Blogger Widgets APEX INSTITUTE : MATHEMATICS Question bank FOR CLASS -VIII SUMMATIVE ASSESSMENT-II 2014

Monday, January 6, 2014

MATHEMATICS Question bank FOR CLASS -VIII SUMMATIVE ASSESSMENT-II 2014








Q.1
Three consecutive integers are such that when they are taken in increasing order and multiplied by 2, 3 and 4 respectively, they add up to 74. Find these numbers.
Q.2
A road roller takes 750 complete revolutions to move once over to level a road. Find the area of the road if the diameter of a road roller is 84 cm and length is 1 m.
Q.3
Simplify 3x (4x −5) + 3 and find its values for
Q.4
Using a2 − b2 = (a + b) (a − b), find
(i)   512 − 492 
(ii)  (1.02)2 − (0.98)2 
(iii) 1532 − 1472
(iv)  12.12 − 7.92
Q.5
Solve: x - 2 = 7
Q.6
A batch of bottles was packed in 25 boxes with 12 bottles in each box. If the same batch is packed using 20 bottles in each box, how many boxes would be filled?
Q.7
Find the amount which Ram will get on Rs 4,096, he gave it for 18 months at  per annum, interest being compounded half yearly.
Q.8
Find and correct the errors in the statement: (a - 4) (a - 2) = a2 - 8
Q.9
Shobo’s mother’s present age is six times Shobo’s present age. Shobo’s age five years from now will be one third of his mother’s present age. What are their present ages?
Q.10
A factory required 42 machines to produce a given number of articles in 63 days. How many machines would be required to produce the same number of articles in 54 days?
Q.11
The population of a place increased to 54000 in 2003 at a rate of 5% per annum
(i)  find the population in 2001
(ii) what would be its population in 2005?
Q.12
Simplify and solve the linear equation 3(5z - 7) - 2(9z - 11) = 4(8z - 13) - 17
Q.13
Simplify.
(i)    (a2 − b2)2 
(ii)   (2x +5)2 − (2x − 5)2
(iii)  (7m − 8n)2 + (7m + 8n)2 
(iv)  (4m + 5n)2 + (5m + 4n)2
(v)   (2.5p − 1.5q)2 − (1.5p − 2.5q)2
(vi)  (ab + bc)2 − 2ab2
(vii) (m2 − n2m)2 + 2m3n2
Q.14
Find and correct the errors in the statement: x + 2x + 3x = 5x
Q.15
Find and correct the errors in the statement: (3x + 2)2 = 3x2 + 6x + 4
Q.16
Vasudevan invested Rs 60000 at an interest rate of 12% per annum compounded half yearly. What amount would he get
(i) after 6 months?
(ii) after 1 year?
Q.17
A closed cylindrical tank of radius 7 m and height 3 m is made from a sheet of metal. How much sheet of metal is required?
Q.18
Calculate the amount and compound interest on
(a) Rs 10800 for 3 years at  per annum compounded annually.
(b) Rs 18000 for  years at 10% per annum compounded annually.
(c) Rs 62500 for  years at 8% per annum compounded half yearly.
(d) Rs 8000 for 1 year at 9% per annum compound half yearly.
(e) Rs 10000 for 1 year at 8% per annum compounded half yearly.
Q.19
Top surface of a raised platform is in the shape of a regular octagon as shown in the figure. Find the area of the octagonal surface.
Q.20
The floor of a building consists of 3000 tiles which are rhombus shaped and each of its diagonals are 45 cm and 30 cm in length. Find the total cost of polishing the floor, if the cost per m2 is Rs 4.
Q.21
Given a cylindrical tank, in which situation will you find surface area and in which situation volume.


