Vedanta Excel in Mathematcs Book -10 Final (2078)

Revision and Practice Time

b) If the upper quartile of the following distribution is 114, determine the value of k.

Wages (in Rs) 50 – 70 70 – 90 90 – 110 110 – 130 130 – 150
No. of workers
4 8 16 k 2

12. a) Construct a cumulative frequency table of class interval 10 and compute the lower
quartile (Q1).
40, 55, 12, 68, 47, 26, 31, 52, 35, 50,
18, 66, 24, 36, 42, 59, 70, 38, 54, 39,
43, 65, 51, 27, 14, 32, 44, 63, 60, 37,
20, 33, 50, 64, 22, 34, 43, 28, 41, 57

b) The marks obtained by 20 students in an examination are given below. Construct
a cumulative frequency table of class interval 20 and compute the upper quartile
of the distribution.
30, 88, 15, 60, 28, 54, 72, 45, 36, 65,
48, 17, 75, 35, 98, 50, 26, 47, 80, 58

Probability

1. a) What is the probability that either A = {1, 3, 5} or B = {2, 4} when a die is
thrown?

b) What is the probability that either A = {3, 6, 9, 12, 15} or B = {7, 14} when a card
is drawn randomly from a pack of cards numbered from 1 to 15?

c) When a die is thrown, find the probability that either A = {2, 4, 6} or
B = {1, 2, 3}.

d) What is the probability that either A = {3, 6, 9, 12, 15} or B = {5, 10, 15} when a
card is drawn randomly from a pack of cards numbered from 1 to 15?

2. a) From a pack of 52 cards, a card is drawn at random. What is the probability of
getting a jack or ace?

b) A card is drawn from a well-shuffled deck of 52 cards. Find the probabilities of the
following events.

(i) It is either a king or a non - faced card. (ii) It is either an ace or a queen.

(iii) It is an ace or a black king or a red queen. (iv) It is a black ace or a red king.

(v) It is nether a jack nor a queen.

(vi) It is neither a diamond king nor a red king.
c) A card is drawn randomly from a deck of 52 cards. Find the probabilities of getting

the following cards.

(i) a red or a face card (ii) an ace or a heart (iii) a king or a black

3. a) When a card is drawn from the number cards numbered from 4 to 40, find the
probability that the card is a multiple of 5 or 8.

b) One card is drawn at random from the number cards numbered from 5 to 30. Find
the probability that the card may be a square numbered or a cube numbered card.

Approved by Curriculum Development Centre, Sanothimi, Bhaktapur 349 Vedanta Excel in Mathematics - Book 10

Revision and Practice Time

c) One card is drawn at random from the number cards numbered from 10 to 21. Find
the probability that the card may be prime number or even numbered card.

d) A card is drawn randomly from a pack of cards numbered from 2 to 25, find the
probability of getting a card having the number exactly divisible by 4 or 7.

e) From the number cards numbered from 1 to 20, a card is drawn at random. Find the
probabilities of getting the following numbers.

(i) A prime or an even number (ii) A prime or an odd number

(iii) The number which is divisible by 3 or 4.

4. a) A box contains 30 balls numbered from 1 to 30. If a ball is drawn randomly, what
is the probability that it will be a factor of 12 or 18?

b) Find the probability that a number chosen at random from the integers between 10
to 20 inclusive is a multiple of 5 or a multiple of 2.

c) Find the probability of occurring the letter B or I while drawing a letter card from
the cards of the word "PROBABILITY".

5. a) There are 3 red, 2 blue and 5 white balls in a box. A ball is taken out randomly.
What is the probability of the ball being blue or white?

b) A basket contains 3 red, 4 black and 5 white balls. A ball is drawn randomly from
the basket. Find the probability of not getting a black ball.

6. a) There are 32 students in a class. 8 boys out of 20 wear cap and 8 girls out of 12
wear spectacles. If a student is chosen at random as the monitor of the class, find
the probability that the student is a boy who wears a cap or a girl who doesn't wear
spectacles.

b) There are 24 pupils in a class. 6 boys out of 10 are good in study and 2 girls out
of 14 are from poor economical background. If a student is to be selected for a
scholarship, what is the probability that the student will be a boy who is good in
study or a girl who has poor economical background?

c) A drawer contains 50 bolts and 150 nuts. Half of the bolts and half of the nuts are
rusted. if one item is chosen at random, find the probability that it is rusted or is a
bolt.

7. a) The probability of occurrence of two events A and B are 0.25 and 0.55 respectively.
If the probability of their simultaneous occurrence is 0.15, find the probability of
the occurrence of A or B.

b) The probability of occurrence of two events X and Y are 0.2 and 0.5 respectively. If
the probability of their simultaneous occurrence is 0.15, find the probability that
neither X nor Y occurs.

c) The probability of solving a mathematical problem by two students A and B are 13
and 14 respectively. If the problem is given to the both students, find the probability

of solving.

8. a) A person is known to hit the target 3 out of 4, where as another person is known to
hit it in 2 out of 3 shots. Find the probability of the target being hit at all when they
both try.

b) A bag contains 4 red and 2 blue balls and another bag contains 3 red and 5 blue
balls. If one ball is drawn from each bag, find the probability that

Vedanta Excel in Mathematics - Book 10 350 Approved by Curriculum Development Centre, Sanothimi, Bhaktapur

Revision and Practice Time

(i) one is red and the other blue (ii) both of them are red

(iii) both of them are of the same colour (iv) both of them are of the different colours

9. a) A bag contains 2 green, 4 white and 3 red balls. If two balls are drawn one by one
with replacement, what is the probability that none is red?

b) A cubical die is thrown two times, find the probability that the first outcome is 5
and the second is an even number.

c) Find the probability of getting a tail on the coin and 4 on the die when a coin is
tossed and a die is rolled simultaneously.

d) A number card is drawn from a pack of cards numbered from 1 to 30 and at the same
time a card is drawn from the well-shuffled pack of 52 cards. Find the probability
of getting a card with number divisible by 5 and the non-faced card.

10. a) A can solve 90% of the problems given in the exercise of probability and B can
solve 70%. What is the probability that at least one of them will solve a problem
selected at random from the exercise?

b) Out of 10 problems Ram makes 3 mistakes and Hari makes 4 mistakes. Find the
probability that a problem randomly selected can be done by them without any
mistake.

11. a) A bag contains 8 black and 6 white marbles. A marble is drawn at random from the
bag and it is replaced, then a second marble is drawn. By using a tree diagram, find
the probabilities of getting the marbles of (i) both of the same colour and (ii) both
of different colours.

b) From a well-shuffled pack of 52 cards two cards are drawn at random replacing the
first card. By using a tree diagram, find the probability that the first card is faced
card and the second is the non-faced card.

12. a) Two children were born in a family. By drawing a tree diagram, find the probability
of having no son.

b) Three children were born in a family. By drawing a tree diagram, find the probability
of getting at least a son.

c) Three children were born in a family. Find the probability that at least two daughters
were born by drawing a tree diagram.

13. a) There are 5 white balls and 4 black balls in a bag. Two balls are drawn randomly
one after the other. Show the probabilities in a tree diagram and also find the
probability of getting two white balls.

b) There are 1 red, 1 blue and 1 green ball in a bag. One ball is drawn randomly and
not replaced, then another is drawn. Show the probabilities in a tree diagram and
also write the sample space.

c) There are one black, one yellow and one white identical pieces of paper in a box.
One piece of paper is drawn randomly and not replaced, then another piece of
paper is drawn. Find the probability of getting at least a black piece of paper by
drawing a tree diagram.

d) There are 1 red, 2 white and 3 black balls of the same shape and size in a basket.
If two balls are drawn randomly in succession without replacement from the
basket, show the probabilities of all possible outcomes in a tree diagram. Find the
probability of getting both balls black.

