Green C Math Class 10

4. Verify experimentally that an exterior angle of a cyclic quadrilateral is equal to its
opposite interior angle.

5. Verify experimentally that the angles subtanded by equal arcs of a circle at the centre
are equal.

Construction:
1. Construct a quadrilateral where ∠PQR = 60°, PQ= QR = 45cm and PS = RS = 61cm.

Also construct ∠PQT equal in area to the quadrilateral.
2. Construct a quadrilateral having AB = 54cm, BC = 5.1cm, CD = 49cm, AD = 6.2cm and

the diagonal BD = 5.8cm. Also construct a triangle equal in area of the quadrilateral.
3. Construct ∠ABC having its one side 9cm.
4. Construct a triangle ABC having a = 5.9cm. b = 6.2cm and C = 5cm. Also construct

parallelogram CDEF having CF = 6cm.
5. Construct a rhombus PQRS in which diagonal PR = 6cm and diagonal QS = 8cm. Also

construct a triangle PSA whose area is equal of the area of rhombus PQRS.

Sets

4 Marks Questions
1. In a survey of people, 48 liked Nepali films, 40 liked English films, 31 liked Hindi

films. 19 liked Nepali and Hindi films, 13 liked Hindi and English, 11 liked Nepali
only and 21 people were found not interested in any film. Find:
(i) How many people liked all the three films?
(ii) How many people were asked this questions?
2. A survey of a group of people showed that 60 liked tea, 45 liked coffee, 30 liked milk.
25 liked coffee as well as tea, 20 liked tea as well as milk, 15 liked coffee as well as
milk and 10 liked all the three. How many people were asked this question? Solve by
drawing Venn-diagram.
3. In a survey of 200 students every student studies at least one of the three subjects
Maths, English or Science. If the number of students who study only one subject is
twice the number of students who study only two subjects and 10% study all three,
find the number of students who study only one subject.
4. In a group of 60 people, 5 did not like any of tea, coffee and milk. If the ratio of
people who like only one, only two and all three is 6:3:2, find the number of people
who like only one.

Profit and Loss

1 Marks Questions

1. If a dozen of banana is bought for Rs. 48 and sold for Rs. 5 per banana, what is the
profit percent?

2. If CP is x and profit is y% then what is SP of that article?

3. What is the cash payment of a bill amounting Rs. 1800 allowing a discount of 5%?

GREEN Mathematics Book-10 295

2 Marks Questions

1. By selling 440 apples a shopkeeper loses the selling price of 60 apples. Find his loss
percentage.

2. After buying some lemons at the rate of 5 for Re 1 and selling them at the rate of 4 for
Re 1, find the profit or loss percent.

3. An article bought for Rs. 450 is sold at a profit of 30%. What is the selling price?

4. A dealer sells goods at cost price. But his 1kg eights only 750 grams. What is his
profit percentage?

5. By selling 75 apples a seller gains the cost price of 15 apples. Find his gain percentage.

4 Marks Questions

1. Shilpa bought a mobile set and a digital camera for Rs. 13000 and sold for them Rs.
13200 thereby gaining 20% on the mobile set and losing 10% on the camera. Calculate
the cost price of each.

2. Shishir bought 4000 oranges at 70 paisa each. But 400 of them were rotten. He sold
2000 oranges at 90 paisa each. If he plans to make a profit of Rs. 200 at what rate must
be sell the rest of the oranges?

3. A man bought a certain number of lichies at 20 per rupee and an equal number at
30 per rupee. He mixed them and sold them at 25 per rupee. Find his gain or loss
percent.

4. A tradesman sells a of sugar at Rs. 60 per kg and loses 20% and another kind of sugar
at Rs. 100 and gains 25%. He mixes them in equal proportion and sells the mixture at
Rs. 120 per kg. What is now the gain percent?

5. A man gained Rs. 3000 by selling a watch allowing 10% discount on the marked
price. If he allows a discount of 40% on the marked price, the loss would be Rs. 3000.
Find the marked price of the watch.

Indices

1 Marks Questions

125 – 1 25 – 1 2x + 3
27 3 9 2 2. Simplify 2x
1. Find the value of o p ÷ o p

3. 3 8a³b­9 ÷ 4 16a4b12 4. Simplify : (1 – xm–n)–1 + (1 – xn–m)–1

5. Simplify : 4(160.5 + 16–0.5)

2 Marks Questions

1. Simplify:

21 × 5x – 25 × 5x– 2 4x+1 × 2 + 6 × 22x + 1

a. 5x+2 – 5x+1 b. 2x

4x+1 × 3 + 2 × 8 3

296 GREEN Mathematics Book-10

c. 4 343m6n7 ÷ 4 7–1m– 2n³ d. (a + b)– 1 × (a – b) (a² – b²)
e. {(x – y)– 4}– a ÷ {(x – y)4}– a
4 Marks Questions

xq q + r – p xr r + p – q xp p + q – r 1 xc – b 1 + xa – c + 1 + xb – a
1. o xr p × o xp p × o xq p 2. + xa +
1 – b 1 + xb – c 1 + xc – a

xa a – b oxx–bcpb – c xc c – a oxxa +c ba – b (xc – a)b 1
x– b x–a (xc – a)a
p p p 1

xb a – b
3. o × × o o p4. × ×

5. 1 + 1 + 1
1 + xa – b + xa – c 1 + xb – c + xb – a 1 + xc – a + xc – b

6. If pqr = 1, prove that : 1 + 1 q–1 + 1 + 1 r–1 + 1 + 1 p–1 = 1
p+ q+ r+

5 Marks Questions

1 a 1 b – a

11 1 oa² – p oa – p

m + (mn²) 3 + (m²n) 3 1 – n3 b² b
1
o p 1. × 2.
m–n
1 b 1 a – b
m3
ob² – p ob + p
a² a

3. {(xa+b) (yc)}a–b {(xb+c)(ya)}b–c {(xc+a)(yb)}c–a

4. (ab– 1 + 1) × b²(b– 2 – a– 2) ÷ 1 – a–1b
a– 1 b– 1(1 + a–1b) a(ab–1 – a– 1b) ab– 1 + 1

22 2 22 2

5. x3 – y 3 o x3 1 1 + x3 – y 3 o x3 1
x+y
x–y 1 + y3p 1 1 – y3p

x3 + y3 x3 – y3

Exponential Equations

1 Mark Questions

1. a. 3x = 27 b. 2x – 4 = 4x – 6 c. pqx – 3 = qpx – 3
d. ( 5 )x – 1 = 25 e. 25x = 25
2 Marks Questions
5x

Solve:

1. 3x + 1 – 3x = 54 2. 23x – 5 × ax – 2 = 2x – 2 a1 – x

3. If a = bx, b = cy and c = az prove that xyz = 1.

4. 2x – 3 . 3x – 4 = 3–1 5. 103y–3 = 1
0.001

GREEN Mathematics Book-10 297

4 Marks Questions 2. 52x + 1 = 5 1
5x 5
Solve:
1. 7m + 343 = 56 4. 5x + 1 = 26 – 51 – x

7m
3. 16p – 5 × 4p + 1 + 64 = 0

5. 2p – 2 – 23 – p = 3

5 Marks Questions

1. If a = xq + r . yp, b = xr + p . y2 and c = xp + q.yr, then prove that aq – 2 br – p . cp–q = 1.

2. If ax . ay + 1 = a7 and a2y . a3x + 5 = a20, show x²y = 27.
3. If ax = by = cz and b² = ac, prove that 1 + 1 = 2.

xzy

Simultaneous Linear Equations

1 Mark Questions

1. If sum of two consecutive odd numbers is 20, then find the numbers.

2. The sum of digits of the number of two digits is 9, if digit in 1 place is 2. Find the
number.

3. The sum of two consecutive numbers is 35. Find the numbers.

4. If the sum of three consecutive numbers is 36, find the numbers.

5. The product of two consecutive numbers is 56. Find the numbers.

2 Mark Questions
1. From the age of a person if two fifths of his age is subtracted, the result becomes 24

years. Find the age of the person.

2. If the sum of two numbers is 24 and their difference is 4, then find the numbers.

3. A number is twice the other. If their sum is 30, find the numbers.

4. Find the number when it is multiplied by 5 and then subtracted by 10 is equal to 5.

5. Two numbers are in the ratio of 3:5. If their sum is 40, find the greater number.

4 Marks Questions
1. If twice the son's age years is added to the father's age the sum is 70. But twice the

father's age is added to the son's age, the sum is 95. Find the present ages of father
and the son.