(a) To find how much it can hold
(b) Number of cement bags required to plaster it
(c) To find the number of smaller tanks that can be filled with water from it.
Q.22
Carry out the multiplication of the expressions in each of the following pairs.
(i)   4p, q + r 
(ii)  ab, a − b 
(iii) a + b, 7a2b2
(iv) a2 − 9, 4a 
(v)  pq + qr + rp, 0
Q.23
Q.24
Factorise the following expressions
(i)   p2 + 6p + 8
(ii)  q2 − 10q + 21
(iii) p2 + 6p − 16
Q.25
Simplify and solve the linear equation 3(t - 3) = 5(2t + 1)
Q.26
One of  the two digits of a two digit number is three times the other digit. If you interchange the digits of this two digit number and add the resulting number to the original number, you get 88.What is the original number?
Q.27
Complete the table of products.
First monomial →
Second monomial↓
2x-5y3x²-4xy7x²y-9x²y²
2x4x²...............
-5y......-15x²y.........
3x²..................
-4xy..................
7x²y..................
-9x²y²...................
Q.28
Simplify and solve the linear equation 0.25(4f - 3) = 0.05(10f - 9)
Q.29
Show that (3x + 7)2 − 84x = (3x − 7)2
Q.30
A milkman sold two of his buffaloes for Rs 20,000 each. On one he made a gain of 5% and on the other a loss of 10%. Find his overall gain or loss.
(Hint: Find CP of each)
Q.31
Find the areas of rectangles with the following pairs of monomials as their lengths and breadths respectively.
(a) (p, q)
(b) (10m, 5n)
(c) (20x2, 5y2)
(d) (4x, 3x2)
(e) (3mn, 4np)
Q.32
The lateral surface area of a hollow cylinder is 4224 cm2. It is cut along its height and formed a rectangular sheet of width 33 cm. Find the perimeter of rectangular sheet?
Q.33
Water is pouring into a cubiodal reservoir at the rate of 60 litres per minute. If the volume of reservoir is 108 m3, find the number of hours it will take to fill the reservoir.
Q.34
Find the area of a rhombus whose side is 6 cm and whose altitude is 4 cm. If one of its diagonals is 8 cm long, find the length of the other diagonal.
Q.35
The sum of three consecutive multiples of 8 is 888. Find the multiples.
Q.36
Lakshmi is a cashier in a bank. She has currency notes of denominations Rs 100, Rs 50 and Rs 10, respectively. The ratio of the number of these notes is 2:3:5. The total cash with Lakshmi is Rs 4, 00,000. How many notes of each denomination does she have?
Q.37
Solve: 6x = 12
Q.38
A mixture of paint is prepared by mixing 1 part of red pigments with 8 parts of base. In the following table, find the parts of base that need to be added.
Parts of red pigment1471220
Parts of base8............
Q.39
Solve and check result: 5x + 9 = 5 + 3x
Q.40
The area of a trapezium is 34 cm2 and the length of one of the parallel sides is 10 cm and its height is 4 cm. Find the length of the other parallel side.
Q.41
The perimeter of a rectangular swimming pool is 154 m. Its length is 2 m more than twice its breadth. What are the length and the breadth of the pool?
Q.42
Find and correct the errors in the following mathematical statement. Substituting x = -3 in
(a) x2 + 5x + 4 gives (-3)2 + 5 (-3) + 4 = 9 + 2 + 4 = 15
(b) x2 - 5x + 4 gives (-3)2 - 5 (-3) + 4 = 9 - 15 + 4 = -2
(c) x2 + 5x gives (-3)2 + 5 (-3) = -9 - 15 = -24
Q.43
Q.44
Solve: y + 3 = 10
Q.45
The price of a TV is Rs 13,000. The sales tax charged on it is at the rate of 12%. Find the amount that Vinod will have to pay if he buys it,
Q.46
Find the side of a cube whose surface area is 600 cm2.
Q.47
Identify the terms, their coefficients for each of the following expressions.
(i)   5xyz2 − 3zy
(ii)  1 + x + x2
(iii)  4x2y2 − 4x2y2z2 + z2
(iv)  3 − pq + qr − rp
  
(vi)  0.3a − 0.6ab + 0.5b
Q.48
A shopkeeper buys 80 articles for Rs 2,400 and sells them for a profit of 16%. Find the selling price of one article.
Q.49
Length of the fence of a trapezium shaped field ABCD is 120 m. If BC = 48 m, CD = 17 m and AD = 40 m, find the area of this field. Side AB is perpendicular to the parallel sides AD and BC.
Q.50
Three consecutive integers add up to 51. What are these integers?
Q.51
A company packages its milk powder in cylindrical container whose base has a diameter of 14 cm and height 20 cm. Company places a label around the surface of the container (as shown in the figure). If the label is placed 2 cm from top and bottom, what is the area of the label.
 