Approved by Curriculum Development Centre, Sanothimi, Bhaktapur 351 Vedanta Excel in Mathematics - Book 10

Answers

1. Sets
Exercise : 1.1

1. a) (i) 40 (ii) 18 (iii) 8 (iv) 12 (v) 10 (vi) 48 b) (i) 20 (ii) 15 (iii) 65 (iv) 35
2. a) (i) 42 (ii) 8 (iii) 15 (iv) 17 b) (i) 15 (ii) 5 (iii) 15 (iv) 25

U (i) 75 (ii) 5 (iii) 40 (iv) 30
PQ

c)
40 5 30

d) (i) 80 15 (iv) 15 e) (i) 34 (ii) 7 (iii) 19 (iv) 22
(ii) 65 (iii) 0

3. a) (i) L U (iii) 40 b) (i) U (ii) 1500
40 25 P BS
30% 30% 20%
ii)10
50

c) C 10 (i) 15 (ii) 120 d) (i) A 20% (ii) 39
U U
F
M

120 15 105 21 6 18

4. a) (i) U (ii) 310 (iii) 140 b) (i) U (ii) 700
TC AB
210 310 140 500 1600 200

90 200
U
ME U
CW
c) (i) 18 4 25 (ii) 4 (iii) 22 d) (i) ii) 40%
10% 40% 20%

7 30%

e) (i) U R U
FM f) (i) W (ii) 900 (iii) 180

(ii) 1,200 20% 50% 10%
35% 30% 25%

10% 20%

Vedanta Excel in Mathematics - Book 10 352 Approved by Curriculum Development Centre, Sanothimi, Bhaktapur

Answers

M U M U S U
g) E 500 S i)
E
h) (i) 400

20% 60% 15% (ii) 600 3000 600 1800 45% 25% 25%

j) (i) 5% (ii) 70 600 5%
U
U
MS CA
5. a) (i) 3000 (ii) 1860
25% 25% 50% 32% 33% 30%

b) (i) U (iii) 135 5% U
EM c) (i) 110 (ii) 115 (iii) SN

(ii) 135 46% 10% 44%

20% 60% 10%

10%

6. a) (i) 34 (iii) U b) (i) 400 (iv) U
(ii) 41 TC CO
(ii) 550 (iii) 375 250 150 300
24 10 41

125

U O U U
MS A
S
c) (i) (ii) 70 d) 4, e) (i) 70 (iii) M

20 25 10 60 10 4 6 (ii) 60 20 50 10

15 6 40

7. a) (i) A U (ii) 2000 b) (i) 1176 (iii) X U c) (i) A U
B Y B
U (iii) 22000 (ii) 535 (ii) 635

12000 1000 10000 535 50 591 (iii) 623 325 212 98

2000 24 15

8. a) 36 b) 15 c) 53% d) (i) Rs 3,00,000 (ii) Rs 5,00,000 (iii) Rs 25,50,000 (iv) 40

1. a) A 6 4 12 B U Exercise : 1.2

53 2 b) (i) 88 (ii) 77 (iii) 80 (iv) 175 (v) 25 (vi) 5 (vii) 38
(viii) 32 (ix) 40 (x) 30 (xi) 20 (xii) 25 (xiii) 25 (xiv) 15

10 8 (xv) 20 c) 5 %
C

UU

2. a) 116, 9 A 34 7 33 B b) (i) 18 (ii) 3 (iii) 15 (iv) 59 P 17 10 20 Q
3 18 8
45 3

30 15
C R 59

Approved by Curriculum Development Centre, Sanothimi, Bhaktapur 353 Vedanta Excel in Mathematics - Book 10

Answers

U U U

3. a) 82 T 19 13 15 C b) 65 E 20 20 15 M c) (i) M 10% 15% S (ii) 5%
1510 30 15%
11 7 5
5 5%
12 N 65 15% 20%
M
20%
C

UU

4. a) (i) 60 (ii) T 200 140 60 R b) (i) 60 (ii) 15 c (i) E7 58 H (ii) 2 (iii) 41
5060 40 62 3

d) (i) B 12 10 15 250 5. a) (i) 14 (ii) 9 (iii) 10 U b) 9
44 6 S 100 S
F
U C 2 93
4 58
S

(ii) 4 (iii) 62

11 1

FB

2. Tax and Money Exchange

Exercise - 2.1

1. a) R% of Rs x b) y × 100% c) p + R% of p 2. a) (i) Rs 1,017 (ii) Rs 3,051 (iii) Rs 19,665
b) (i) Rs 1,400 x (ii) Rs b) Rs 2,610.30
5,500 (iii) Rs 21,600 3. a) Rs 1,808

4. a) Rs 3,600 b) Rs 9,700, Rs 1,455 c) Rs 3,042 5. a) 14% b) 13% 6. a) Rs 45,878 b) Rs 7,458

7. a) 13% b) 14% 8. a) 30% b) 5% loss 9. a) Rs 16,000 b) Rs 25,000

10. a) Rs 3,04,535 b) Rs 2,51,086 c) Rs 88,592

Exercise - 2.2

1. a) Rs x – Rs y b) Rs a – Rs b c) discount × 100% d) M.P. – S.P. × 100%
M.P. M.P.

2. a) Rs. 891 b) 15% c) Rs 1,850 d) Rs 1,356 e) 15% f) Rs 1,700

3. a) Rs 774 b) Rs 1,640 c) Rs 3,420 d) 11 1 % e) Rs 1,406 f) Rs 1,356
g) Rs 2,560 h) Rs 1,460 4. a) (i) Rs 1,260 9

(ii) Rs 11,340 (iii) Rs 12,814.20 b) (i) Rs 3,200

(ii) Rs 3,616 5. a) Rs 4,968 b) Rs 2,983.20 6. a) Rs 1,250 b) Rs 1,500 c) Rs 2,750

d) 8% e) 12% f) Rs 6,160 7. a) Rs 7,593.60 b) Rs 3,767.40 c) 11.11% d) 15%

8. a) 18.75% b) 10.5% c) Rs 4,875, Rs 3,750 d) Rs 600, Rs 780 e) 4% f) 20% , 14 2 %
g) Rs 50 9. a) Rs 100 d) Rs 1,500 7
b) Rs 1,000 c) Rs 1,050, Rs 1,200

10. a) Rs 10,000 b) Rs 14,000 c) 20% d) Rs 2,700 e) Rs 1,615.46

11. a) 25% b) 20% 12. a) 20% b) 40% 13. a) Rs 225 b) Rs 300 c) Rs 1,875, Rs 1,892. 25

d) Rs 15,000 14. a) 6% b) 5% c) 7.5% 15. a) 4% b) 3% c) 2.78%

16. a) 25% b) 5% c) Rs 7,500 d) 10.33% profit

Exercise - 2.3

1. a) NRs 28,080 b) NRs 1,13,355 c) NRs 94,689 d) NRs 98,820 e) NRs 90,576

f) NRs 4,500 g) NRs 61,500 h) NRs 1,00,860

2. a) INR ( ) 1,12,500 b) USD ($) 1,572.05 c) GBP (£) 1,197.60 d) RM 6,428.57

3. a) (i) GBP (£) 4,000 (ii) CAD ($) 6,700 (iii) EUR ( )4,500 (iv) AUD ($) 6,500

b) (i) USD ($) 3,750 (ii) CAD ($) 5,010 (iii) EUR ( ) 3,360 (iv) AUD ($) 4,860

c) (i) USD ($) 2,200 (ii) GBP (£) 1,800 (iii) CAD ($) 2,960 (iv) AUD ($) 2,880

d) (i) USD ($) 3,000 (ii) GBP (£) 2,400 (iii) EUR ( ) 2,680 (iv) AUD ($) 3,880

e) (i) USD ($) 4,560 (ii) GBP (£) 3,720 (iii) EUR ( ) 4,140 (iv) CAD ($) 6,180

Vedanta Excel in Mathematics - Book 10 354 Approved by Curriculum Development Centre, Sanothimi, Bhaktapur

Answers

4. a) NPR 92,625 b) (i) NPR 1,40,070 (ii) NPR 5,60,280 c) (i) NPR 96,900
(ii) NPR 1,700 (iii) NPR 1,275
d) NPR 4,64,870 e) Gain NPR 6,400 f) Loss Rs 55,000
5. a) Nepal b) London
c) NPR 77,000 7. a) $ 520 6. a) NPR 7,51,450 b) 38.27% profit
d) $ 130.09 e) $ 64.04 b) £ 60 c) 13,800 Yen
f) QAR 1,653.44 g) $ 24.78

3. Compound Interest

Exercise - 3.1

R T 1 + R T 1 1 + R 2T
100 100 200
1. a) (i) CA = P 1 + (ii) CI = P – (iii) CA = P

1 + R 2T –1 R T MR
200 100 1200
(iv) CI = P b) CA = P 1 + . 1 +

c) CI = P 1 + R T. 1 + MR –1 d) CA = P 1+ R1 1+ R2 1+ R3
100 1200 100 100 100

2. a) Rs 408 b) Rs 4,965

3. a) Rs 100, Rs 100 b) (i) Rs 2,646 (ii) Rs 3,510 c) (i) Rs 1,261 (ii) Rs 1,623

d) (i) Rs 5,202 (ii) Rs 18,522 e) (i) Rs 204 (ii) Rs 2,522

4. a) Rs 24 b) Rs 1,550 c) Rs 61 d) Rs 275.40 e) Rs 17.30 f) Rs 42 g) Rs 24,451.88

5. a) Rs 10,692 b) Rs 16,844 c) Rs 19,091 6. a) Rs 486 b) Rs 6,305

7. a) Rs 12,000 b) Rs 30,000 c) Rs 32,000 d) Rs 24,000 e) 25,000 f) 5% p.a., Rs 7,200

8. a) 2 years b) 3 years c) 3 years 8. a) 4% p.a. b) 10% p.a.