2. The ages of two girls are in the ratio of 5:7. Eight years ago their ages were in the ratio
of 7:13. Find their present age.

3. A number consists of two digits. If the number formed by reversing its digits is
added to it, the sum is 121 and if same number is subtracted from it, the remainder
is 27. Find the number.

298 GREEN Mathematics Book-10

4. If a number of two digits is divided by the sum of the digits, the quotient is 6 and
the number is greater by 9 then the number formed by reversing the digits. Find that
number.

5. If 3 is added to the numerator of a fraction, the value of the fraction becomes 8. When
7

3 is added to denominator of the fraction, the value of the fraction becomes 1 . What
4

is the value of the fraction? Find it.

5 Marks Questions

1. The combined price of 1 pen and 3 copies is Rs. 210. The combined price of 3 pens
and 5 copies of same quality is Rs. 430. What is the combined price of 1 pen and 1
copy? Find it.

2. Rama said to Rabina "I was twice as old as you were when I was as old as you are."
If the sum of their ages is 30 years, find their ages.

3. Points A and B are 90km apart from each other on a highway. A car starts from A and
another from B at the same time. If they go in the same direction they meet in 9 hours
and if they go in opposite direction, they meet in 9 hours. Find the speed of each car.
7

4. The quotient of a two digit number and the number obtained by interchanging the
digits is 7 . If the difference of the digits is 3, find the number.
4

5. In an examination 80% students passed. If 15 less had appeared and 10 less passed,
the ratio of total to pass would have been 5:1. How many students passed and how
many appeared in the examination?

Simplification of Algebraic Expressions

1 Mark Questions 1
y
b a x–
a b
1. (1 – ) ÷ (1 – ) 2. 1
x
2 Marks Questions y–

1. (b – 1 – a) – (c – 1 – b) 2. x + x + x2
c) (b b) (a x – 2a x + 2a x2 – 4a2

3. 2a 1 3b – 2a
– 4a2 – 9b2

4 Marks Questions

1. 2 + 2 + 1
(x–2)(x–3) (x–1)(3–x) (1–x)(2–x)

2. 1 a + 1 a + 1 2a + 16a³
– 2a + 2a + 4a² 16a4 –1

GREEN Mathematics Book-10 299

3. 3 + x – 3 – x – 12x – 24x³
3 – x 3 + x x2 + 9 x4 + 81

4. 2a – b – 2a + b + 16a³
4a² – 2ab + b² 4a² + 2ab + b² 16a4 + 4a²b² + b4

5. x3 – x3 – 1 – 1
x–1 x+1 x–1 x+1

6. (a – b)2 – c2 + (b – c)2 – a2 + (c – a)2 – b2
a² – b2 – 2bc – c2 b² – c2 – 2ca – a2 c² – a2 – 2ab – b2

7. 1+ 1 + 2
2 ( 2 – x) 2( 2+ x) 2+x

5 Marks Questions

1. 1 + 1 + 1 – 2a4
2a3 (a – x) 2a3 (a + x) a2 (a2 + x2) a8 – x8

2. 1 – (a 1 1)2 + 2 – 2
(a + 1)2 (a + 2)2 + (a + 1) a+2

3. ( 1 + 1 ) (a + b – c) + ( 1 + 1 ) (b + c – a + 6) + ( 1 + 1 ) (c + a – b)
a b b c c a

4. 1 + 2 + 4 + 8
a+1 x2 + 1 x4 + 1 a8 – 1

5. (a + 1)2 ÷ 1 + a
a
1 – a + a2 + a + 1

Trigonometry

1 Mark Questions

Find the area of the triangles given below:

A

1. 2. X 3. X

80° 6.5cm

B 70° Y ZY Z
7.5cm C Ratio of sides2 : 3:4
Perimeter = 30cm
2 Marks Questions Perimeter = 54

Find the area of the quadrilaterals given below:

1. D M C 2. 10cm C 3. 6cm C
D
A D
60°
9cm

B

5cm
N 8cm
5cm
A B
AC = 3DN = 2BM = 24cm 8cm

A B

300 GREEN Mathematics Book-10

4 Marks Questions
1. An aeroplane flying horizontally 1 km above the ground is observed at an elevation

of 60°. After 10 seconds, its elevation is observed to be 30°. Find the speed of the
aeroplane in km/hr.
2. A man on a cliff which is 30 3 m high observes a boat at an angle of depression of
30° which is approaching the shore to the point immediately beneath the observer
with a uniform speed. Six minutes later, the angle of depression of the boat is found
to be 60°. Find the time taken by the boat to reach the shore.
3. The horizontal distance between two towers is 70m. The angles of depression of the
top of the first tower, when seen from the top of the second tower is 30°. If the height
of the second tower is 120m, find the height of the first tower.
4. What is the angle of elevation when a lamp at the top of a lamp post 80 3 m high
is observed from a distance of 240m?
5. From a cliff 61.6m high the angle of depression of the top of a 10.6m high tree was
found to be 60°­ . Find the distance between the cliff and the tree.
6. A girl 1.75 m tall is 50m away from the tower 51.75m high. What is the angle of ele-
vation of the top of the tower from her eye?
7. From the top of a tower of 45 m high, the angle of depression of the top of a pole of
13m high lying in front of the tower is observed and found to be 45°. Find the dis-
tance between the tower and the pole.
8. A 15m high tree was broken by the wind and the top of the tree makes an angle of
45° with the ground. Find the length of broken part.

Statistics

1 Mark Questions
1. Find the mean (x) of the data: 50, 60, 70, 80, 90.

2. The mean of a, b, c and d is 12. What will be the mean of a, b, c, d and e if e = 50?
Y

3. Find the class for Q1, Q2 and Q3 from the given ogives. Frequency 12
10

8

6

4

2

2 Marks Questions OX
10 20 30 40 50

(Marks)

1. If the mean of 6 observations x, x + 3, x + 6, x + 9, x + 12 and x + 15 is 18, find the mean

(x) of the first four observations.

2. If Σfx = 240 + 15p, N = 17 + p and mean (x) = 14.25, find the value of p.
3. 2x + 1, 3x + 1, 3x + 5, 5x – 7, 63 and 70 are in the ascending order. Q1 = 20, find the value

of x.
4. Construct a frequency distribution table from the data given.

5, 10, 5, 10, 20, 22, 22, 24, 10, 2, 10, 25

GREEN Mathematics Book-10 301

4 Marks Questions
1. In the given distribution table, N = 20, and arithmetic mean (x)= 33.5. Find the val-

ues of p and q.

x 10 – 20 20 – 30 30 – 40 40 – 50 50 – 60
3 q
f 4 p6

2. Find the value of x if N = 18 from the data given.

Class 0 – 10 10 – 20 20 – 30 30 – 40 40 – 50 50 – 60
2
f 1x243

3. Find the missing frequencies from the data, if N = 60 and Q2 = 28.5.

Class 0 – 10 10 – 20 20 – 30 30 – 40 40 – 50 50 – 60
20 15 y 5
f 5x

4. If Q3 = 60, find the value of w.

x 10 – 20 20 – 30 30 – 40 40 – 50 50 – 60 60 – 70 70 – 80
f 4 5w8 766

5. From the marks distribution of 30 students, 2 frequencies are missing. However
median marks is known as 45. Find the values of missing frequencies.

Marks 20 – 30 30 – 40 40 – 50 50 – 60 60 – 70
f 3 ? 10 ? 4

Probability

1 Mark Questions

1. What is the probability of an event other than sure and impossible event?

2. Write the sample space when a die is tossed twice.

3. If A, B and C are mutually exclusive events, write the probability of the occurrence

of either A or B or C.
2 Marks Questions

1. a. A and B are two mutually exclusive events. If P(A) = 50% and P(B) = 30%, find

P(A∪B) and P (A∪B).

b. If P(X) = 0.6, P(Y) = 0.5 and X and Y are non-mutually exclusive events, find
P(X∩Y).

2. There are 4 green and 6 white balls in a bag. Two balls are drawn randomly one
after other with the replacement of the first ball. Find the probabilities of the fol-
lowing events :

a. both are green b. both are white

3. Two dice are rolled two times. Find the probability of getting

a. 1 in first and 6 in second.