Q.52
The number of boys and girls in a class are in the ratio 7:5. The number of boys is 8 more than the number of girls. What is the total class strength?
Q.53
Q.54
Diagram of the adjacent picture frame has outer dimensions = 24 cm × 28 cm and inner dimensions 16 cm × 20 cm. Find the area of each section of the frame, if the width of each section is same.
Q.55
A VCR and TV were bought for Rs 8,000 each. The shopkeeper made a loss of 4% on the VCR and a profit of 8% on the TV. Find the gain or loss percent on the whole transaction.
Q.56
A loaded truck travels 14 km in 25 minutes. If the speed remains the same, how far can it travel in 5 hours?
Q.57
Factorise
(i)   (l + m)2 − (l − m)2
(ii)  9x2y2 − 16
(iii) (x2 − 2xy + y2) − z2
(iv)  25a2 − 4b2 + 28bc − 49c2

Q.58
Complete the table:
 First expressionSecond expressionProduct
(i)
(ii)
(iii)
(iv)
(v)
a
x + y -5
p
4p2q2
a + b + c
b + c + d
5xy
6p2 - 7p + 5
p2 - q2
abc
...
...
...
...
...
Q.59
If a box of sweets is divided among 24 children, they will get 5 sweets each. How many would each get, if the number of the children is reduced by 4?
Q.60
The diagonals of a rhombus are 7.5 cm and 12 cm. Find its area.
Q.61
I purchased a hair-dryer for Rs 5,400 including 8% VAT. Find the price before VAT was added.
Q.62
There is a narrow rectangular plot, reserved for a school, in Mahuli village. The length and breadth of the plot are in the ratio 11:4. At the rate Rs 100 per meter it will cost the village panchayat at Rs 75000 to fence the plot. What are the dimensions of the plot?
Q.63
Subtract the following.
(a) 4a − 7ab + 3b + 12 from 12a − 9ab + 5b − 3
(b) 3xy + 5yz − 7zx from 5xy − 2yz − 2zx + 10xyz
(c) 4p2q − 3pq + 5pq2 − 8p + 7q − 10 from 18 − 3p − 11q + 5pq − 2pq2 + 5p2q
Q.64
Following are the car parking charges near a railway station up to
                      4 hours        Rs 60
                      8 hours        Rs 100
                      12 hours      Rs 140
                      24 hours      Rs 180
Check if the parking charges are in direct proportion to the parking time.
Q.65
Using identities, evaluate.
(i)   712 
(ii)  992 
(iii) 1022 
(iv)  9982
(v)  (5.2)2
(vi)  297 × 303 
(vii) 78 × 82
(viii) 8.92 
(ix)  1.05 × 9.5
Q.66
A scooter was bought at Rs 42,000. Its value depreciated at the rate of 8% per annum. Find its value after one year.
Q.67
The organizers of an essay competition decide that a winner in the competition gets a prize of Rs 100 and a participant who does not win gets a prize of Rs 25. The total prize money distributed is Rs 3000. Find the number of winners, if the total number of participants is 63.
Q.68
Factorise the expressions and divide them as directed.
(i)  (y2 + 7y + 10) ÷ (y + 5)
(ii) (m2 - 14m - 32) ÷ (m + 2)
(iii) (5p2 - 25p + 20) ÷ (p - 1)
(iv)  4yz(z2 + 6z - 16) ÷ 2y(z + 8)
Q.69
Q.70
Simplify.
(i)    (x2 − 5) (x + 5) + 25
(ii)   (a2 + 5) (b3 + 3) + 5
(iii)  (t + s2) (t2 − s)
(iv)  (a + b) (c − d) + (a − b) (c + d) + 2 (ac + bd)
(v)   (x + y) (2x + y) + (x + 2y) (x − y)
(vi)  (x + y) (x2 − xy + y2)
(vii) (1.5x − 4y) (1.5x + 4y + 3) − 4.5x + 12y
(viii) (a + b + c) (a + b − c)
Q.71
In a model of a ship, the mast is 9 cm high, while the mast of the actual ship is 12 m high. If the length of the ship is 28 m, how long is the model ship?
Q.72
Find the product.
(i)   (5 − 2x) (3 + x) 
(ii)  (x + 7y) (7x − y)
(iii) (a2 + b) (a + b2
(iv) (p2 − q2) (2p + q)
Q.73
Using (x + a) (x + b) = x2 + (a + b) x + ab, find
(i)  103 × 104
(ii)  5.1 × 5.2
(iii) 103 × 98
(iv)  9.7 × 9.8
Q.74
Q.75
A square and a rectangular field with measurements as given in the figure have the same perimeter. Which field has a larger area?
(a)
(b)
Q.76
Multiply the binomials.
(i)     (2x + 5) and (4x − 3) (ii) (y − 8) and (3y − 4)
(iii)   (2.5l − 0.5m) and (2.5l + 0.5m) (iv) (a + 3b) and (x + 5)
(v)    (2pq + 3q2) and (3pq − 2q2)
Q.77
Divide as directed.
(i)   5(2x + 1) (3x + 5) ÷ (2x + 1)
(ii)  26xy(x + 5) (y - 4) ÷ 13x(y - 4)
(iii) 52pqr (p + q) (q + r) (r + p) ÷ 104pq(q + r) (r + p)
(iv) 20(y + 4) (y2 + 5y + 3) ÷ 5(y + 4)
(v)  x(x + 1) (x + 2) (x + 3) ÷ x(x + 1)
Q.78
Find and correct the errors in the statement: 
Q.79
The ages of Rahul and Haroon are in the ratio 5:7. Four years later the sum of their ages will be 56 years. What are their present ages?