10. a) 5%p.a, Rs 16,000 b) 10% p.a., Rs 5,000 c) 12% p.a., Rs 1,25,000

11. a) 10% p.a., Rs 4,000 b) 10% p.a., Rs 12,000 c) 10% p.a., Rs 4,500 d) 7% p.a., Rs 5,000

12. a) Rs 3,000, Rs 7,000 b) Rs 5,000, Rs 4,000 c) In account Y because it gives more interest. d) 12.75%
e) 2.44% less interest f) Rs 19,152.80

4. Population Growth and Compound Depreciation

Exercise - 4.1

1. a) P 1 + R T b) P 1+ R T– 1 c) P 1+ R1 1+ R2 1+ R3
100 100 100 100 100

2. a) 34,020 b) 10% p.a. c) 2.1 % p.a. d) 32,000 e) 1,56,250 f) 35,937
3. a) 36,300 b) 3,70,440 c) 18,522 d) 10% p.a.
4. a) 2 years b) 2 years c) 5% p.a. d) 10,000 e) 1,14,444
5. a) 3,95,808 b) 24,000 c) 20,000 b) 7,96,875
6. a) 1,94,922 b) 27,360 7. a) 8,505 d) Rs 5,12,000
8. a) 23.15 cm b) 2 × 102 c) Rs 21,296

Exercise - 4.2

R T 1 – 1 – R T R1 1– R2 1– R3
100 100 100 100 100
1. P1 – b) P c) P 1–

2. a) Rs 4,18,500 b) Rs 15,60,000 c) 6% p.a.

3. a) Rs 49,572 b) Rs 82,308 c) Rs 1,31,220 d) Profit Rs 780

4. a) Rs 90,000 b) Rs 18,00,000 c) Rs 1,84,000 d) 240 shares

5. a) Rs 37,044 b) Rs 6,82,920 6. a) 2 years b) 2 years c) 3 years d) 2 years
8. a) Rs 31,464 b) Rs 5,12,244
7. a) 5% p.a. b) 10% p.a. c) 20% p.a. d) 12% p.a.

Approved by Curriculum Development Centre, Sanothimi, Bhaktapur 355 Vedanta Excel in Mathematics - Book 10

Answers

5. Mensuration (I): Plane Surface
Exercise - 5.1

1. a) 1 pq cm2 b) 1 xy cm2 c) 3 k2 cm2 d) 1 n 4m2 – n2 cm2
2 2 4 4

e) 1 (x + y + z) (x + y – z) (x + z – y) (y + z – x) cm2
4
2. a) (i) 40 cm2 (ii) 24 cm2 (iii) 84 cm2 b) 48 cm, 96 cm2 c) 36 3 cm2 d) 8 2 cm2

e) 10 cm f) 4 3 cm2 g) 26 cm 3. Show to your teacher. 4. a) 168 cm2
b) 250.29 cm2 c) 222 cm2 d) 2.07 cm2
e) 194.87 cm2 f) 1,008 cm2 5. a) (i) 222 cm2

(ii) 12 cm, 13 cm b) (i) 138 cm2 (ii) 15 cm, 13 cm c) 1.36 hectare 6. a) 108 m2 b) 10 cm

c) 120 m2 d) 216 m2 7. a) 336 cm2 b) 26 cm, 28 cm c) 4 m, 6 m d) 6 m, 8m, 10 m

8. a) Rs 2,016 b) Rs 3,024 c) Rs 27,74,100 d) Rs 23,520 9. a) 336 m2

6. Mensuration (II): Cylinder and Sphere

Exercise - 6.1
(bbdi)))ii3(()ii,))032l8S4(S0xS 3p+c2m22),m32,388((gii)iic))(mil43)(2SSS,+p(1330x2,2)7+8+0yScc2))mm((i32i)i2)(iSi23ibS)((A12x3+S–l
1. a) (i) 2Sxy (ii) 2Sx(x + y) (iii) Sx2y a)
m3
(ii) 2S(A + a) (b + A – a) (iii) Sb(A + a) (A – a) y3)

2. e) (34i)S6(6x03 – y3) f) (i) 2Sx2 (ii) 3Sx2
a) cm2 (ii) 968 cm2 (iii) 2,310 cm3

3. a) (i) 2,640 cm2 (ii) 3,872 cm2 (iii)18,480 cm3 b) 1,188 cm2 c) 14 cm d) 7 cm e) 7 cm

4. a) 5 cm b) 20 cm c) 50 cm d) 12 m e) 14 cm f) 90 cm

g) 7 cm 5. a) 156 m2 b) 77 cm2 6. a) 5,544 cm2 , 38,808 cm3 b) 3,850 cm2, 22,458.3 cm3

c) (i) 693 cm2 (ii) 1,039.5 cm2 (iii) 2425.5 cm3 d) S cm3 e) 462 cm2 f) 486 S cm3
7. a) 924 cm2 b) 8,316 cm2 8. a) 3 cm 12 c) 21 cm

b) 7 cm

9. a) (i) 5,280 cm2 (ii) 8,052 cm2 (iii) 55,440 cm3 b) (i) 2,552 cm2 (ii) 9,240 cm3

c) 2,013 cm2, 6,930 cm3 d) 880 cm2 e) 8,624 cm2

10. a) 2,156 cm3, b) 179.67 cm3 c) 4 times 11. a) 1,320 cm3, 4,620 cm3 b) 3,080 cm3

12. a) 1,320 cm3 b) 352 cm3 13. a) 25 cm b) 5,600 14. a) 1.08 cm b) 5 m

15. a) 38,808 cm3 b) 5,544 cm2 16. a) (i) 2,772 cm2 (ii) 4,158 cm2 (iii) 19,404 cm3

b) (i) 1,232 cm2, (ii) 5,749.33 cm3 c) 308 cm2, 462 cm2 17. a) 616 cm2 b) 462 cm2

18. a) 3S cm2 b) 1 19. a) 18 cm b) 144 cm c) 2 cm d) 5 20. a) 6.3 mm b) 16
27
21. a) (i) 3,333 cm2 (ii) 3,679.5 cm2 (iii) 16,285.5 cm3 b) (i) 4,752 cm2 (ii) 5,368 cm2 (iii) 30,389.33 cm3

c) (i) 572 cm2 (ii) 726 cm2, (iii) 1,642.67 cm3 d) (i) 749.76 cm2 (ii) 749.76 cm2 (iii) 1,419.26 cm3
22. a) 7 cm b) 26 cm 23. a) Rs 26,136 b) Rs 2,900.48, Rs 739.20 c) Rs 1,848 d) Rs 14,619.73 e) Rs 13,147.20

7. Mensuration (III): Prism and Pyramid

Exercise - 7.1

1. a) (i) s(s – x ) (s – y ) (s – z ) (ii) (x + y + z)l (iii) (x + y + z)l + 2' b) 24 cm2 c ) 126 cm2

d) 270 cm2 e) 20 cm f) 365 cm2 g) 288 cm2 h) 410 cm3 i) 180 cm3 (j) 8 cm k) 20 cm

2. a) 6 cm2, 240 cm2, 252 cm2, 120 cm3 b) 40 cm2, 434.1 cm2, 514.1 cm2, 600 cm3

c) 15.6 cm2, 311.8 cm2, 343 cm2, 270.2 cm3 d) 8 5 cm2, 400 5 cm2 416 5 cm2, 800 cm3
e) 54 cm2, 1,260 cm2, 1,368 cm2, 1,890 cm3 f) 30 cm2, 450 cm2, 510 cm2, 450 cm3

3. a) (i) 24 cm2 (ii) 360 cm2 (iii) 408 cm2 (iv) 360 cm3

b) (i) 2,160 cm2 (ii) 2,412 cm2 c) (i) 682.8 cm2 (ii) 782.8 cm2

Exercise - 7.2 3 1
3 2 3
1. a) 2xy sq. units, (x2 + 2xy) sq. units b) 2 pq sq. units, ( 43 p2 + pq) sq. units c) m2n cu. units
d) 132 k2h cu. units 2. a) 146. 5 cm2 b) 188.8 cm2
c) 504 cm2 d) 171.7 cm2

