QUESTION BANK
SUB.: MATHS
Ch. 6 ALGEBRAIC EXPRESSIONS AND IDENTITIES(Extra)
Type-I (1 Mark)
1. Find the product of (𝑦 4 − 𝑥 4 ) and (𝑥 2 + 𝑦 2 ) .
2.Find the product : ( 2x – 5 )( x + 4 )
3. Find the product : ( x – 4 )( x+ 4 )( x2 + 16 )
4. 11. 𝑥 +
1
𝑥
= 5 then the value of 𝑥 2 +
1
𝑥2
is _______
5. 12. 𝑥 −
1
𝑥
= 5 then the value of 𝑥 2 +
1
𝑥2
is _______
Type-II ( 2 Marks)
6. Find the value of p if 4p = 992 - 392
3
5
7.Find the product of ( 𝑥 2 𝑦 3 −
2 4 2
𝑥 𝑦 )
3
𝑎𝑛𝑑 (𝑥 4 − 3 𝑦 2 )
8. Find the product of ( -7x2 + 3y3 ) and ( -7x2 - 3y3 )
Type- III (3 or 4 Marks )
1
9. Simplify : 7 (7𝑥 2 − 7𝑦 2 )(𝑥 2 + 𝑦 2 )(𝑥𝑦)
10. Find the product (𝑥 − 3𝑦)(𝑥 + 3𝑦)(𝑥 2 + 9𝑦 2 ) and verify the result for x = 2 and y = 3.
1
1
11. If 𝑥 + 𝑥 = 4 , find the value of 𝑥 4 +
12. If 𝑥 −
1
𝑥
𝑥4
= 3 , find the value of 𝑥 4 +
1
𝑥4
.
.
1 2
13. If (𝑥 + 𝑥) = 25 , find the value of 𝑥 4 +
1
𝑥4
.
14. Using the identities, evaluate the following (i) (997)2 (ii) 100.3 × 99.7 (iii) 8.6 × 8.7
15. Simplify : 𝑥 2 𝑦(𝑥 − 𝑥𝑦 3 ) + 𝑥𝑦 3 (5𝑥 2 𝑦 − 11𝑥 2 𝑦) − 𝑥 2 𝑦(3 − 12𝑥𝑦)
16. Using the identities, evaluate the following:
6.43 ×6.43 −0.43 ×0.43
(i)
6.86
(ii)
147 ×147 −47 ×47
147 + 47
17.Find the continued product:
(i)
(−𝑥 − 3)(𝑥 − 3)(𝑥 2 + 9𝑦 2 ) (ii) (1 − 4𝑦)(1 + 4𝑦)(1 + 16𝑦 2 )
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Std. : VIII
QUESTION BANK
SUB.: MATHS
Ch. 12 Understanding Quadrilaterals
TYPE-I ( 1 MARK )
1. How many sides does a regular polygon have if the measure of each exterior angle is 180 ?
2.How many diagonals are there in octagon ?
3.How many diagonals are there in a polygon having 10 sides ?
4. Write the formula to find sum of the interior angles of n sides polygon.
5.What is diagonal of polygon?
6.Define: (i) convex polygon (ii) Concave polygon
7.In a trapezium ABCD, AB ∥ CD. If ∠ 𝐴 = 560 , then find ∠ 𝐷 ?
8.If one angle of a rhombus is 500, find the other angle.
9.What is the minimum interior angle possible for a regular polygon ?
10. What is the maximum exterior angle possible for a regular polygon ?
TYPE-II ( 2 MARK )
11. How many sides does a regular polygon have if the measure of each interior angle is 1500 ?
12. How many diagonals are there in a polygon having 13 sides ?
13. Is it possible to have a regular polygon each of whose interior angle is 450 ?
14. Is it possible to have a regular polygon each of whose exterior angle is 750 ?
15.Adjacent angles of parallelogram are in the ratio 4 : 5.Find their values.
16.One side of a parallelogram is 7.2 cm and other side is thrice of it. Find the perimeter of the parallelogram.
17.Find the side of a rhombus whose perimeter is 52 cm. When this rhombus will be a square ?