302 GREEN Mathematics Book-10

b. not 1 in first and not prime number in second.
c. not getting 5 in both drawing.

d. A card is drawn from the set of number cards from 8 to 27. Find the probability

that the card drawn is exactly divisible by 6 or 4?

4. a. A die is rolled once. Find the probability of getting a multiple of 2 or a multiple
of 3.

5. A problem of Mathematics is given to two students A and B. Their chance of solv-
1 1
ing the problem are 2 and 3 respectively. What is the probability that both of

them will solve the problem?

6. A bag contains 7 black and 5 white balls. Two balls are drawn randomly one by
one without replacing the first ball.

a. Show the probabilities of all events in a tree diagram.

b. Find the probability that the first is black and second is white.

c. Find the probability that the first is white and second is black.

d. Find the probability that both of them are of different colour.

7. A class contains 20 boys and 30 girls. If two students are selected at random, show
the probability of selecting a boy and a girl on a tree diagram.

Compound Interest

1 Mark Questions

1. If principal (P) = P, Time = T and rate of interest = R, compound amount (CA) =
....................

2. The compound interest and the compound amount are CI and CA respectively.
Write down the relation among:

i. P, T, R and CI (yearly) ii. P, T, R, CA (half yearly)

2 Marks Questions

1. At what rate percent per annum compound interest of Rs. 625 will amount to Rs.
729 in 2 years?

2. In what time will Rs. 8000 amount to Rs. 10648 at 10% compound rate of interest?

3. Find the rate of interest if the compound interest on Rs. 15625 for 3 years is Rs. 1951.

4. Find the compound amount if principal (P) = Rs.500, R (Rate of interest) = 12%,
Time (T) = 2 years.

5. The population of a city at present is 170,000 and it grows at the rate of 2% yearly.
What will be the population after 2 years?

6. In how many years will the population of a city be 66550 from 50,000 if the popula-
tion growth rate is 10% yearly?

7. The present price of a scooter is Rs. 95000. If it is depreciated at 6% per year, what
will be the price of the scooter after 2 years?

GREEN Mathematics Book-10 303

4 Marks Questions

1. Sabin borrowed Rs. 1,30,000 from Sadan at the rate of 21% per annum. Find simple
interest and compound interest at the end of 2 years compounded yearly.

2. The simple interest on a sum of money in 2 years is Rs. 36 less than the compound
interest compounded yearly, if the rate of interest is 12%, find the sum.

3. The sum of simple and compound interest in 2 years is Rs. 202.50 and the rate of
interest is 5% yearly, find the sum.

4. According to the yearly compounded interest in what time will the compound in-
terest on Rs. 400000 at the rate of interest 6.5% yearly be Rs. 83179.85?

5. According to the system of semi annual compound interest of a sum of money it
amounts to Rs. 400 in 1 year and Rs. 441 in 2 years. Find the rate of interest.

6. The population of a town increases every year by 10%. At the end of two years the
total population of the town was 30,000. If 5800 people were added by migration,
what was the population of the town in the beginning?

H.C.F. and L.C.M.

1 Marks Questions b. 45a4x5y², 54a³x6y³ and 72a5x3y
Find the H.C.F. of: d. (a – b)2 + 4ab and a2 – b2
a. 12x² – 27 and 4x² + 6x
Find the L.C.M. of :

c. 2x2 – 2y2 and x2 + 2xy + y2

2 Marks Questions 2. 8m³ + n³ and 16m4 + 4m²n² + n4
Find the H.C.F. of: 4. x3y – xy3, 3x + 3y and (5x – 5y)
1. 6x² – x – 1 and 54x4 + 2x

3. p² – 4pq + 4q² and p² + 3pq – 10q²

4 Marks Questions
Find the H.C.F. of:
1. a³ + b³, a³ – a²b + ab² and a4 + a²b² + b4
2. x³ – 1, x4 + x² + 1 and x³ + 1 + 2x² + 2x
3. p² – 4, p³ – 8 and p³ + 8
4. a² – b² + 2bc – c², (a + b)² – c² and (a + b – c)²

5 Marks Questions
Find the H.C.F. and L.C.M. of:

1. a2 – 2bc – b2 – c2, b2 – 2ca – a2 – c2 and c2 – 2ab – a2 – b2

2. x2 – 2x + 1 – 2xy + 2y and x2 – 4xy + 4y2 + 2x – 4y – 3
3. a2 – b2 + a + 3b – 2 and a2 – 2ab + b2 + 5a – 5b + 6
4. x2 – 4y2 – 3x + 2y + 2 and x2 – 4xy + 4y2 + 2x – 4y – 3

304 GREEN Mathematics Book-10

Answers

Unit 1 Sets

Ex. : 1.1

1. 2. Show to your subject teacher.

3. 20% 4. 100, 50 5. 113 6. 4 7. 450 8. 30, 40
11. 5% 12. 5 13. 100 14. 43, 11
9. 200 10. 25, 20

15. 30% 16. 8, 58

Unit 2 Profit and Loss

Ex. : 2.1

1. 2. Show to your subject teacher

3 a. Rs. 1710 b. Rs. 495 c. Rs. 700 d. Rs. 11000 e. Rs. 500

f. Rs. 1200 g. Rs. 1200 h. Rs. 1650 i. Rs. 3051 j. Rs. 135

k. Rs. 495 l. Rs. 247

4. Rs. 5744.25 5. Rs. 152550 6. Rs. 18000 7. Rs. 10000 8. Rs. 16154.58/5744.25

10. Rs. 5000 11. Rs. 1350 12. Rs. 20000, Rs. 17850 13. Rs. 300 14. Rs. 225

15. 9.73% 16. 13% 17. 17% 18. Rs. 43507.25
2
19. a. Rs. 100 b. Rs. 3000,Rs.3500 c. 4% d. 20%, 14 7 % e. Rs. 1000
1 2
20. a. 20%, 33 3 % b. 20%, 14 7 %

21.a. Rs. 2125 b. Rs. 35000, Rs. 25000 c. 10.5% loss d. Rs. 20,000, Rs. 17850

Ex. : 2.3 b. $9.42 c. IC 328.13

2. a. £3.82 b. $1.45 c. £35 d. £18 e. $70 f. $70
g. $722
3. a. £24 b. 1275 Bhat h. 34.97
f. £300 b. Rs. 40,000
4. a. $599.94 c. NRs. 1026.67
5. a. £59.136
c. £60 d. Rs. 90,000

Unit 3 Compound Interest, Population Growth and Compound Depreciation

Ex. : 3.1

1. 2. Show to you subject teacher.

3. (i) CI = P qo1 + R T – 1r CA = P qo1 + R T
100 100
p pr

(ii) CI = P qo1 + R 2T – 1r CA = P qo1 + R 2T
200 200
p pr

4. R = 8% 5. R = 5% 6. Rs. 17.29 7. Rs. 300 8. Rs. 400
9. T = 3 yrs 10. R = 4% 11. Rs. 6243.584 and Rs. 2243.584 12. Rs. 627.20
13 Rs. 57298.5, Rs. 53550 14. Rs. 54600 and Rs. 60333 15. Rs. 150
16. Rs. 405 17. Rs. 24009 18. Rs. 6000 19. Rs. 2500 20. Rs. 8000
21. Rs. 12000 22. Rs. 250,000 23. Rs. 1000 24. Rs. 800 25. R = 10%, Rs. 6000
26. R = 10% and Rs. 10,000 27. R = 5% and Rs. 1200
28. R = 15% and Rs. 8000 29. T = 2yrs 30. T = 3 yrs
31. 3 years 32. 8% 33. 10% 34. 10%
35. 20%, Rs. 7500 36. 10%, Rs. 12000