3. a) 486 m3 b) 384 cm3 c) 300 cm3 d) 1,385.64 cm3 e) 138.56 cm3

4. a) 360 cm2, 400 cm3 b) 242.35 cm2, 166.28 cm3 c) 660 cm2, 600 cm3

5. a) 96 cm2, 48 cm3 b) 384 cm2, 384 cm3 c) 576 cm2, 512 cm3 d) 360 cm2, 400 cm3
h) 756 cm2, 853.2 cm3
e) 800 cm2, 1,280 cm3 f) 1,296 cm2, 1,728 cm3 g) 868 cm2, 1,500.05 cm3

Vedanta Excel in Mathematics - Book 10 356 Approved by Curriculum Development Centre, Sanothimi, Bhaktapur

Answers

6. a) 288 cm3 b) 1,584 cm3 c) 756 cm3 d) 4,608 cm3 e) 148 cm3 f) 36 cm3
c) 760 cm2 d) 673.3 cm2
7. a) 336 cm2 b) 864 cm2 c) 48 cm3 d) 400 cm3
c) 264 cm3 d) 1,824 cm3
8. a) 700 cm2 b) 384 cm2

9. a) 5 cm b) 1,584 cm2 10. a) Rs 4,920 b) Rs 21,600

Exercise - 7.3
1
1. a) Sab sq. units b) Sx(x + y) sq. units c) 3 Sx2y cu. units
2. a) 330 cm2
b) 1,496 cm2 c)1,078 cm3 3. a) 37.71 cm3 b) 550 cm2 c) 2,816 cm2

4. a) 10 cm b) 7 cm c) 5 cm 5. a) (i) 264 cm2 (ii) 47.14 cm2 (iii) 188.57 cm2

b) (i) 620.18 cm2 (ii) 678.86 cm2 (iii) 704 cm2 c) (i) 3,080 cm3 (ii) 1,018.29 cm3

(iii) 314.29 cm3 d) 1,540 cm3 e) 1,496 cm2

6. a) 550 cm2, 704 cm2, 1,232 cm3 b) 2,200 cm2, 2,816 cm2, 9,856 cm3

c) 188.57 cm2, 301.71 cm2, 301.71 cm3 d) 2,310 cm2 , 3,696 cm2, 12,936 cm3

7. a) 1,056 cm3 b) 5,852 cm3 c) 1,659.42 cm3 d) 1,950.67 cm3 e) 754.28 cm3

f) 12,936 cm3 g) 2,200 cm3 h) 2,112 cm3 i) 2,310 cm3

8. a) 5,104 cm2 b) 1,056 cm2 c) 3,318.86 cm2 d) 858 cm2 e) 214.5 cm2

f) 2,851.2 cm2 9. a) 12,936 cm3 b) 1,232 cm3 c) (i) 2,816 cm2 (ii) 9,856 cm3

10. a) (i) 550 cm2 (ii) 704 cm2 b) 2,200 cm2, 2,816 cm2 c) 10 m

11. a) 2,970 m2 , Rs 3,71,250 b) 208.56 m2 12. a) 9 cm b) 7 cm 13. a) Rs 18,975 b) Rs 30,140

Exercise - 7.4

1. Show to your teacher 2. Show to your teacher

3. a) (i) 1,500 l (ii) 2,700 l (iii) 4,800 l (iv) 10,000 l (v) 15,500 l

b) (i) 2 m3 (ii) 3.5 m3 (iii) 7.4 m3 (iv) 12.8 m3 (v) 20 m3

4. a) Rs 3,150 b) Rs 3,000 c) Rs 30,600 5. a) 10,000 l b) 6,000 l c) 9,240 l d) 11,000 l

6. a) Rs 16,500 b) Rs 52,500 7. a) (i) Rs 7,800 (ii) Rs 27,300 b) Rs 27,170 8. Rs 1,58,625

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

Exercise - 8.1

1. a) 2x (x + 2) b) 2xy (x – 1) c) 3a2b2(2a + 3b) d) 4a2b2(a + b – 2) e) (p – q)

2. a) (a + b) b) a(a – 2) c) (x + 3) d) (x + y) e) 4(x + 5)

f) x(x + 2) g) (a – b – 1) h) (x2 + 2xy + 4y2) i) (p + 2) j) (x2 + 2xy + 2y2)
k) (a2 + a + 1) c) (2x + 3)
l) (4x2 + 2x + 1) 3. a) (a + 2) b) (x – 3)

d) (x – 2) e) (a + 2) f) (m – 1) g) (a – b) h) (x – 4y)

i) x(x + 5) j) (x2 + x + 1) k) (4x2 – 6xy + 9y2) l) (x2 – xy + y2) m) (a + b + c)

n) (3x + 2y + 2z) o) (x – y + 1)

Exercise - 8.2

1. a) 6x2 (x2 – 1) (x + 3) b) 12x3 (x + 2) (x2 – 9) c) 24a2b2(a + b) (a3 – b3) d) (x2 – 4) (x2 – 9)

e) (a – 3) (a – 4) (a – 5) 2. a) 6x2 (x + 2) b) ax (x2 – 1) c) 10x4y4 (2x + y)
d) xy(x2 – y2) e) 2x(4x2 – 1) f) a3 – b3 g) (x + 3) (x2 – 4)

h) 3(x2 – 9) (x2 – 3x + 9) i) a2b2 (a2 – b2) (a2 + ab + b2) j) (x2 – xy + y2) (x3 – y3) k) (a2 + ab + b2) (a3 + b3)
l) 2x(2x – 1) (27x3 + 1)
d) (x4 – y4) (x2 + xy + y2) 3. a) (a2 – 4) (a3 – 8) b) (a – 3)2 (a3 + 27) c) a(a2 – 1) (a2 – 4)

e) 2x2(3x – 2) (2x – 1) (x3 – 8) f) x2 (x + 1) (x + 3) (x3 – 27)

g) a2(a + 1) (a + 2) (a3 – 8) h) a(a – 1) (a4 + a2 + 1) i) (a + b + c) (a + b – c) (b + c – a) (c + a – b)

j) (x4 – y4) (x2 – xy + y2) k) (x + 1) (x + 2) (x + 3) l) 12x (x – 2) (x + 3) (x – 4)

9. Simplification of Rational Expressions

Exercise - 9.1
1 – x
1. a) a2 – a + 2 b) 8p c) 1 + x d) 20
a–1 p2 – 4 (x + 4) (x + 6)

Approved by Curriculum Development Centre, Sanothimi, Bhaktapur 357 Vedanta Excel in Mathematics - Book 10

Answers

e) 2a3 f) 1 – 5x g) a + 4 h) x2 + y2
a2 – b2 (x – 1) (x2 – 1) a2 – 1 (x + y) (x2 – y2)

i) 1 j) 1 2. a) 0 b) 9
(x – y) (y – z) (a – b) (a – c) (x + 2) (x – 3) (x – 4)

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

c) 3x – 7 d) 5 4. a) 2x 4
(x – 2) (x – 3) (a – 3) (a – 4) (a – 5) x+2 b) a + b

c) 8xy3 d) 2ab e) 2 f) 8x2y2
x4 – y4 a2 – b2 x2 – 1 x4 – y4

5. a) – 4x b) 2(x – 3) c) 2(x – y) d) 4
(x2 – 3x + x2 – xy + y2 1 + a2 + a4
(1 + x2 + x4) 9)

e) 2(2a – b) f) 2(3x – 1) 6. a) 1 b) 1
4a2 – 2ab + b2 9x2 – 3x + 1

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

8. a) 32x b) 16a c) 6a2x d) 2(a2 + 1)
(x2 – 9) (x2 – 25) (a2 – 1) (a2 – 9) (x2 – a2) (4x2 – a2)

e) (x2 + 1) f) 6 9. a) 2x b) 2a
a (a2 – 1) (a + 2) x4 – 1 a4 – 1

c) 4x d) 2x2 10. a) 8 b) 8 1 c) 8x d) 8a7b
x4 – 1 1 – a8 a8 – x8 – 1 a8 – b8

e) 8x7 f) 4b2 g) 4a h) 16x i) 8x j) 4a2
x8 – y8 a2 – b2 1 + 4a2 x8 – 1 1 – x2 1 – a4

k) 16x3y7 l) 1 m) 8x7 n) 8a7b
x8 – y8 1 – a8 x8 – 1 a8 – b8

10. Indices

Exercise - 10.1

1. a) 1 b) 8 c) 2 d) 2 e) 16 f) 2
5 3 3 25 3
2. a) 1
k) 4 b) 4 c) 1 d) 5 e) 3 f) 1 g) 5 h) 1 i) 2 j) 1
3

l) 1 m) 1 n) 1 o) 27

3. a) 9 b) a c) 9 d) 8 e) a2
16a2x2 25a2b2 27a3b3

f) 3 5 g) 3xy2 h) 6x2y4z i) 1 j) 1
2 (x + y)2 (a + b)2
b2

4. a) 1 b) 1 c) 1 d) 1 e) 1 f) 1 g) 1 h) a2b2c2
xyz
h) 1 i) 1
5. a) 1 b) 1 c) 1 d) 1 e) 1 f) 1 g) 1 b) 1 c) 1 j) 1
8. a) 1 d) 1
k) 1 l) 1 m) 1 n) 1 o) a2(z2 – y2) p) 1 6. a) 1
b) 1
a x+y x 2a a a+b x x+y
b y b y
7. a) b) c) d) x e)
y