Q.80
Find and correct the errors in the statement: (2x)2 + 5x = 4x + 5x = 9x
Q.81
Q.82
Solve and check result: 3x = 2x + 18
Q.83
Simplify and solve the linear equation 15(y - 4) - 2(y - 9) + 5(y + 6) = 0
Q.84
An ant is moving around a few food pieces of different shapes scattered on the floor. For which food - piece would the ant have to take a longer round? Remember, circumference of a circle can be obtained by using the expression c = 2πr, where r is the radius of the circle.
(a)
(b)
(c)
Q.85
Q.86
Solve: 6 = z + 2
Q.87
Q.88
Find and correct the errors in the statement: 2x + 3y = 5xy
Q.89
Factorise the expressions
(i)  (lm + l) + m + 1
(ii)  y(y + z) + 9(y + z)
(iii) 5y2 − 20y − 8z + 2yz
(iv) 10ab + 4a + 5b + 2
(v)  6xy − 4y + 6 − 9x
Q.90
Find and correct the errors in the statement: 5y + 2y + y - 7y = 0
Q.91
Find and correct the errors in the statement: 
Q.92
Find the common factors of the terms
(i)    12x, 36
(ii)    2y, 22xy
(iii)   14pq, 28p2q2
(iv)   2x, 3x2, 4
(v)    6abc, 24ab2, 12a2b
(vi)   16x3, −4x2, 32x
(vii)  10pq, 20qr, 30rp
(viii)  3x2y3, 10x3y2, 6x2y2z
Q.93
Find the product.
Q.94
Use the identity (x + a) (x + b) = x2 + (a + b)x + ab to find the following products.
(i)    (x + 3) (x + 7) 
(ii)   (4x +5) (4x + 1)
(iii)  (4x − 5) (4x − 1) 
(iv)  (4x + 5) (4x − 1)
(v)   (2x +5y) (2x + 3y)
(vi)  (2a2 +9) (2a2 + 5)
(vii) (xyz − 4) (xyz − 2)
Q.95
If Chameli had Rs 600 left after spending 75% of her money, how much did she have in the beginning?
Q.96
Factorise the expressions and divide them as directed.
(i)  5pq(p2 - q2) ÷ 2p(p + q)
(ii) 12xy(9x2 - 16y2) ÷ 4xy(3x + 4y)
(iii) 39y3(50y2 - 98) ÷ 26y2(5y + 7)
Q.97
Describe how the two figures at the right are alike and how they are different. Which box has larger lateral surface area?
Q.98
Mohan wants to buy a trapezium shaped field. Its side along the river is parallel to and twice the side along the road. It the area of this field is 10500 m2 and the perpendicular distance between the two parallel sides is 100 m, find the length of the side along the river.
Q.99
Find the amount and the compound interest on Rs 10,000 for   years at 10% per annum, compounded half yearly. Would this interest be more than the interest he would get if it was compounded annually?
Q.100
Solve and check result: 8x + 4 = 3(x − 1) + 7
Q.101
Solve and check result: 5t − 3 = 3t − 5
Q.102
Sum of two numbers is 95. If one exceeds the other by 15, find the numbers.
Q.103
A 5 m 60 cm high vertical pole casts a shadow 3 m 20 cm long. Find at the same time -
(i)  the length of the shadow cast by another pole 10 m 50 cm high
(ii) the height of a pole which casts a shadow 5 m long.
Q.104
Add the following.
(i)   ab − bc, bc − ca, ca − ab
(ii)  a − b + ab, b − c + bc, c − a + ac
(iii) 2p2q2 − 3pq + 4, 5 + 7pq − 3p2q2
(iv) l2 + m2, m2 + n2, n2 + l2, 2lm + 2mn + 2nl
Q.105
Q.106
A farmer has enough food to feed 20 animals in his cattle for 6 days. How long would the food last if there were 10 more animals in his cattle?
Q.107
Rashmi has a road map with a scale of 1 cm representing 18 km. She drives on a road for 72 km. What would be her distance covered in the map?
Q.108
Arif took a loan of Rs 80,000 from a bank. If the rate of interest is 10% per annum, find the difference in amounts he would be paying after years if the interest is
(i)  Compounded annually
(ii) Compounded half yearly
Q.109
Work out the following divisions.
(i)   (10x − 25) ÷ 5
(ii)  (10x − 25) ÷ (2x − 5)
(iii) 10y(6y + 21) ÷ 5(2y + 7)
(iv)  9x2y2(3z − 24) ÷ 27xy(z − 8)
(v)   96abc(3a − 12)(5b − 30) ÷ 144(a − 4) (b − 6)
Q.110
Baichung’s father is 26 years younger than Baichung’s grandfather and 29 years older than Baichung. The sum of the ages of all the three is 135 years. What is the age of each one of them?
Q.111
I borrowed Rs 12000 from Jamshed at 6% per annum simple interest for 2 years. Had I borrowed this sum at 6% per annum compound interest, what extra amount would I have to pay?
Q.112
Subtract: 3l (l − 4m + 5n) from 4l (10n − 3m + 2l)
Q.113
Find and correct the errors in the statement: 4(x - 5) = 4x - 5
Q.114
The diagonal of a quadrilateral shaped field is 24 m and the perpendiculars dropped on it from the remaining opposite vertices are 8 m and 13 m. Find the area of the field.
 