GREEN Mathematics Book-10 305

Unit 3 Compound Interest, Population Growth and Compound Depreciation

Ex. : 3.2

A. Show to you subject teacher

B. 2. a. 74088 b. 176868 c. 16000 d. 260100 e. T = 3 years

f. T = 3 years g. T = 2 years h. T = 2 years

3. a. Rs. 83942 b. Rs. 8381 c. Rs. 121086 d. Rs. 120,000 e. Rs. 85000

f. R = 10% g. R = 5% h. R = 10.5%

C. 4. a. 20,000 b. 24000 c. 10,000 d. 114444 e. R = 5%

5. a. R = 3.2 % b. R = 4.76% c. R = 7.2% d. Rs. 4,30,000 e. Rs. 1,55,0000

f. i. Rs. 132.09 ii. Rs 78.003 g. i. Rs. 10172526.04 ii. Rs. 82944000

6. a. 3 yrs b. 20,000 c. 11,68,467 nearly d. 3.2%

Unit 4 Mensuration

Ex. : 4.1 1
2
1.a. i. P = 120m ii. p= p + b+ h, A = . p b iii. 3 x2 cm2
v. x
iv. A = S(S – X)(S–Y)(S – Z) 4 = 4 4y2 – x2 cm2
A

vi. A = 11.6cm2

b. i. 5cm ii. 10.5cm2, 21cm2 iii. 16cm2 iv. 48cm2

2. a. 42cm² b. 30cm² c. 24cm² d. 13.6cm2 e. 97.8cm² f. 36cm²
g. 50m2 h. 62.3cm2

3. a. 24cm² b. 62.3cm2 c. 11.62cm2 d. 19200m2

4. a. 222cm² b. 2.07cm² c. 23.23cm2
5. a. 50cm
b. 12cm, 16cm c. 28m, 26m d. 6cm, 8cm, 10cm

Ex. : 4.2 b. i. 600cm2 ii. 660cm2 iii. 600cm2
1. a. LSA = 240cm2
c. Cross section, 6cm2 d. 240cm3 e. 30cm f. 112.5cm3
2. a. 126cm2 b. LSA = 450cm2 c. TSA = 760cm2 d. h = 20cm
3. a. i. LSA = 900cm2 ii. TSA = 960cm2 iii. V = 900cm3
b. i. LSA = 480cm2 ii. TSA = 535.42cm2 iii. Vol = 554.25cm3
c. i. LSA = 240cm2 ii. TSA = 264cm2 iii. Vol = 180cm3
d. i. LSA = 1025cm2 ii. TSA = 1159.73cm2 iii. Vol = 1684cm3
e. i. LSA = 240cm2 ii. TSA = 288cm2 iii. Vol = 240cm3
4. a. i. TSA = 281.4cm2 ii. v = 205.75m3 b. BC = 7.5cm c. h = 15cm d. each side = 11.18cm
5. a. 20cm b. 660cm2

Ex. : 4.3

1. Show to your subject teacher.
2. a. CSA = 220cm2 b. i. CSA = 924cm2 ii. TSA = 1232cm2 iii. v = 3234cm3
c. TSA = 784cm2 d. TSA = 2640cm2
3. a. v = 3080cm2 b. v = = 1617cm3

4. a. r = 22.13cm b. h = 20 cm c. r = 5cm d. h = 7cm e. h = 14cm

5. a. i. TSA = 154cm2 ii. v = 179.66cm3 b. i. TSA = 1039cm2 ii. v = 2425.5cm3
22 ii. v = 0.52cm3
c. i. TSA = 7 cm2 d. TSA = 924cm2

306 GREEN Mathematics Book-10

Unit 4 Mensuraion

Ex. : 4.3 Cont.
6. a. 7cm b. 616cm2

7. a. 2552cm2, 9240cm3 b. 8624cm3 c. 4 times d. 715cm3
c. 3600cm d. 512.05
8. a. 4:9 b. 1:2

9. a. 9cm b. 30.91cm

10. 2156cm3 11. 11cm

12. a. 2258.66cm3 b. 6827.33cm3

13. a. 1342cm2 b. 528cm2

14. a. 10cm b. 26cm

Ex. : 4.4
1. Show to your subject teacher.

2. a. v = 128cm2 b. LSA = 160cm2 c. 360cm2

d. i. 100cm2 ii. 13cm iii. 400cm3 iv. 260cm2

3. a. v = 106.68cm3 b. LSA = 252cm2 c. 260cm2 d. 384cm3 e. 384cm3

4. a. h = 9cm b. h = 10cm 5. a. 1280cm3 b. 363.33cm3 c. 400cm3

d. 1280cm3 e. 166.27cm3 f. 39cm3

6. a. 576cm2 b. 384cm2 c. 360cm2 d. 1824cm2 e. 926.29cm2 f. 1200cm2

7. a. TSA = 384cm2 b. TSA = 600cm2 8. a. v = 48cm3 b. v = 400cm2

9. a. i. TSA = 414cm2 ii. Vol = 900cm2 b. h = 9cm

Ex. : 4.5

1. Show to your subject teacher.

2. a. v = 308cm3 b. A = 113.14cm2 c. v = 176cm3 d. CSA = 204.28cm2
c. v = 254.57cm3
3. a. v = 37cm3 b. v = 301.71cm3 c. TSA = 44cm2 d. r = 14cm
c. r = 7cm d. TSA = 209.22cm2
4. a. TSA = 282.85cm2 b. TSA = 301.71cm2 c. TSA = 770cm2

5. a. l = 13cm b. l = 7cm

6. a. TSA = 3318.85cm2 b. TSA = 1056cm2

e. TSA = 528cm2

7. a. v = 1414.28cm3 b. v = 5852cm3 c. v = 1642.67cm3 d. v = 117.33cm3

e. v = 1950.67cm3 f. v = 2004.05cm3

8. a. h = 9cm b. h = 7cm c. v = 13552cm3

9. a. TC = Rs. 13533.86 b. TC = Rs. 55000 c. Rs. 517.44 d. TC = Rs. 4576

e. Total mass = 1388.7kg (approx.) 10. a. 432cm2, 552cm3 b. 10cm

Unit 5 H.C.F. and L.C.M.

Ex. : 5.1

1. a. 8x²y² b. 2x + 3 c. 1
c. 9a³x³y
2. a. 6p²q² b. 3cd d. (x + y) e. c + d
c. 3x + 1
3. a. 2(x – a) b. 2x + 3y
c. x – 4y
4 a. 3p – 2 b. a² – ab + b²

5. a. 4m² – 2mn + n²

6. a. a – 1 b. a(x + 3) d. 2x + 3 e. 1

GREEN Mathematics Book-10 307

Unit 5 H.C.F. and L.C.M.

Ex. : 5.1 Cont.

7. a. a(a + 3b) b. a² – ab + b² c. 1 d. c(2c + 1)

e. 2p² – 3pq + 7q² f. x² + x + 1 g. 1 – 2x

8. a. a – b b. x + 2 c. a + b + c d. 3x + 2y + 2z e. (3m + 2n + r)

f. x – 2 g x + 2 h. 4m² – 6mn + 9n² i. a2 – ab + b2 j. m(2m + 3n)

k. a² + 2a + 4 l. x(x + 5) m. z(2z – 3)

9. a. (a + b) b. (1 – 2x) c. 1 d. (a + b + c) e. (a + b + c)

f. (a – b + 2) g. (x – 2y – 1)

Ex. : 5.2

1. a. 60a³b³ b. (a – b)2 (a2 + ab + b2) c. 2(x + y)2 (x – y)

d. (20(x3 – y3) e. 2(9x2 – 4y2) f. 10xy (2x2 – y)

g. 6(x – y)2 (x + y) h. 5(x + 2y)2 i. (a + b)2 (a – b)

2. a. (x² – y²) (x + 2y) b. (p – 2q)² (p + 5q)

c. 36x³ (x – a)² (x + a) (x² + ax + a²) d. 60m3a3b3

e. 2(a – 1) (a – 2) (a2 + 2a + 4) f. 2x(2x – 1) (3x + 1) (9x2 – 3x + 1)

g. (a – 2)2 (a – 3) h. 15xy (x2 – y2) i. 4(a3 + 8b3)

3. a. m³x2(x – 1) (x – 2) ( x + 3) b. (2x – 3y) (2x + 3y)( 4x² – 6xy + 9y²) (4x² + 6xy + 9y²)

4. a. 24a²b² (a4 – b4) b. (x³ – y³) (x³ + y³) c. (p³ – 8) (p³ + 8)

d. a² (a + 1) (a² – 4) (a² + 2a + 4) e. (x + y + z) (x – y + z) (x + y – z) (y + z – x)

f. 3 (x – 3a)² (x + 3a) (2x – a) g. a6 – 1 h. (x – 3) (x + 4) (x + 5) (x + 7)

i. (3b + 1) (2b – 1) (b + 2) j. 2 (x² – 2x – 8) (x³ – 8) k. a (a – 1) (a4 + a² + 1)

l. (x2 – ax + b2) (x² + ax – b²) m. (a + b – c)² (a – b + c) (a + b + c)

5. a. (a + b) (a³ + b³) b. (1 – 2x) (1 + 3x + 5x2) (1 + 2x + 8x3)

c. (2x + 3y – z) (2x – 3y + z) (3y + z – 2x)

d. (a + b + c) (a – b + c) (a – b – c) (b – c – a) (c – a – b)

e. (a + b + c) (a – b) (b – c) (c – a) f. (a – b + 2) (a + b – 1) (a – b + 3)

g. (x – 2y – 1) (x – 2y + 3) (x + 2y – 2)

6. a. (x+2)2 b. (a – 2b)
x

Unit 6 Indices and Surds

Ex. : 6.1

1. a. 25 b. 9 c. 1 d. 3 e. 1 f. 217 g. 14
h . 7 i. 4 1000

j. 8 k. 5 l. 125

2. a. x8 b. m3 c. x6 d. y2+b e. am+n f. p7 g. b2
h. a9 i. 1 j. a l. a12 m. x4y8 n. ( x )
q. z k. (x + 1)
y5
o. am+n p. x7 r. 1
y3

308 GREEN Mathematics Book-10

Unit 6 Indices and Surds

Ex. : 6.1 Cont.