Exercise - 10.2 7
2
1. a) 8 b) 3 c) 1 d) 3 e) – 2 f) 2 g) h) 3 i) 3 j) – 2
2

k) –2 l) 4 m) – 3 n) 8 o) 4 p) 0 q) – 3 r) 1
5 3 2

Vedanta Excel in Mathematics - Book 10 358 Approved by Curriculum Development Centre, Sanothimi, Bhaktapur

Answers

2. a) – 2 b) 3 c) 3 d) 5 e) 5 f) 0 3. a) 0, 2 b) 2, 3 c) 1, 2 d) 2, 3
e) 1, 2 f) 1, 2 2 h) 2, – 2 i) – 1, 2 j) 1, 3 k) 0, – 3 l) 1, 2 m) 2, – 2
n) 2, – 2
g) 0, 2
1. a) 8 2
2. a) 30 o) 2, – 2 p) 1, – 1 5. a) 2 years b) 3 years
3. a) 0
b) 10 3 11. Surds
b) 12
b) 0 Exercise - 11.1

c) 3 5 d) 4 3 4 e) – 4 3 7 f) – 2 4 6
e) 5 3 2 f) 4 2
c) 9 3 2 d) 5 e) 0 f) 16 3 3

c) 14 5 d) 3

g) 4 4 5 h) 15 2 + 3 4 4 4. a) 1 b) 2 c) 2 d) 5 + 2 6

e) 2(4 – 15 ) f) 2(x – x2 – a2 ) g) 9 – 6 h) 6 + 10

5. a) a + b b) x + 3 c) 3 5 – x d) x – 2 e) 3x – 4 f) 7 + 5x
e) 4
6. a) 1 b) 1 c) 2 d) 1 f) 11
2 12 3 4 3 13 3 2

Exercise - 11.2

1. a) 2 – 1 b) – 3 – 2 c) 5 + 2 d) 2 (2 3+ 2)
5 15 – 5)

e) 5 (3 7 –2 3) f) 2 (2 3– 6) g) 1 (6 + 6) h) 4 (2
51 3 2 7

2. a) 3 + 2 2 b) 2 – 3 c) 5 – 2 6 d) 4 + 15 e) 2 6 – 5

f) 6 + 15 g) a – a2 – b2 h) x – x2 – 1 i) a – a2 – 4
k) 3+ b 2
6+
j) a + a2 – 25 15 l) 2 + 2 – 6
5 6 2

3. a) 14 5 b) 13 3 c) 11 5 d) 25 3 e) 17 2 f) –7
5 3 10 12 10 42

4. a) 4 b) 10 c) 10 d) 4 ax e) 4x x2 – 1 f) 2(2a2 – 1)
x–a

5. a) 47 5 – 35 b) 991 2 c) 1 ( 30 – 2 5) d) 0 e) 2 30 – 7 f) 0
2 80 2

6. a) 2x b) 2a c) 4x d) x2
b 3

Exercise - 11.3

1. a) 24 b) 6 c) 3 d) 3 e) 9 f) 22 g) 41 h) 8 i) 5 j) 4
l) –5 2. a) 16 e) 25 f) 2 g) 6 h) 2 i) 2
k) – 3 b) 16 c) 16 b) 1 c) 1 d) 4 g) 49 h) 20 i) 28
a) 4 2 j) 4
3. b) 8 c) 7 d) 4 e) 1 f) 25 g) 1, 5 h) 0 i) 3 d) 5
5 5
b) 64 c) 1 6. a) 81 b) 36 c) 100
4. a) 1 d) 2 e) 5 f) 1
f) 7 7. a) 14 e) 15 f) 29
5. a) 4 d) 49 e) 36 f) 16
9 25
5
e) 12 b) 6 c) 2 d) 5

Approved by Curriculum Development Centre, Sanothimi, Bhaktapur 359 Vedanta Excel in Mathematics - Book 10

Answers

12. Equations
Exercise - 12.1

1. a) x=3 b) x = 4 c) x = 2 d) x = 31 e) x = 55
y=1 y=2 y=1 y = 11 y = 25

f) x = 70 g) x = 3 h) x = 4 i) x=8
y = 30 y=2 y=6 y=4
d) 18,6
2. a) 35, 25 b) 20, 10 c) 33, 26 e) 9, 5
i) 36 years, 12 years j) 35 m, 25 m
f) Rs 325, Rs 175 g) 30 years, 8 years h) 42 years, 7 years

3. a) Rs 75, Rs 45 b) 3, 2 c) 5, 6

4. a) 7 b) 4 c) 3 d) Rs 25,000, Rs 15,000 e) Rs 8,000, Rs 6,000
9 9 8

5. a) 40 years, 15 years b) 32 years, 12 years c) 42 years, 12 years.

d) 14 years, 10 years e) 47 years, 7 years f) 45 years, 13 years

g) 29 years, 5 years h) 58 years, 25 years i) 29 years, 5 years.

j) 45 years, 15 years k) 34 years, 6 years r) 50 years, 30 years

m) 15 years, 21 years n) 19 years, 15 years.

6. a) 97 b) 46 c) 63 d) 39 e) 27 f) 84

g) 38 h) 59 i) 76 j) 72 k) 36 l) 45

7. a) Rs 30, Rs 15 per km b) Rs 25, Rs 5 per day 8. a) 5, 7 b) Rs 60, Rs 90 9. a) 12 : 00

b) 65 km/hr, 60 km/hr 10. a) 17 m, 9 m b) 180

5 Exercise - 12.2
+–6
1. a) +– 3, b) +– 5 7 c) +– d) 1, 2 e) 2, 3 f) – 3, – 6 g) – 2, 4
h) – 4, 7 5 2. a) d) 9 e) 3, 8
i) – 3, 4 b) +– 8 c) +– 5 f) 15, 6 g) 24 f) 2
3. a) 4, 6 d) 14, 16 e) 11, 13
b) 14, 4 c) 8, 5

h) 4, 6 i) 8 4. a) 63 or 36 b) 54 c) 38 d) 92

e) 24 f) 24 g) 36 h) 28 i) 17

5. a) 17 years, 12 years b) 9 years, 7 years c) 28 years, 18 years d) 16 years, 9 years

e) 17 years, 13 years f) 9 years, 4 years g) 12 years, 6 years h) 10 years, 6 years

i) 15 years, 10 years. j) 29 years, 5 years 6. a) 2 b) 6 7. a) 9 m, 7 m

b) 56 m c) 3 m d) 9 m, 7 m e) 19 m, 13 m f) 8 m, 5 m

8. a) 6 cm, 8 cm, 10 cm b) 3 cm, 4 cm c) 6 cm, 8 cm d) 15 cm, 20 cm, 25 cm

9. a) Longer side is to be decreased by 20% to make it a square b) 20 m

10. a) 20 m, Rs 40 per meter b) 33 31% 11. a) 20 b) 8

13. Geometry: Area of Triangles and Quadrilaterals

Exercise - 13.1

1. a) 112.5 cm2 b) 82.5 cm2 c) 44.4 cm2

2. a) 50 cm2 b) 20 cm2 c) 22.5cm2 d) 8 cm2 e) 9 cm2 f) 25 cm2
o) 6 cm
g) 25 cm2 h) 40 cm2 i) 20 cm2 j) 40 cm2 k) 60 cm2

l) (i) 276 cm2 (ii) 288 cm2 (iii) 55 cm2 m) 64 cm2 n) 8 cm

14. Geometry: Construction

Show to your teacher. 15. Geometry: Circle
Exercise - 15.1

1. a) 75°, 75° b) 140° c) 110° d) 62° e) 55° f) 60° g) 50° h) 140° i) 75°
n) 18°, 42°
j) 30° k) 78°, 39° l) 52°, 104° m) 40° o) 35°, 55° p) 25°, 25°

