the form of a ring whose inner and outer circumference are 8 m and 132 m, respectively. Find the breadth of the track.
5. Find the area of a circular ring whose inner and outer radii are 16 cm and 19cm, respectively.
6. In a circular garden of 50 m radius, a pond is constructed in the form of a circle with radius 20 m. Find the area of the land left-out.
Chapter-15 Data Handling
Q-1 Find the mode and median of the following data :
13, 16, 12, 14, 19, 12, 14, 13, 14
Q-2 Answer the following questions.
4. A dice was thrown 10 times and the following outcomes were recorded. 1, 2, 5, 4, 3, 5, 6, 1, 6, 5 Prepare a frequency table and find the mean, mode and median.
Q-3 There are six marbles with numbers 1 to 6. Find the probability of drawing a marble with the number :
(a) 3
(b) 5
Q-4 Find the probability that a student :
(a) has chosen at random, does not like science as a subject
(b) likes science as a subject.