18.Find fourth angle of a quadrilateral ,if three angles are 700 , 400 and 500.Is it a convex or concave ?
19.A window frame has one diagonal longer than the other. Is the window frame a rectangle? Why or why not ?
20.If an angle of a parallelogram is two-third of its adjacent angle, find the angle of the parallelogram.
TYPE-III (3 OR 4 MARKS)
21. The four angles of a quadrilateral are in ratio of 1: 2 : 4: 8 . Find there measures.
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22.The diagonals of a rhombus are 16 cm and 30 cm. Find the length of the side of the rhombus.
23 In figure -1 ,ABCD is a parallelogram. AE and BE are angle bisectors of
D
C
∠ A and ∠ B respectively .Show that ∠ AEB = 900
FIG-1
A
B
24. KLMN is an isosceles trapezium whose diagonals cut at X and KL is parallel to NM . If ∠KNL = 250, ∠KMN = 300 ,
find (i) ∠KXN , (ii) ∠MLN .
25. Adjacent angles of parallelogram are ( 2x -10)0 and (6x + 30)0.Find the measure of all of the angles of the
parallelogram .
26.In a parallelogram ABCD, mark two points E and F on the diagonal AC on either side of O,the point of intersection
of the diagonals AC and BD, such that AE = CF. Prove that BEDF is a parallelogram.
27. In fig-2,ABCD and APQR are parallelogram. If ∠ C = 630 , what are the measures of ∠𝑃𝑄𝑅 and ∠ 𝐴𝑅𝑄 ?
K
z
650
y
D
80 0
C
R
Q
L
w
1250
J
x
I
A
P
FIG-2
B
FIG-3
28. In fig-3,find : (i) x (ii) y (iii) z (iv) x + y + z + w .
29.Name the quadrilaterals whose diagonals:
(i) bisect each other , (ii) are perpendicular bisector of each other , (iii) are equal.
30.Explain how a square is
(i) a quadrilateral?
(ii) a parallelogram?
(iii) a rhombus?
(iv) a rectangle ?
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Ch: 15 Areas
TYPE-I ( 1 MARK )
1. Find the area of a square whose perimeter is 24 cm .
2. Find the area of a circle whose circumference is 44 cm .
3.Find the area of a triangle, whose base is 13 cm and corresponding altitude is 4.
4.Find the area of a trapezium, sum of two parallel sides is 24 and distance between them is 7 cm.
5.Find perimeter of square whose area is 225 cm2.
TYPE-II ( 2 MARK )
6.A square of side 30 cm and a rectangle of length 40 cm has same perimeter. Which has greater area ?
7.The area of trapezium is 352 cm2 and the distance between its parallel sides is 16cm.If one of the parallel sides is
of length 25 cm, find the length of the other.
8.Find perimeter of the given figures:
15 cm
14
cm
21 cm
(i)
(ii)
9. The area of trapezium is 480 cm2 and the distance between its parallel sides is 8cm.If one of the parallel sides is
of length 96 cm, find the length of the other.
10.The are of a trapezium of height 40 cm is 160 cm2. If one of the parallel sides is 60 cm, find the other side.
TYPE-III ( 3 OR 4 MARK )
11. The base of a parallelogram is thrice its height. If its area is 432 m2, find the length of the base and height of the
parallelogram.
12.A footpath 1 m wide is constructed along the border inside a square garden of side 20 m.Find the (i) area of the
path (ii) cost of making path at rate of Rs 225 per m2.
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13. The base of a parallelogram is thrice its height. If its area is 867 m2, find the length of the base and height of
the parallelogram
14.The ratio of the parallel sides of a trapezium is 2 : 3 . The distance between them is 15 cm. If the area of the
trapezium is 600 cm2,find the lengths of parallel sides.
15.Find the area of shaded region in the given figure.
28
16. In figure -2 , ABCD is a trapezium, ECB is a triangle and AECD is a parallelogram. Area of △ BCE = 180 cm2,
EB = 5 cm, CD = 25 cm. Find the area of the trapezium ABCD
D
A
FIG-2
C
E
B
fig-3
17.In fig-3,frame has outer dimensions 22 𝑐𝑚 × 14 𝑐𝑚 and inner dimensions 18 cm × 10 cm.Find the area of each
section of the frame, if width of each section is same.