Vedanta Excel in Mathematics - Book 10 360 Approved by Curriculum Development Centre, Sanothimi, Bhaktapur

Answers

2. a) 50° b) 110° c) 122° d) 120° 3. a) 158°, 101° b) 60° c) 110° d) 108°
e) 48° f) 90° g) 60° h) 70° l) 85°, 35°
(ii) 80° i) 38°, 49° j) 110° k) 36°
(iii) 140°
4. a) 75°, 30° b) (i) 140 c) 12 cm c) 65° d) 20°
c) 35°
k) 30°, 60° Exercise - 15.2
s) 64°
1. a) 5 cm b) 8 cm c) 145° d) 2 cm e) 8 cm f) 24 cm

2. a) 40°, 30 b) 105° d) 15 e) 30° f) 30° g) 80° h) 40°, 55°, 15°
l) 29°, 61 m) 33° n) 58° o) 60° p) 111°
i) 80° j) 80°

q) 48°, 48° r) 60° t) 70°

3. a) 65°, 65° b) 30° d) 70° e) 60° f) 60°

16. Trigonometry
Exercise - 16.1

1. a) 20 m, 20 2 m b) 40 m, 80 m c) 75 m, 75 3 m d) 80 m, 160 m

e) 40 3 m f) 62 m g) 120 m h) 64.64 m

2. a) 60° b) 30° c) 45° d) 60° 3. a) 60 m b) 36 3 m c) 40 3 m
h) (i) 6.5 m (ii) 3.75m
d) 20 3 m e) 12.5 m f) 15 3 m g) 150 2 m

4. a) 10 3 m b) 60 3 m c) 20.2m 5. a) 8 3 m b) 174.8m c) 2.35m d) 53 m
e) 45 3 m f) 22.68 m 6. a) 17.6m
b) 95m 7. a) 71.7 m b) 23.09 m c) 80.2 m d) 12 m

8. a) 30° b) 30° c) 45° 9. a) 21.73m b) 6.5m c) 12m d) 10m

10. a) 109.28m b) 400m Exercise - 16.2

1. a) 24cm2 b) 90cm2 c) 25 3 cm2 d) 7cm2 e) 60 2 cm2 f)16 3 cm2

g) 30cm2 h) 24cm2 2. a) 24 3 cm2 b) 12cm2 c) 40 3 cm2 d) 40cm2
g) 80 3 cm2 h) 80cm2 3. a) 405cm2
e) 600 3 cm2 f) 48 3 cm2

b) 45.25cm2 c) 7.5cm2 d) 40.6cm2 4. a) 60 3 cm2 b) 35.7 3 cm2

5. a) 60° b) 70° c) 60° 6. a) 9cm b) 8cm c) 8cm

7. a) 30° b) 45° c) 120° d) 60° 8. a) 6cm b) 10cm c) 12cm d) 5 2 cm

9. a) 48 3 cm2 b) 68.8 cm2 c) 80 cm2 d) 64cm2 e) 390 3 cm2 f) 108 cm2

10. a) 45° b) 6 cm c) 8 cm d) 10 cm

17. Statistics

Exercise - 17.1

1. a) 30 b) 40 2. a) 13 b) 20 3. a) 250 b) 480 4. a) 10 b) 12 c) 5
d) 120 e) 10 5. a) 24 e) 46.5
b) 43 c) 75 d) 50.64 6. a) 28.6 b) 45

7. a) 10 b) 20 c) 12 Exercise - 17.2

1. a) 26 b) 42.5 c) 41.67 d) 40 2. a) (30 – 40) b) (25 – 35)
c) (65 – 80) d) (60 – 70)
b) 34 3. a) 35 b) 70 c) 93.6 d) 26
4. a) 33.5 e) 32.5
d) 294.4 5. a) 10 b) 20 6. a) 28.5 b) 31 c) 67.5
b) 36
8. a) Rs 14.17 7. a) 47.92 b) 46.25 c) 55 d) 53.75 e) 70

c) 45

Exercise - 17.3

1. a) (30 – 40) b) (20 – 30) c) (20 – 30) 2. a) (20 – 40) b) (10 – 15) c) (5 – 10)

3. a) (75 – 90) b) (60 – 80) c) (40 – 50) 4. a) (20 – 30), 20 b) (15 – 20), 17.5

Approved by Curriculum Development Centre, Sanothimi, Bhaktapur 361 Vedanta Excel in Mathematics - Book 10

Answers

18. Probability

Exercise - 18.1

2. a) P(A‰ B) = P(A) + P(B) b) P(X ‰ Y ‰ Z) = P (X) + P(Y) + P(Z) c) P(A ‰ B) = P(A) + P(B) – P(A ˆ B)

3. a) 5 b) 2 c) 3 d) 0.5 e) (i) 4 (ii) 1 4. a) 1 b) 7 c) 3 d) 0.45
6 3 13 5 5 2 25 8
11 1 1 3 12
5. a) 2 b) 1 c) 2 d) 13 e) 13 f) 3 g) 2 h) 26 i) 11 j) 13
13 13 13 4 13

6. a) (i) 1 (ii) 1 (iii) 2 (iv) 2 (v) 2 b) 13 7. a) (i) 1 (ii) 3 (iii) 7 (iv) 8
3 2 3 3 3 36 3 10 30 15

b) 11 c) 16 8. a) (i) 2 (ii) 5 (iii) 2 b) 7 9. a) 8 b) 4 c) 7 d) 4
34 21 3 9 9 10 13 13 13 13
1
10. a) (i) 2 (ii) 1 (iii) 1 (iv) 4 b) 6 c) 7 d) 3 e) 4
5 3 2 5 11 11 9

Exercise - 18.2

1. a) P(A ˆ B) = P(A) × P(B) b) P(X ˆ Y ˆ Z) = P (X) × P(Y) × P(Z) c) Independent 2. a (i) 1
4

ii) 1 iii) 3 iv) 3 b) 1 c) 3 d) 10 3. a) 1 b) 1 (ii) 144
4 4 4 12 65 13 169 676 169

(iii) 1 (iv) 12 (v) 1 4. a) (i) 9 (ii) 4 (iii) 6 (iv) 4 (v) 9 b) (i) 35 (ii) 1
169 169 2 25 25 25 25 25 256 16

(iii) 45 (iv) 5 (v) 121 c) 14 5. a) 0.98 b) 3
128 64 256 27 5

Exercise - 18.3 1 P(H1H2)= 1 × 1 = 1
2 2 2 4
P(H2) =

P(H1) = 12 H P(H1T2)= 1 × 1 = 1
2 2 4
1. a) T P(T ) = 1
2 2
H
T P(H H P(H 2) = 1 P(T1H2)= 1 × 1 = 1
1 2 2 2 4
) 1
= 2
T
P(T 1 1 1
2 ) = 1 P (T1T2) = 2 × 2 = 4
2

Possible out comes = {H1H2, H1T2, T1H2, T1T2}

P(H ) = 12 P(H1H2H3) = 1
8
H 3

=12 T P(T3) = 1 P(H1H2T3) = 1
2 8
P(H ) H
T
2

H P(H3) = 1 P(H1T2H3) = 1
2 8
=12 T
P(T ) = 1
b) ) 2 2 1
H 8
T P(H 1 P(T P(H1T2T3) =
3
1 ) = 21
(i) 8
1 P(T1H2H3) = 1
1 P(H 3) = 2 8
(iv) 2 H
P(T ) =21 H P(H2) = 1 T P(T3) = 1 P(T1H2T3) = 1
1 T 2 2 8
H
3 1 P(T ) =21 T P(H3) = 1 1
(ii) 8 (iii) 2 2 2 8

3 P(T1T2H3) =
v) 8
P(T ) = 21 P(T1T2T3) = 1
3 8

Vedanta Excel in Mathematics - Book 10 362 Approved by Curriculum Development Centre, Sanothimi, Bhaktapur