Q.115
During a sale, a shop offered a discount of 10% on the marked prices of all the items. What would a customer have to pay for a pair of jeans marked at Rs 1450 and two shirts marked at Rs 850 each?
Q.116
A machine in a soft drink factory fills 840 bottles in six hours. How many bottles will it fill in five hours?
Q.117
Find and correct the errors in the statement: x(3x + 2) = 3x2 + 2
Q.118
Daniel is painting the walls and ceiling of a cuboidal hall with length, breadth and height of 15 m, 10 m and 7 m respectively. From each can of paint 100 m2 of area is painted. How many cans of paint will she need to paint the room?
Q.119
The shape of a garden is rectangular in the middle and semi circular at the ends as shown in the diagram. Find the area and the perimeter of the garden.
[Length of rectangle is 20 - (3.5 + 3.5) metres]
Q.120
A flooring tile has the shape of a parallelogram whose base is 24 cm and the corresponding height is 10 cm. How many such tiles are required to cover a floor of area 1080 m2?
Q.121
The shape of the top surface of a table is a trapezium. Find its area if its parallel sides are 1 m and 1.2 m and perpendicular distance between them is 0.8 m.
Q.122
Add: 2x (z − x − y) and 2y (z − y − x)
Q.123
Maria invested Rs 8,000 in a business. She would be paid interest at 5% per annum compounded annually. Find.
(i)  The amount credited against her name at the end of the second year
(ii) The interest for the 3rd year.
Q.124
A man got a 10% increase in his salary. If his new salary is Rs 1,54,000, find his original salary.
Q.125
Q.126
Factorise the following expressions
(i)   7x - 42
(ii)  6p - 12q
(iii) 7a2 + 14a
(iv) −16z + 20z3
(v)  20l2m + 30 alm
Q.127
Carry out the following divisions.
(i)   28x4 ÷ 56x
(ii)  −36y3 ÷ 9y2
(iii) 66pq2r3 ÷ 11qr2
(iv)  34x3y3z3 ÷ 51xy2z3
(v)  12a8b8 ÷ (−6a6b4)
Q.128
In a Television game show, the prize money of Rs 1,00,000 is to be divided equally amongst the winners. Complete the following table and find whether the prize money given to an individual winner is directly or inversely proportional to the number of winners?
Number of winners124581020
Prize for each winner
(in Rs)
1,00,00050,000...............
Q.129
Simplify a(a2 + a + 1) + 5 and find its values for
(i)   a = 0,
(ii)  a = 1,
(iii) a = − 1.
Q.130
Suppose 2 kg of sugar contains 9 × 106 crystals. How many sugar crystals are there in 
(i)  5 kg of sugar? 
(ii) 1.2 kg of sugar?
Q.131
Find and correct the errors in the statement: 
Q.132
A grandfather is ten times older than his granddaughter. He is also 54 years older than her. Find their present ages.
Q.133
A suitcase with measures 80 cm × 48 cm × 24 cm is to be covered with a tarpaulin cloth. How many metres of tarpaulin of width 96 cm is required to cover 100 such suitcases?
Q.134
Solve: 14y - 8 = 13
Q.135
Factorise the following expressions
(i)    5x2y − 15xy2