3. a. 36n b. a6 c. x13y14 d. a11b6 e. a2 f. 2m

g. 1 h. pq
xy
b. 1 c. x 5. a. 625 b. 36443 c. 245
4. a. 1 2401
m2 1
43
6. a. 1 2
b. 1 c. 3

7. a. 3a4 b. 2ab2 c. 2x2y d. 3x4y4 e. 6x5y2 f. 6a5b5 g. 3x2y3

h. 6xy5 i. b6 j. 1
(a+b)
2 1
8. a. 3 b. 1 c. 343 d. 7 e. 9 f. 2 g. 1

h. 1 i. 1 j. 1
15

9. a. 1 b. 1 c. 1

10. a. 1 b. 1 c. 1 d. 1 e. 1 f. 1 9. 1

h. 1 i. 1

11. a. o a pm+n b. o b pa–b c. a
b a b

12. a. 1 b. 1 c. 1 d. 1

Ex. : 6.2

1. a. x = 3 b. x = – 3 c. x = 2 d. x = 8 e. x = 2
j. 2
f. x= 1 g. – 1 h. 4 i. –3 e. 2 k. – 1
2 2 j. 0 2
e. 1 and 2
2. a. – 2 b. 5 c. 2 d. 2 j. 1, 2
2
f. 1 h. 5 i. 0 k. 1
g. –2

3. a. –2 and 2 b. 3 and 2 c. 2 and –1 d. 0 and –3

f. –2 and 2 g. 0, –3 h. 2, –2 i. 0, 2

k. 1, 2 l. 1, 2 4. h. 0

Ex. : 6.3 b. 4 3 c. 5 5 d. 5 13 e. 10 14 f. 10 2

1. a. 4 2

g. 2 3 h. 1

2. a. 8 3 b. 6 3 c. a2 – x2 d. 5 + 3 3 e. 19 – 9 5 f. 23

g. 8 + 2 15

3. a. 5 3 b. 7 5 c. 8 3 7 d. 16 2 e. 12 2 f. 3 a
4. a. 6 b. –43 4 c. 3 3 d. 11 3
c. 20 5 d. 8 3 e. 9 3
j. 39 3 2
5. a. 2 2 –16 5 b. 3 5 i. 0 e. 0 f. 63 2
g. 183 4 h. 0
k. 3 5 +16 4 3 l. 2 +2 2
3

GREEN Mathematics Book-10 309

Unit 6 Indices and Surds
Ex. : 6.3 Cont.

6. a. 30 b. 20 c. 20 d. 12 e. 6 392 f. 12 432
h. 2x4y3 e. 3 3 f. 2ab
g. 120 3 b. 36 i. 6ab3 j. 4a4b7 e. 77 – 24 10
h. 1
7. a. 11 c. 25 3 5 d. 8
6 3 3

g. 2x2y3

8. a. 12 – 10 2 b. –38 c. 33 d. 21 + 6 6

f. a2–a +a–1 g. a + b + a2–b2 h. 6
5
9. a. 1 b. –9 c. 5

Ex. : 6.4

12.. aa.. 36( 32+ 1) bb.. 233+ 3 c. 10 d. 2 e. 2
5 d. 3 2 – 2 e.
2 5 –2 3
c. 7 + 4 3 3

f. 47 + 21 5 33
2


3. a. 6 – 15 + 3 b. 30 + 2 3 – 3 2 c. a2 + a4 – 1 d. 27 + 10 2
23
6 12
4. a. 8 b. 6 c. 10

5. a. – 2 3 b. (4x –xaa) c. 8 d. 1 e. 0
3

1 3 –3 2 – 6 ) g. 3 3 –3 2(1 – x)
f. 2 (4 2 h. x i. 0
17 4 72
6. a. a = 2, b = –1 b. a = 7 , b = 7 c. a = 5 , b = – 5 d. 13 , 5
19 19

7. i. 16 ii. 2 65 iii. 5 –3 3 8. 1 9. 99
2

Ex. : 6.5 b. 10 c. 16 d. 1 e. – 5 f. – 1 g. 4
i. 3 9 2 2
1. a. 2 b. 5
b. 15 j. 9 d. 3 e. 126 f. 8 g. 6
h. 4 b. 1 c. 25 4 e. 7 g. 4
c. 253 e. 4 g. 9
2. a. 10 c. 2 d. 5 f. 81

3. a. 2 c. 36 d. – 1 f. 4
4 3
4. a. 1 c. 5
h. 1 b. 4 d. 16 e. 1 f. 16
5. a. 4
h. 4 i. 4
6. a. 5
h. 6 b. 9 d. 16 e. 9 f. 1 g. 5
20
5
i. 8

310 GREEN Mathematics Book-10

Unit 6 Indices and Surds
Ex. : 6.5 Cont.

7. a. 4 b. 12 c. 25 d. 9 e. 136 f. (p 2–qq)²
c. 1 m
j. 9
8. a. 45k b. 36 c. 3a d. 4 e. 4 f. 1 g. 4

h. 439 i. 1256

9. a. 45 b. 5 d. 4 e. ± 15 f. 43 or 1
2 d. 4 17 4

10. a. 3 b. 5 c. 4 e. 5 and 4 f. 4
8 3

Unit 7 Simplification of Algebraic Expressions

Ex. : 7.1

1. a. 152a b. a + b c. –2y d. 5a – b e. 5(x + 1)
x² – y² a² – b² x² – 1

f. 3 g. a + b h. –b i. x
a y
b b. a–22–abb2 d. m(m–2n– n2)
2. a. a2 – b2 c. 0

e. 8a31–8a2b7b3 f. 4a²3–b9b2 g. (a – 1) (a 2– 2) (a – 3) h. ba((ba – 3a)
– b)

i. a²a–bb2 j. x²3–x42 a2

3. a. 4 b. 4 c. 4 d. (a + 6a + 19
– 5) (a 2) (a + 3)
(x –2) (x – 1) (x – 3) (a – 1) (a 2) (a – 3) (a – – 3) (a + 4)

e. (x – 1 – 3)
2) (x

4. a. 8a7b b. 0 c. 8a3b4 d. 1 +4a4a2
a8 – b8 a8 – b8

5. a. 11–66b38 b. a–28–abb2 c. 654681x–7x8

6. a. 9x22(3+x3–x 1) 1 b. m22–(mm–nn+)n2 c. a22+(aa+c c) d. 4a22 (–22aa–bb+) b2
+ + c2

e. y22(–22–yy+)4 f. 12+(1x++xx)2

7. a. 6a(2x2 – a2) b. 6a c. 16a d. 32x
(x2 – a2) (4x2 – a2)
(a2 – 1) (4a2 – 1) (a2 – 9) (a2 – 1) (x2 – 25) (x2 – 9)
e. 2x

8. a. 1 b. –1 c. 1 d. –1

GREEN Mathematics Book-10 311

Unit 7 Simplification of Algebraic Expressions

Ex. : 7.1 Cont.