Answers

P(R2) = 3 P(R1R2) = 9
8 64

3 3R 15
8 64
P(R ) = 5W P(W ) = 5 P(R1W2) =
2 8
1

c) 3R = 3 15
5W 8 64
P(W P(R 2) P(W1R2) =
1 ) = 5 3R
8
5W
P(W 25
2 ) = 5 P (W1W2) = 64
8
P(R1W2) + P(W1R2) = 15
32

P(B2) = 160 P(B1B2) = 9
6B 25
d) 4W P(W2) = 140
P(B1) = 160
P(B1W2) = 6
25

6B

4W P(W ) 6B P(B2) = 160 6
1 4W 25
= 104 P(W1B2) =

P(W ) = 140 P (W1W2) = 4
2 25

(i) 13 (ii) 12
25 25

P(K2) = 542 P(K1K2) = 1
169

e) 542 4K P(K 12
2 169
P(K ) = 48K ) = 5428 P(K1K2) =

1

4K

48K P(K 4K P(K2) = 542 P(K1K2) = 12
1 169
) = 5428

1 48K P(K
169 2
(i) ) = 5428 P (K1K2) = 144
169

f) 1 P(S1S2) = 1
2 4
P(S2) =

1 S 1
P(S 1) = 2 4
D P(D ) = 1 P(S1D2) =
2 2

S

D P(D ) 1 P(S 2) = 1 1
1 2 2 4
= S P(D1S2) =

D

(i) 3 P(D ) = 1 P (D1D2) = 1
4 2 2 4

Approved by Curriculum Development Centre, Sanothimi, Bhaktapur 363 Vedanta Excel in Mathematics - Book 10

Answers

g) P(S2) = 1 P(S1S2) = 1
2 4

1 S 1
4
P(S ) = 2 D P(D ) = 1 P(S1D2) =
2 2
1

S

D P(D ) 21 P(S 2) = 1 1
1 2 4
= S P(D1S2) =

D

P(D ) = 1 P (D1D2) = 1
2 2 4
1
(i) 4

h) P(S2) = 1 P(S1S2) = 1
2 4

1 S 1
4
P(S ) = 2 D P(D2) = 1 P(S1D2) =
2
1

S

D P(D ) 1 P(S 2) = 1 1
1 2 2 4
= S P(D1S2) =

D

(i) 1 P(D ) = 1 P (D1D2) = 1
4 2 2 4

i) P(S1S2S3) = 1
8
1
) = 2
P(S
S 3
D
=12 P(D3) = 1 P(S1S2D3) = 1
S 2 8
) D
P(S
2

S P(S3) = 1 1
2 8
D P(S1D2S3) = 1
P(D ) = 1 P(S1D2D3) = 8
=12 2 2

P(S ) P(D ) = 21
3
1

S 1 1
P(S 3) = 2 8
D P(D1S2S3) = 1
P(D1S2D3) = 8
P(D ) =21 P(S2) = 1 S P(D3) 1
1 2 D 2

S =

D P(D 1
2 2
) =21 P(S3) = P(D1D2S3)= 1
8
S
D P(D
3
7 ) = 1 1
8 2 8
(i) P(D1D2D3) =

Vedanta Excel in Mathematics - Book 10 364 Approved by Curriculum Development Centre, Sanothimi, Bhaktapur

Answers

P(S1S2S3) = 1
8
12
P(S ) =

S 3
D
j. =12 P(D3) = 1 P(S1S2D3) = 1
S 2 8
) D
P(S
2

S P(S3) = 1 1
2 8
D P(S1D2S3) =
P(D2) = 1 P(S1D2D3) = 1
=12 2 8
) P(D
P(S 3 ) = 21
1

S 1

D P(S ) = 2 P(D1S2S3) = 1
8
P(D S 3
1 D
) =21 P(S2) = 1 P(D3) 1 1
2 2 8
S = P(D1S2D3) = 1
P(D1D2S3) = 8
D P(D 1
2 2
) =21 P(S3) =

(i) 1 (ii) 1 (iii) 7 S P(D
2 8 8 D 3

) = 1 P(D1D2D3) = 1
2 8

2. Show to your teacher.

P(B2) = 172 P(B1B2) = 14
39

3. a) P(B1) = 183 7B 10
39
5W P(W ) = 152 P(B1W2) =
2

8B

5W P(W ) 8B P(B2) = 182 10
1 4B 39
= 135 P(W1B2) =

P(W ) = 142 P (W1W2) = 5
2 38

Sample space {B1B2, B1W2, W1B2, W1W2}

Approved by Curriculum Development Centre, Sanothimi, Bhaktapur 365 Vedanta Excel in Mathematics - Book 10

Answers

b) P(R2) = 2 P(R1R2) = 1
6 7

3 2R 2
P(R 1) = 7 7
4B P(B2) = 4 P(R1B2) =
6
3R

4B P(B ) 74 P(R 2) = 3 2
1 6 7
= 3R P(B1R2) =

3B

P(B ) = 3 P (B1B2) = 2
2 6 7

4. a) (i) 35 (ii) 15 (iii) 35 (iv) 31
132 22 66 66

P(B2) = 161 P(B1B2) = 7
22

172 6B 35
132
P(B ) = 5W P(W ) = 151 P(B1W2) =
2
1

7B

5W P(W ) 7B P(B2) = 171 35
1 4W 132
= 125 P(W1B2) =

P(W ) = 141 P (W1W2) = 5
2 33

b) (i) 2 (ii) 7 (iii) 17 (iv) 1 (v) 14
9 15 45 15 45

2 P(R1 R2) = 1
= 15
9
) 5
P(R P(R2) = 9 P(R1 B2) = 1
2 6

103 2R P(Y ) = 92 P(R1 Y2) = 1
5B2Y 2 15

=

) 39 1
6
P(R ) = P(B1 R2) =
1
2
3R P(B1) = 5 3R P(R
5B 10
2Y 4B 4 P(B1 B2) = 2
2Y P(B2) = 9 9
P(Y = 92
P(Y 2 ) 1
9
) P(B1 Y2) =

1

=210 5B3R P(R2) = 3
1Y 9
P(Y1 R2) = 1
15
P(B
2 ) = 5
9
P(Y
P(Y1 B2) = 1
) 9

2

=19

P(Y1 Y2) = 1
45
5. a) (i) 3 (ii) 7 35
95 38 (iii) 38

b) (i) 1 (ii) 11 (iii) 95 (iv) 1 c) 38
221 221 663 663 85

Vedanta Excel in Mathematics - Book 10 366 Approved by Curriculum Development Centre, Sanothimi, Bhaktapur

Revision and Practice Time

Set

P U U
J EM
30 10 40
1. (i) (ii) 125 (iii) 1625 2. (i) 40 (ii) 70 (iii)
U
1000 125 625 MS
40% 20% 30%
3. 10 250 4. (i) 20% (ii) 60% (iii)
U
CB

30 10 25

10 10%
C VU
M U
275 100 75 6. (i) 24 (ii) 22 (iii) E

5. (i) 175 (ii) 325 (iii)

12 6 18

50 4

7. (i) M U 8. (i) 104 (ii) 76 (iii) U
S (ii) 500 (iii) 75 MS
76 20 104
20% 60% 15%

9. (i) S 5% 10. (i) U (ii) 300 (iii) 120
20% 70% U VC
M 10% 50% 30%

(ii) 2,250 (iii) 1,575

10% 10%

N U M FU
320 T 12. (i) 18 (ii) 38 (iii)
11. (i) 320 (ii) 240

24 18 38

240

13. (i) 300 (ii) 375 (iii) U 14. (i) U 90
FS CF
300 150 225
40 10 30
75

Approved by Curriculum Development Centre, Sanothimi, Bhaktapur 367 Vedanta Excel in Mathematics - Book 10

Answers

N U E U
15. J 16. N

, 150 , 80, 10

110 30 40 30 20 80

10

17. (i) 5 (ii) U 18. (i) 8 (ii) 256 (iii) Q U
WS 24 8 D
12
100 5 30

T CU M 256
19. (i) 75 (ii) 15 (iii) 20. U
S

(i) 30 (ii) 40

45 75 75 30 10 40

21. (i) 24 (ii) 16 (iii) 15 15 U
U 22. (i) 42 (ii) 45 (iii) SM

MS 27 15 18

10 14 16

23. (i) 110 (ii) M U 24. (i) 180 (ii) U
30 S FB
20 50 25% 20% 30%

10 25%

Z U 26. (i) 100 (ii)180 (iii) U
25. G AB

, 15 50 100 130

30 15 5

10 20
A
BU C U
28. (i) 38 (ii)32 (iii) F

27. 100,

21 17 28 18 20 12

29. (i) 34 10
U U
30. (i) 5 (ii) M 20 5 20 S
MS
(ii) 60 (iii) 20 (iv) 50 10 5 15

30 20 4 25
H

6

Vedanta Excel in Mathematics - Book 10 368 Approved by Curriculum Development Centre, Sanothimi, Bhaktapur

U U Answers

31. T 27 15 M1 (i) 5 (ii) 11 32. M 12 35 P (i) 108 (ii) 22 35. 11
11 60
1018 5
17 5 15

10 13 22
M2 C

U U

33. (i) P 15 F (ii) 55 (iii) 30 34. (i) E 5 80 J (ii) 230 (iii) 260
25 15 60
10 5 5 10 1015