(ii)   10a2 − 15b2 + 20c2
(iii)  −4a2 + 4ab − 4 ca
(iv)  x2yz + xy2z + xyz2
(v)  ax2y + bxy2 + cxyz
Q.136
A cuboid is of dimensions 60 cm × 54 cm × 30 cm. How many small cubes with side 6 cm can be placed in the given cuboid?
Q.137
Factorise the expressions
(i)   ax2 + bx
(ii)  7p2 + 21q2
(iii) 2x3 + 2xy2 + 2xz2
(iv) am2 + bm2 + bn2 + an2
Q.138
Factorise the following expressions.
(i)   a2 + 8a + 16
(ii)  p2 − 10p + 25
(iii) 25m2 + 30m + 9
(iv) 49y2 + 84yz + 36z2
Q.139
Diameter of cylinder A is 7 cm, and the height is 14 cm. Diameter of cylinder B is 14 cm and height is 7 cm. Without doing any calculations can you suggest whose volume is greater? Verify it by finding the volume of both the cylinders. Check whether the cylinder with greater volume also has greater surface area?
 
Q.140
Solve and check result: 4z + 3 = 6 + 2z
Q.141
Find and correct the errors in the statement: 
Q.142
Fifteen years from now Ravi’s age will be four times his present age. What is Ravi’s present age?
Q.143
In a laboratory, the count of bacteria in a certain experiment was increasing at the rate of 2.5% per hour. Find the bacteria at the end of 2 hours if the count was initially 5,06,000.
Q.144
Q.145
Classify the following polynomials as monomials, binomials, trinomials. Which polynomials do not fit in any of these three categories?
x + y, 1000, x + x2 + x3 + x4, 7 + y + 5x, 2y − 3y2, 2y − 3y2 + 4y3,
5x − 4y + 3xy, 4z − 15z2
ab + bc + cd + da, pqr, p2q + pq22p + 2q