9. a. 2(x x b. 14 – bb2 c. 0 d. 4 8
– 1) – x2

1 2x4 1 d. (1 + a – a3)
10. a. x – 1 b. a8 – x8 c. – a – x

a2b2 8x7 1 1
e. a4 – b4 f. x8 – 1 g. a8 – 1 h. (a + 2)2

–4x 1
i. 1 + x2 + x4 j. 3 k. (y + 2)2 l. 6

m. 3 2(a + c) 1 p. 4)(x 5 (x –
a2 – 1 n. a2 + ac + c2 o. x – 1 (x – – 5) 3)

q. 1
b–a

Unit 8 Equations

Ex. : 8.1

1. Show to your subject teacher.

2. 13 and 6 3. 24 years and 6 years 4. 20 and 35 5. boy 35 days, girl 70 days

6. a. 7 b. 56, 16 c. 12, 8 d. 13

e. 42 years f. 3,8, g. 12 and 17

7 a. Pen Rs. 40 and pencils Rs. 55 b. Rs. 26 and Rs. 12 c. 1966 A.D.

d. 5 years e. 45, 15 years f. 16, 24 years g. 1
4
h. 69 i. 72 j. 19 years, 15 years

k. 29 years, 5 years l. 37 m. 72

n. 42 o. 79 p. 97 q. 76

r. 13 years and 54 years s. 15 years and 21 years

t. 38 years and 6 years u. 20 years and 15 years

v. 64 or 2 w. 38
3

Ex. : 8.2

1. a. ± 1 b. ± 4 c. 15 or 0 d. 0 or –1 e. ± 2 15 f. ± 2 34
2 3
g. 7, 0 h. ± 14 i. ± 6 j. ± 10 k. 0 or l. 0 or
2. a. 0 or 5 c. 4, – 2
3. a. 1 b. 3 , 7 c. –3, 5 d. 9±5 2 e. –2 or 4
25 25 2
b. – 1, 0

4. a. 12cm, 16cm b. 7 c. 20 d. 9, 11 e. 13 f. 9

g. 7 h. 13

5. a. 13, 15 b. 18, 6 c. 4,5 d. 20, 40 e. 32m, 20m

f. (– 10 and – 8) or (8 and 10) g. 2 years h. 20 ft, 26 ft. i. 12cm, j. –34, –33
k. 12, –12 l. 6, 8, 10 m.
16, 18 n. 6, 8, 10

6. a. 63 b. 6 yrs c. 38 d. 12 yrs, 7 yrs e. 12, Rs. 30

312 GREEN Mathematics Book-10

Unit 9 Area of Plane Figures

Ex. : 9.1 b. A = 48cm2 c. A = 20cm2
A = 28cm2
1. a. A = 15cm2 iii. A = 56cm2
e. A = 24cm2
2. a. BC = 5cm, AB = 8cm b. c. A = 48cm2 c. AD = 9.6cm
b. A = 135cm2
3. a. i. A = 56cm2 ii. A = 112cm2

c. A = 30cm2 d. A = 19.5cm2

4. a. A = 24cm2 b. A = 9cm2

5. 6. 7. 8. 9. Show to your subject teacher.

Unit 10 Constructions
Ex. : 10.1

Show to your subject teacher.

Unit 11 Circle

Ex. : 11.1

1. a. AB = CD b. PQ = RS c. AC = BD d. MN ||PQ e. 111°

2. a. ∠AOC = 2∠ABC b. i. ∠QPS + ∠QRS = 180° ii. ∠PQR + ∠RSP = 180°

c. i. ∠BAC = ∠BDC ii. ∠ABD = ∠ACD d. ∠ABE = ∠EDC e. ∠QPT = 90°, ∠RSU = 90°

3. Show to your subject teacher.

4. a. ∠APB = ∠CQD b. AB = CD

5. a. ∠ABC = 90° b. i. ∠QPR = ∠QSR ii. ∠PQS = ∠PRS iii. ∠QPS + ∠QRS = 180°

ii. ∠PQR + ∠QPS = 180°

6. a. 64° b. 70° c. 36°

7. a. x = 80° b. x = 60°, y = 30° c. y = 50°, z = 50°

8. a. x = 40°, y = 110° b. x = 100° c. x = 65°

9. a. x = 70°, y = 110° b. x = 120° c. x = 35°, y = 55°

10. a. x = 55°, y = 125° b. x = 115°, y = 115° c. x = 50°, y = 40°, z = 100°

11. a. x = 40°, y = 30° b. x = 20°, y = 70° c. x = 90°

12. a. x = 120° b. x = 110°, y = 70° c. x = 60°, y = 120°

13. a. x = 120°, y = 60° b. x = 80°, y = 110°, z = 70° c. x = 27°

14. a. 20° b. 70° c. x = 35°, y = 50°

15. a. 30° b. 135° c. ∠P = 120°, ∠S = 140° d. 70°

Ex. : 11.2

1. a. 30° b. 26° c. 30° 2. a. 100° b. 65° c. 50°
3. a. x = 20°, y = 80° b. x = 44°, y = 114° c. x = 70°, y = 30°, z = 30° c. 8cm
4. a. x = 40° b. x = 60° c. x = 115° 5. a. 12cm b. 3cm
6. a. x = 50°, y = 90°, z = 40° b. x = 30°, y = 25°, z = 55° c. x = 69° c. 30°
7. a. 100° b. i. 60° ii. 60° iii. 30°
8. a. 6cm b. 30° c. 1cm 9. a. x = 26°, 64° b. 40°
10. a. 40° b. 60° c. 65°

GREEN Mathematics Book-10 313

Unit 12 Trigonometry

Ex. : 12.1

1. a. 5cm2 b. 4 3 cm2 c. 29.84cm d. 12.18cm2 e. 16 3 cm2 f. 25 3 cm2
g. 9cm2
2. a. 10.79cm2 h. 10.5cm2 i. 24cm2
3. a. 24.38cm2
g. 46cm2 b. 8 3 cm2 c. 28.57cm2 d. 40 3 cm2 e. 12 3 cm2 f. 22.9m2
m. 27.46cm2
b. 37.5cm2 c. 60cm2 d. 12cm e. 45° f. 24cm2

h. 60° i. 16.61cm2 j. 2.07cm2 k. 136.76cm2 l. 6cm

n. 150 2 cm2 o. 4 cm

Ex. : 12.2 b. 60m c. 174.8m d. 34.64m e. 2.34m f. 68m
b. 79.94m c. 45m d. 31.6m
1. a. 20.78m b. 13.86m c. 261.6m d. 28.86m e. 34.64m f. 91.7m g. 160.41
2. a. 25m b. 77.94m c. 60m d. 123.9m e. 51.6m f. 136.83m g. 79.58m
3. a. 101.5m b. 34.64m c. 48.5m d. 360m
4. a. 123.92m b. 6.9m 7. a. 30° b. 30° c. 45°
5. a. 34.64m b. 96.96m 9. a. 115.36m b. 52m c. 41m
6. a. 20.78m
8. a. 7.5m

Ex. : 12 : UT b. 12 3 cm2 2.a. 20 3 cm2 b. 119.73cm2 3.a. 9cm2 b. 10cm
b. 56cm2
1. a. 9cm b. 240cm2 5.a. 1400cm2
4. a. 15cm2
6. 9.5m 7. 30.46m 8. 24.6m

Unit 13 Statistics

Ex. : 13.1 b. 4 c. 5 d. 16, 17
d. 45
1. a. c
d. 19.6
2. a. 70 b. 25 c. 10 d. 5
j. 9
3. Show to your subject teacher.

4. a. 35.33 b. 411.84

5. a. 30.33 b. 39.72 c. 1019.6
c. 24
6. a. 20 b. 360 c. 95 e. 12 f. 5
i. 3 e. 71 f. 15
7. a. 60 b. 9.625

g. 20 h. 12

8. a. and b. Show to your subject teacher.

9. a. 30 b. 5 c. p = 4, q = 3

314 GREEN Mathematics Book-10

Unit 13 Statistics

Ex. : 13.2 b. x + 1, x + 2, x + 3, x + 4, x + 5, x + 7

1. a. 5, 10, 12, 18, 20, 22, 30

N – c.f N – c.f 3N – c.f

2. a. L + 4 × i b. L + 2 × i c. L + 4 f × i
ff

3. a. 7.5 b. 10 c. 7 d. 6.9 e. 100.75
4. a. 35 j. 10-20 and 2
b. 40 c. d. e. f. g. h. i. Show to your subject teacher.

5. a. 60 b. c. Show to your subject teacher. d. 6

6. a. 20 b. 20 – 30 c. 40 – 50 d. e. Show to your subject teacher.