18.In-fig-2, ABCD is a trapezium in which AB ∥ DC, AB = 25 cm, CD = 13 cm, AD = 10 cm and BC = 10 cm. Find the area
of the trapezium.
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19. Find the area of the fields. All dimensions are in m. (figure- 4 and 5)
Fig-4
fig-5
fig-6
20 In fig-6, ABCD is a quadrilateral in which diagonal AC = 88 cm; DL ⊥ AC, BM ⊥ AC, DL = 31.5 cm, and BM = 21.5 cm.
Find the area of quadrilateral ABCD.
17.Data Handling
TYPE-I ( 1 MARK )
1.The number of times a particular entry occurs in a set of data is known as ____________ .
2.The mid-value of a class-interval is called its _____________ .
3.The difference between upper and lower class limits of a group is called ___________ .
4.What is class-mark of the class 220 – 260 ?
5.An experiment whose outcomes cannot be predicted exactly in advance is called ______________ .
6. Probability of an event always lies between ________ and ___________ .
7.A number from 1 to 20 is chosen at random. The chance of choosing a number greater than 12 is _____ chance.
8.An _____ is the result of a single trial of an experiment.
9. . A number from 1 to 20 is chosen at random. The chance of choosing a number less than 8 is ____ chance.
10.Write types of experiments.
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TYPE-II ( 2 MARK )
11.Define : (i) Random experiment (ii) Deterministic experiment
12. Answer the following : (i) What is the class mark of 10 - 18 ? (ii) Find class size of 15 - 19 .
13. Answer the following : (i) What is the lower limit of 100 - 200 ? (ii) What is upper limit of 500 - 550 .
14.Write 2 events which have 0 probability .
15. Write 2 events which have 1 probability .
16. Write 2 events which have 0.5 probability .
17.Identify whether the following experiments are deterministic or random : (i)Weighing a coin (ii) Tossing a coin.
18.A coin is tossed. What is the probability of getting a head ?
19.A die is thrown. It is which type of experiment ? What are all possible outcomes ?
20.Difference of lower limit of 205-215 and upper limit of 500-600.
TYPE-III ( 3 or 4 MARK )
21.The table shows the number of students opting different subjects in a college:
Subject
No. of Students
English
45
Mathematics
60
Physics
20
Chemistry
30
Commerce
25
Draw a pie-chart to represent the above data.
22. Construct a frequency table for the following marks obtained by 45 students using class intervals, one of them
being 15 – 20.
12
14
22
20
23
24
11
17
08
04
01
07
19
25
20
11
05
17
19
13
15
16
15
09
10
25
24
23
16
13
20
22
11
14
15
19
20
25
23
22
06
02
23
24
15
23.A number is selected randomly from the numbers 1,2,3,4, ....., 20.
Find the probability of getting : (i) an even number (ii) an odd number (iii) a prime number (iv) a composite number
24.An urn contains 16 red balls and 12 blue balls. A ball is drawn from the urn without looking into the urn. Find the
probability of getting : (i) a red ball (ii) a yellow ball (iii) a blue ball (iv) blue or red ball .
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25. The distribution of weight (in kg) of 100 people is given below:
Weight ( in kg )
40-45
45-50
50-55
55-60
60-65
65-70
70-75
Frequency
10
25
27
16
10
7
5
Draw a histogram to represent the above data.
26.The pie-chart given in figure-4 shows the annual agricultural production
Gram
wheat
of an Indian state . If the total production of all the commodities is 81000
tonnes , find the production (in tonnes ) of (i) Wheat (ii) Sugar (iii) Rice (iv) Gram .
Note:
rice
sugar
( Degree: 120 , 100, 60, 80 respectively for (i) to (iv) )
27.Given below is is a table which shows the year-wise strength of a school.
Year
2009-2010
2010-2011
No. of Students
800
975
Draw a histogram to represent the data.
2011-2012
1100
2012-2013
1400
2013-2014
1625
******************
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