Q.146
Hasan buys two kinds of cloth materials for school uniforms, shirt material that costs him Rs. 50 per meter and trouser material that costs him Rs 90 per meter. For every 2 meters of the trouser material he buys 3 meters of the shirt material. He sells the materials at 12% and 10% profit respectively. His total sale is Rs 36,660. How much trouser material did he buy?
Q.147
Find the height of a cuboid whose base area is 180 cm2 and volume is 900 cm3?
Q.148
The ages of Hari and Harry are in the ratio 5:7. Four years from now the ratio of their ages will be 3:4. Find their present ages.
Q.149
If each edge of a cube is doubled,
(i)  how many times will its surface area increase?
(ii) how many times will its volume increase?
Q.150
Find and correct the errors in the statement: (y - 3)2 = y2 - 9
Q.151
Q.152
A photograph of a bacteria enlarged 50,000 times attains a length of 5 cm. What is the actual length of the bacteria? If the photograph is enlarged 20,000 times only, what would be its enlarged length?
Q.153
Which of the following are in inverse proportion?
(i)   The number of workers on a job and the time to complete the job.
(ii)  The time taken for a journey and the distance travelled in a uniform speed.
(iii) Area of cultivated land and the crop harvested.
(iv) The time taken for a fixed journey and the speed of the vehicle.
(v)  The population of a country and the area of land per person.
Q.154
Add: p (p − q), q (q − r) and r (r − p)
Q.155
Q.156
Show that (9p − 5q)2 + 180pq = (9p + 5q)2
Q.157
A football team won 10 matches out of the total number of matches they played. If their win percentage was 40, then how many matches did they play in all?
Q.158
Divide the given polynomial by the given monomial.
(i)   (5x2 − 6x) ÷ 3x
(ii)  (3y8 − 4y6 + 5y4) ÷ y4
(iii) 8(x3y2z2 + x2y3z2 + x2y2z3) ÷ 4x2y2z2
(iv) (x3 + 2x2 + 3x) ÷ 2x
(v)  (p3q6 − p6q3) ÷ p3q3
Q.159
Use a suitable identity to get each of the following products.
(i)    (x + 3) (x + 3)
(ii)   (2y + 5) (2y + 5)
(iii)  (2a − 7) (2a − 7) 
(iv)  (1.1m − 0.4) (1.1 m + 0.4) 
(v)   (a2 + b2) (− a2 + b2)
(vi)  (6x − 7) (6x + 7) 
(vii)  (− a + c) (− a + c)
(viii) (7a − 9b) (7a − 9b)
Q.160
Rukhsar painted the outside of the cabinet of measure 1 m × 2 m × 1.5 m. How much surface area did she cover if she painted all except the bottom of the cabinet?
Q.161
A positive number is 5 times another number. If 21 is added to both the numbers, then one of the new numbers becomes twice the other new number. What are the numbers?
Q.162
If 60% people in city like cricket, 30% like football and the remaining like other games, then what per cent of the people like other games? If the total number of people are 50 lakh, find the exact number who like each type of game.
Q.163
Find the product of the following pairs of monomials.
(i)   4, 7p 
(ii)  − 4p, 7p 
(iii) − 4p, 7pq
(iv) 4p3, − 3p 
(v)  4p, 0
Q.164
The cost of an article was Rs 15,500. Rs 450 were spent on its repairs. If it is sold for a profit of 15%, find the selling price of the article.
Q.165
Two persons could fit new windows in house in 3 days.
(i)  One of the persons fell ill before the work started. How long would the job take   now?
(ii) How many persons would be needed to fit the windows in one day?
Q.166
Solve and check result: 2x − 1 = 14 − x
Q.167
Rehman is making a wheel using spokes. He wants to fix equal spokes in such a way that the angles between any pair of consecutive spokes are equal. Help him by completing the following table.
Number of spokes4681012
Angle between a pair of consecutive spokes90°60°........
(i) Are the number of spokes and the angles formed between the pairs of consecutive spokes in inverse proportion?

(ii) Calculate the angle between a pair of consecutive spokes on a wheel with 15 spokes.