7. a. 30 b. 32.14 c. 80.5 d. 3 e. 72

8. a. 16.81 b. 10 c. 10 d. 8, 7 e. 63.33 f. 50

g. 14.1 h. 12 i. 7 and 6

Ex. : 13.3

1. Show to your subject teacher.

2. a. i. 100 ii. 94 iii. 137 iv. 70
25, 47
b. i. Show to your subject teacher. ii. b. 150 – 200

3. a. 18, 30, 39 b. 25, 60, 62 4. a. 40 – 60

Unit 14 Probability

Ex. : 14.1

1. to 6. Show to your subject teacher.

7. a. 4 b. 9 c. 13 d. 6 e. 9

25 25 25 25 25

8. a. 10 b. 4 c. 14 d. 12 10. 1

27 27 27 169 221

9. a. 1 b. 144 c. 1 e. 1

169 169 169 4

11. a. 1 b. 1 c. 3 d. 3 b. 1

4 4 4 4 6

12. a. 1 b. 5 c. 25 13. a. 1 iii. 4

36 12 36 12 15

14. a.i. 3 ii. 1 iii. 2 iv. 2 e. 7
44 33
26
b. 3 c. 1 d. i. 3 ii. 7 f. 11
e. 2
10 15 10 10 13
3
15. a. 2 b. 3 c. 1 d. 1 21. 35%
20. 2
13 26 13 2
3
16. a. 7 b. 4 c. 8 d. 6

13 13 13 13

17. a. 1 b. 1 c. 2 d. 5

2 2 3 6

18. a. 2 b. 2 19. a. 1 b. 2

3 3 6 9

GREEN Mathematics Book-10 315

Unit 14 Probability

Ex. : 14.2

1. a. i. 9 ii. 5 iii. 5 iv. Yes

18 18

b. i. Yes ii. S = {HH, HT, TH, TT} iii. 1 iv. 1
44
c. i. 7 ii. 12 iii. No. iv. No, independent

2. a. {HH, HT, TH, TT} b. 1 3. a. 7 b. 1 c. 1

4. a. 9 b. 16 4 8 8 8

49 49 c. 25 5. b. 35 c. 35 d. 35

49 132 132 66

6. a. 3 b. 1 c. 1 7. 24 8. {RG, RB, GR, GB, BR, BG}

4 4 2 49

9. a. 11 10. 1 11. 1 12. 1 13. 35 14. 1

221 36 221 4 69 8

16. i. 4 ii. 5 iii. 6
35 7 35

Answers of Revision Problems for Examination

Profit and Loss

1 Marks: 2. (x + xy ) 3. Rs. 1710
1. 25% 100
2 Marks:

1. 15 15 % 2. 25 3. Rs. 585 4. 33 313% 5. 25%
19 2. 75 paisa
4. 1700 % 5. Rs. 20000
4 Marks: 31

1. Rs. 8000, Rs. 5000 3. 4%

Indices 2. 8 3. 1 4. 2x 5. 17

1 Marks: b. 65 c. 7m2n d. (a – b) e. (x – a)5a
1. 1
2 Marks: 2. 1 3. 1 4. 1 5. 1
1. a. 1
4 Marks: a+b 4. o a+b p 5. 2
1. 1
5 Marks: 2. o a p 3. 1 a–b

1. 1 b

316 GREEN Mathematics Book-10

Exponential Equation

1 Marks:

1. 3 2. 8 3. 4 4. 5 5. 2
3
2 Marks:

1. 3 2. 3 4. 3 5. 2
4 Marks: 2

1. 2 and 1 2. –1 and 1 3. 4 and 1 4. 1 and –1 5. 2 and 3

Simultaneous Linear Equn

1 Marks:

1. 9 and 11 2. 72 3. 17 4. 11 and 13 5. 7 and 8
2 Marks: 4. 3
4. 5 and 4 5. 25
1. 60 2. 14 and 10 3. 10 and 20 4. 63 or 36 5. 36
4 Marks:
105
1. 4 and 15 yrs 2. 21 and 15 yrs 3. 74 5. 75 students
5 Marks:

1. Rs. 110 2. 18 and 12 yrs 3. 30km/hr

Simplification of Algebraic Expresstions

1 Marks:

1. –b 2. x
a y

2 Marks:

1. 0 2. 3b 3. x²3–x42 a2
4 Marks: 4a² – 9b2

1. 4 2. 4a 3. 654681x–7x8 4. 4a22 (–22aa–bb+) b2 5. 2x 6. 1
(a – 5) (a – 3) 1 + 4a2

5 Marks: 1 4. 6 1
2x4 2. (1 + a – a3) 3. (a + 2)2 5. x – 1

1. a8 – x8

Trigonometry 2. 27 15 cm2 3. 25 3 cm2

1 Marks:
1. 18.12cm2

2 Marks:

1. 240cm2 2. 40 3 cm2 3. 34.03m2

4 Marks:

1. 4156.92km/h 2. 3 minutes 3. 79.58m 4. 30° 5. 50 3 m 6. 45°

7. 32m 8. 8.78m

GREEN Mathematics Book-10 317

Statistics 2. 19.6 3. 18, 30, 39
2. 3
1 Marks: 2. 6 3. 6.2 4. Show to your subject teacher.

1. 70 3. 12, 3 4. 2 5. 9, 4

2 Marks:
1. 15
4 Marks:
1. p = 4, q = 3

Probability

1 Marks:

Show to your subject teacher.
2 Marks:

1. a. 4 b. 9 2. a. 1 3. b. 16 4. a. 2 b. 2

25 25 216 21 3 3

5. 2 6. b. 35 c. 35 d. 35 7. 24

3 132 132 66 49

Compound Interest

1 Marks:

Show to your subject teacher.

2 Marks: 2. T = 3 yrs 3. Rs. 627.20 4. 176868 4. T = 3 years
1. R = 8%

5. Rs. 83942

2 Marks:

1. Rs. 54600 and Rs. 60333 2. Rs. 8000 3. Rs. 2500 4. Rs. 1000

5. 10% 6. 20,000

H.C.F. and L.C.M. 2. 9a³x³y 3. 2(x + y)2 (x – y) 4. (a + b)2 (a – b)

1 Marks:
1. 2x + 3
2 Marks:

1. 3x + 1 2. 4m² – 2mn + n² 3. (p – 2q)² (p + 5q) 4. 15xy (x2 – y2)

4 Marks:

1. a² – ab + b² 2. x² + x + 1 3. (p³ – 8) (p³ + 8) 4. (a + b – c)² (a – b + c) (a + b + c)

5 Marks:

1. (a + b + c) 2. (x – 2y – 1) 3. (a – b + 2) (a + b – 1) (a – b + 3)

4. (x – 2y – 1) (x – 2y + 3) (x + 2y – 2)

318 GREEN Mathematics Book-10

Model Set for SEE Exam for 2074

Group A [6 × 1 = 6]

1. If a, b and c are length of sides of a triangle ABC, write the formula of area of triangle.

2. The circumference of the base of cylinder is 44cm and its height 14cm. Find the curved

surface area. A

3. Find the H.C.F. of a³b and a²b³.

4. In the adjoining figure, O is centre of circle. Write the relation of O

∠BAC and ∠BOC . BC

A D P

5. In the given figure ABCD is parallelogram and area of triangle

PBC is 20sq. cm. Find the area of parallelogram ABCD. BC

6. The mean of a, b, c and d is 12. If a = 18, what will be the mean of b, c and d?

Group B (17 × 2 = 34)

7. If $ 30 = Rs. 2160 and £ 10 = Rs. 1980, how many $ can be changed of £ 80?

8. The population of a city at present is 1,70,000 and it grows at the rate of 2% per
annum. What will be population after 2 years?

9. If the area of an equilateral triangle is 6 3 cm², find its perimeter.

10. In the adjoing figure AC = 5cm, A'B' = 3cm and CC' = 10cm. A A'
13cm
Calculate its area. O 5a

11. Find the volume of adjoing figure. 13cm BC C'

12. Simplify : 2.9x + 1 – 32x + 1 10cm
9x + 1 + 32x

13. Simplify : 3 54 – 3 16 + 2 3 250

14. Solve : 3 2x + 1 = 3 8

15. A natural number added to three times of its reciprocal given, the result of 4. Find the
positive number.

16. Simplify : a(a + b) + a(a – b) A D
b² – a² b² – a² E

8cm 5cm C
A
17. In the figure, ABCD is parallelogram AE⊥BC, AF⊥BC, AF =

5cm, AB = 8cm and AD = 10cm. Calculate the length of AE.
BF

18. In the figure O is the centre of circle. ∠ABC = 60°, 60° B
O
∠BDC = 20° and AD//BC, find ∠BCD. P S E
20° D
20°
C

19. In the adjoining figure, QR is a tangent and O is the O A 5cm
centre of circle. If QS = SR, ∠SRQ = 20°, calculate x R 8cm 45° C
∠PQS.
Q 75°
B

20. In the figure, AB = BD, 8cm, AC = CD = 5cm ∠ABC = 75° and ∠ACB D
= 45°. Find the area of quadrilateral ABCD.

GREEN Mathematics Book-10 319

21. If the median of data 20, 30, a, 40, 50 and 60 is 39, find the value of a.

22. From the number cards, numbered from 7 to 27, a card is drawn at random. Find the
probability of getting a card having prime number or even number.