(iii) How many spokes would be needed, if the angle between a pair of consecutive spokes is 40°?
Q.168
Solve: 7x - 9 = 16
Q.169
Factorise
(i)   x2 + xy + 8x + 8y

(ii) 15xy − 6x + 5y − 2
(iii) ax + bx − ay − by
(iv) 15pq + 15 + 9q + 25p
(v)  z − 7 + 7xy − xyz
Q.170
A man’s age is three times his son’s age. Ten years ago he was five times his son’s age. Find their present ages.
Q.171
Q.172
Q.173
A contractor estimates that 3 persons could rewire Jasminder’s house in 4 days. If, he uses 4 persons instead of three, how long should they take to complete the job?
Q.174
Obtain the product of
(i)   xy, yz, zx 
(ii)  a, − a2, a3
(iii) 2, 4y, 8y2, 16y3
(iv) a, 2b, 3c, 6abc 
(v)  m, − mn, mnp
Q.175
Sum of the digits of a two-digit numbers is 9. When we interchange the digits, it is found that the resulting new number is greater than the original number by 27. What is the two-digit number?
Q.176
Arun bought a pair of skates at a sale where the discount given was 20%. If the amount he pays is Rs 1,600, find the marked price.
Q.177
Q.178
Half of a herd of deer are grazing in the field and three fourths of the remaining are playing nearby. The rest 9 are drinking water from the pond. Find the number of deer in the herd.
Q.179
Factorise
(i)   a4 − b4
(ii)  p4 − 81
(iii) x4 − (y + z)4
(iv) x4 − (x − z)4
(v)  a4 − 2a2b2 + b4
Q.180
There are two cuboidal boxes as shown in the adjoining figure. Which box requires the lesser amount of material to make?

          (a)                                          (b)
Q.181
Find the ratio of the following:
(a) Speed of a cycle 15 km per hour to the speed of scooter 30 km per hour.
(b) 5 m to 10 km
(c) 50 paise to Rs 5
Q.182
Show that (a − b) (a + b) + (b − c) (b + c) + (c − a) (c + a) = 0
Q.183
Find and correct the errors in the statement: (2x)2 + 4(2x) + 7 = 2x2 + 8x + 7
Q.184
I have a total of Rs 300 in coins of denomination Re 1, Rs 2 and Rs 5. The number of Rs 2 coins is 3 times the number of Rs 5 coins. The total number of coins is 160. How many coins of each denomination are with me?
Q.185
Obtain the volume of rectangular boxes with the following length, breadth and height respectively.
(i)   5a, 3a2, 7a4 
(ii)  2p, 4q, 8r 
(iii) xy, 2x2y, 2xy2
(iv) a, 2b, 3c
Q.186
Convert the following ratios to percentages.
(a) 3:4
(b) 2:3
Q.187
Factorise
(i)   4p2 − 9q2
(ii)  63a2 − 112b2
(iii) 49x2 − 36
(iv) 16x5 − 144x3
Q.188
Q.189
Find and correct the errors in the statement: 3x + 2x = 5x2
Q.190
Find the following squares by suing the identities.
(i)   (b − 7)2
(ii)  (xy + 3z)2
(iii) (6x2 − 5y)2
(iv) (0.4p − 0.5q)2 
(v)  (2xy + 5y)2
Q.191
Find and correct the errors in the statement: 
Q.192
Find and correct the errors in the statement: 
Q.193
Factorise the following expressions.
(i)   4x2 − 8x + 4
(ii)  121b2 − 88bc + 16c2
(iii) (l + m)2 − 4lm 
(iv)  a4 + 2a2b2 + b4

Q.194
Two numbers are in the ratio 5:3. If they differ by 18, what are the numbers?
Q.195
Subtract: 3a (a + b + c) − 2b (a − b + c) from 4c (− a + b + c)
Q.196
Find and correct the errors in the statement: (2a + 3b) (a - b) = 2a2 - 3b2
Q.197
Kamala borrowed Rs 26400 from a Bank to buy a scooter at a rate of 15% p.a. compounded yearly. What amount will she pay at the end of 2 years and 4 months to clear the loan?
Q.198
72% of 25 students are good in mathematics. How many are not good in mathematics?
Q.199
Show that (4pq + 3q)2− (4pq − 3q)2 = 48pq2
Q.200
On Sunday 845 people went to the Zoo. On Monday only 169 people went. What is the per cent decrease in the people visiting the zoo on Monday?

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