23. Two children were born in a family. By drawing a tree diagram find the probability of
both are sons.

Group C (10 × 4 = 40)

24. In a group and 200 students the ratio of students who like Maths and English is 3:5. If
60 of them like both subjects and 10 of them like none of the subjects then by drawing
Venn-diagram, find how many of them like Math only and English only.

25. The marked price of t.v. is 25% above the selling price and the cost price is 30% less

than its marked price, find discount percent and gain percent.

26. The area of curved surface area of a solid cylinder is equal to 2 of the total surface
area. If the total surface area is 924 cm², find its volume. 3

27. Find the H.C.F. of a³ – 2a²b + 2a²b + 2ab² – b³, a4 + a²b² + b4, 4a4 + 4ab4

28. The present ages of two brothers are 15 years and 22 years. After how many years, the
product of their ages will be 408?

29. Find the value of p from the following data if Q3 = 35.5

Class 0 – 10 20 – 30 10 – 20 40 – 50 30 – 40 50 – 60
10 2
Frequency 6 12 p' 4

30. A free of height 60m standing on a bank of a river is observed from the opposite bank
of the river and found the angle of elevation to be 60°. What is width of the river?

31. Prove that area of parallelograms on the same base and between same parallel lines
is equal.

32. Verify experimentally that angles on same segment of circle are equal.

33. Construct a triangle equal in area and quadrilateral ABCD having AB = BC = 5cm, CD
= AD = 4.5cm and ∠ADB = 75°.

Group D (4 × 5 = 20)

34. The compound amount of a certain sum of money in 2 years and 3 years becomes Rs.

8820 and Rs. 9261 respectively. Find the sum and rate of interest. Also find the simple

interest in 4 years of the same sum and rate of ++. 24cm
35. Find the total surface area and volume of given square solid pyramid 25cm

with sides:

36. 5 2 – 8 2 + 3 10
2( 2 + 1) 2_ 10 5+ 2
P

37. In the given figure PQRS is a cyclic quadrilateral, ST = QR and RP

is bisector of ∠ARS. Prove that T
i. area of DPQR = area of DPST Q

S

ii. PR = PT R

320 GREEN Mathematics Book-10

Model Questions

Issued by CDC

Subject: Maths F.M. 100
Time: 3 hrs. P.M. 32

Group 'A' [6 × 1 = 6]

1. Write the formula for finding the rate of discount when discounted amount and marked price
are given.

2. What is the area of an equilateral triangle whose one side is 'a' unit long?

3. If (am × an) ÷ ap = ax then express x in terms of m, n and p.

4. Write down the relation between the area of a parallelogram and a triangle standing on the

same base and between the same parallel lines. b

5. In the given figure if O is the centre of the circle then what is the value of x? x°

6. In the following data write down the series where the median lies. 60°
x 20 – 30 30 – 40 40 – 50 50 – 60 60 – 70 ac

c.f 16 36 61 77 80



Group 'B' [17 × 2 = 34]

7. How much more is Rs. 360 than the value including 13% VAT in Rs. 2700?

8. A farmer bought a tractor for Rs. 400,000 and sold it after using some time at 10% depreciation

rate per year. What is the cost of the tractor after 2 years?

9. The capacity of a cylindrical metal tank of height 1 m. is 1500 liters. How much square metres

of metal sheet would be needed to make its base?.

10. I f 27 metal spheres of radius 'x cm' each are melted to form a single sphere of radius 'y cm'. Find

the value of the ratio x: y.

11. T he slant height of a conical tent is 10 m and the radius of its base is 7m. Find the cost of cloth

required to prepare the tent at the rate of Rs. 300 per square meters.

12. Find the HCF of : (x3 – xy2), (x – y)

13. Simplify: 125 – 45 + 5

14. Simplify : 146­ × 155
356 × 65

15. Simplify : x 1 2 – 4 4
– x2 –
16. If the sum of two numbers is 128 and their difference is 16 then find the numbers.

dc f

17. In the given figure AE//DF and B is midpoint of AE. If the area of DAEF is 20 be
square centimetres, then find the area of parallelogram ABCD. c

18. In the given figure, ABCD is a cyclic quadrilateral. If ∠ADE = 75° then find the f
value of ∠ADC and ∠ABC.

o

19. In the given circle, AB is a tagent. BC is diameter and ∠BAO = 32°. a 32° b
find the value of ∠AOB.

a

20. In the given figure AB = 8 cm, BC = 6 cm and area of DABC is 12cm2. 8cm
Find the value of ∠ABC.
b
c 6cm

GREEN Mathematics Book-10 321

21. In a continuous series, mean value = 24.625. Sum of frequency (N) = 55 + a and sum of product
of frequency and mid value (∑fm) = 1345 + 25 a then find the value of a.

22. A cubical dice is thrown two times, find the probability that the outcomes is 5 in first throw and
odd number in second throw.

23. Three red and two white balls of the same size are kept in a box. Two drowns are made one

after the other (without replacement). Show the probabilty of getting red and white balls in the

tree diagram.

Group 'C' [10 × 4 = 40]

24. In a group of 150 people, 12o like to play volleyball, 85 football and 25 like to play none of the

game.

i) Show the above information in a Venn-diagram.

ii) How many people like to play both games?

iii) How many people like to play volleyball only?

25. After allowing 20% discount andthen levying 13% Value Added Tax(VAT), the value of the

watch will be Rs 904. Find the marked price of the watch.

26. An umbrella is made by stitching 10 triangular pieces of cloth of two different colours, each

piece measuring 15 cm, 41 cm and 28 cm. How much cloth is required for the umbrella? If the

cost of 1cm2 is Rs. 0.50, find the total cost of cloth.

27. Find the LCM of: x4 + x2 + 169, x3 + x (x + 13) + 4x2

28. A rectangular field is 16 m. long and 10 m. wide. There is a path of uniform width all around it
having an area of 120 m2. Find the width of the path.

29. Prove that the area of parallelogram PQRS and PQMN standing on same base and the same
parallels are equal in area.

30. Construct a triangle ADE equal in area to the quadrilateral ABCD in which AB = BC 5.5 cm, CD
= DA = 4.5 cm and ∠A = 60°.

31. Verify experimentally that angale AKB at the centre is twice the inscribed angle ACB subtended
by the same are AB. (Two figures with at least 3 cm raddi are necessary.)

32. Ath the centre of a circular pond, there is a pole of 11.62 m high above the surface of water,
From a point on the edge of a point, a man of 1.62 m high observed the angle of elevation of the
top of the pole and found to be 60°. Find the diameter of the pond.

33. The following are the marks obtained by students in mathematics in an examination.

15, 12, 23 35, 46, 57, 18, 12, 39, 51, 32, 43, 25, 59, 18, 38, 45, 40, 32, 33

i) Make a frequency table of class interval 10.

ii) Find the third quartile.

Group 'D' [4 × 5 = 20]

34. By what percent more is the yearly compound interest on Rs. 2000 for 3 years at 10% p.a. than

simple interest on Rs. 3000 for 2 years at 8% p.a. Find it.

35. In a marriage ceremony of Pemba's Daughter he has to make arrangement for accommodation
of 150 persons. For this purpose, he plans to build a conical tent in such a way that each person
must have 4 sq.m of the space on ground and 20 cubic m of air to breath. What should be the
height of the tent? Find it.

36. If a + b + c = 0, prove that: d
1 + 1 + 1 =1 c
1+ xa + x-b 1 + xb + x-c 1 + xc + x-a
37. In the given figure, 0 is the centre of the circle. AB is the diameter and DO ⊥ AB. a o b

Prove that ∠AEC = ∠ODA. e

322 GREEN Mathematics Book-10