15 20 70 K 20
L

Tax and Money Exchange

1. Rs 5,000 2. loss, Rs 42,000 3. loss, Rs 55,000 4. Profit Rs 7,500.31 5. profit 3.54 %

6. Rs 1,500 7. Rs 50 8. Rs 560 9. Rs 70 10. Rs 190

11. Rs 1,500 12. Rs 108 13. Rs 3,000, Rs 2,300 14. 23.07%, 18.34% 15. Rs 3,00,000

16. Rs 3,20,000 17. Rs 8,215.60 18. Rs 3,238.40 19. Rs 2,700 20. Rs 80 21. Rs 8,000, Rs 680

22. Rs 1,092 23. Rs 856, Rs 749 24. Rs 2,300 25. 6.25% 26. Rs 4,000, Rs 3,842

27. 25% 28. Rs 2,500, Rs 2,000 29. Rs 5,250 30. Rs 800 31. Rs 4,000, Rs 3,740

32. 10% 33. 26%, 13% 34. 40% 35. Rs. 300

36. (i) Rs 24,375 (ii) Rs 27,625 (iii) Rs 30,115.80 37. (i) Rs 1,950 (ii) Rs 2,145 (iii) Rs 18,645 38. Rs 975

Compound interest, Population Growth and Depreciation

1. 2.5% 2. Rs 6,620 3. 10%, Rs 1,60,000 4. Rs 2,866.50 5. Rs 12,000 6. Rs 16,000
7. Rs 113.08 8. Rs 10,000 9. Rs 4,000 10. Rs 42,000 11. Rs 12,000 12. Rs 800
13. Rs 2,588.43, Rs 3,411.57 14. Rs 400 15. Rs 2,200, 251 yrs. 16. Rs 20,000 17. 2 years
21. 1427 %
18. Rs 8,000 19. 8% P.a., Rs 5,000 20. 3 years 22. 8% P.a 23. (i) Rs 9,000,

Rs 8,275 (ii) Rs 2,013.89 less 24. Rs 10,330.58 25. Rs 8,000 26. 10% P.a., Rs 16,000

27. 20 % P.a., Rs 1,875 28. Rs 40,000 29. Rs 9,000 30. (i) Rs 30,000 (ii) Rs 33,300

31. Rs 12,750, 4% 32. (i) Rs 50,000 (ii) Rs 1,575 33. 50,000 34. 1,27,308

35. 5 % P.a. 36. 2 years 37. 10,000 38. 1,89,280 39. 3 years 40. Rs 4,73,850
41. Rs 1,25,000 42. 10 % P.a. 43. 4.76 % P.a. 44. B.S. 2080 45. 4 % p.a., 2%

46. 500, Rs 46,381.75 profit 47. Rs 9,67,200, 28.96%

Mensuration

1. a)35 cm 2. 42 cm 3. 8 cm 4. 9 cm

5. a) 7 m b) 4,620 cm3 c) 11,000 cm2, 57750 cm3 d) 5 cm e) 2,640 cm2

f) 12,320 cm3 g) 1,260 cm2, 1,414 cm2, 2,695 cm3 h) 192.5 l i) 3,850 cm3 j) 962.5 m3

6. a) (i) 7,392 cm2 (ii) 45,994.67 cm3 b) 1,68,168 cm3 c) 924 cm2 d) 216

e) 5 cm f) 12 cm g) 3,696 cm2 h) 4,851 cm3 i) 31.5 cm

7. 7,603.2 cm2, Rs 380.16 8. Ram, 5,082 cm3 9. (i) Rs 11,880 (ii) 707.85 kg 10. (i) Rs 33,585

(ii) 16,843.75 l 11. 60 12. Rs 2,860 13. Rs 9,900 14. 3cm, 5 cm

15. 3 16. 21 min 17. Rs 3,520 18. 3.5 cm 19. 6 cm, 31 cm

20. 1.05 m, 4 m, 16.67 m2 21. a) 24 cm b) 30 cm c) 1,440 cm2, 1,548 cm2 d) 360 cm2, 360 cm3
e) 2,952 cm2, 6,300 cm3
f) 15 m, Rs 96,850

Approved by Curriculum Development Centre, Sanothimi, Bhaktapur 369 Vedanta Excel in Mathematics - Book 10

Answers

22. a) 400 cm3 b) 576 cm2 c) 868 cm2 d) 864 cm2 e) 384 cm3
f) 1,568 cm3
g) 384 cm2, 384 cm3 h) 6000 cm3

23. a) 480 cm2, 768cm3 b) 6.24m2.1.104 m3 c) 5,120 cm3 d) 2,112 cm3 e) 216 cm2

24. a) 902 cm2, 1518 cm2 b) 2,310 cm2, 3,696 cm2, 12,936 cm3 c) 550 cm2, 704 cm2, 1,232 cm3
d) 314.29 m3 e) 550 cm2, 1,232 cm3 f) 2,200 cm2, 2,816 cm2

g) 2,310 cm2, 3,696 cm2

25. a) (i) 2,464 cm2, 7,392 cm3 (ii) 7,656 cm2, 54,516 cm3 (iii) 4,576 cm2, 22,176 cm3

(iv) 858 cm2, 19,50.67 cm3

b) 44,352 cm2, 7,50,288 cm3 c) 14,322 cm2, 1,21,968 cm3 d) 10 cm e) 5 cm

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

1. a) HCF : x(x + 2) b) HCF : 3x(x – 5) c) HCF : (a + b – 6)
LCM : x (x2 – 4) LCM : 3x(x2 – 25) LCM : b(a – b) (a + b – 6)

d) HCF : (m – n – 1) e) HCF : p(p + 1) f) HCF : ab(3a – b)

LCM : mn(m + n) (m – n – 1) LCM : p(p – 1) (p + 1)2 LCM : 6ab (3a + b) (3a – b)2

g) HCF : (a + b) h) HCF : (x – 2)
LCM : ab(a + b)2 LCM : 2ax(x + 2) (x – 2) 2

i) HCF : 3x(x + 1) j) HCF : ab(ab – 2)
LCM : 18x(x – 1) (x3 + 1) LCM : ab (ab + 2) (a3b3 – 8)

k) HCF : (x – 1) l) HCF : (a + 1)
LCM : (x – 1) (x2 + 1) (2x2 + x + 2) LCM : (a + 1) (a2 – 4) (2a2 – 3a + 2)

m) HCF : (4a2 – 2a + 1) n) HCF : (4x2 + 2x + 1)
LCM : (8a3 + 1) (4a2 + 2a – 1) LCM : (1 – 8x3) (1 + 2x – 4x2)

o) HCF : (p2 – 2p + 4) p) HCF : (4a2 – 2ab + b2)
LCM : (p3 + 8) (p2 + 2p + 4) LCM : (2a + b) (16a4 + 4a2b2 + b4)

q) HCF : (x2 + 5x + 13) r) HCF : (3k2 + 4k + 5)
LCM : x(x4 + x2 + 169) LCM : 2k(9k4 + 14k2 + 25)

s) HCF : (x – 1) (x – 3) t) HCF : (x + 1) (x + 2)
LCM : (x2 – 1) (x2 – 9) LCM : (x2 – 1) (x2 – 4)

u) HCF : v) HCF : (x + y – 11)
LCM : LCM : (x + y – 11) (x – y + 1) (x – y + 11)

w) HCF : (xy – x + y +1) x) HCF : (xy + 3x + 2y – 6)
LCM : (1 – x) (xy – x + y + 1) (xy + x – y + 1) LCM : (x – 2) (xy + 3x + 2y – 6) (xy – 3x – 2y – 6)

y) HCF : 6x(2x + 1) z) HCF : x4 + x2y2 + y4
LCM : 180x (x – 1) (8x3 + 1) LCM : x(x6 – y6)

2. a) HCF : 1 b) HCF : y(2x – 1)
LCM : 72ab(a + 1) (a – 3) (a2 – 4) LCM : 60xy(2x + 1) (3x – 1) (8a3 – 1)

c) HCF : mn(2m + 3n) d) HCF : x(2x + 1)
LCF : mn(2m – 3n) (4m – 5n) (8m3 + 27n3) LCM : x(2x – 1) (8x3 + 1)

e) HCF : x(x2 + x + 1) LCM : x(x6 – 1)
f) HCF : p(p2 – p + 1) LCM : p (p3 + 1) (p2 + p + 1) )
g) HCF : x2 + xy + y2 LCM : x(x2 – xy + y2) (x3 – y3)
h) HCF : (y2 + y + 1) LCM : y6 – 1
i) HCF : (a2 – a + 1) LCM : a6 – 1
j) HCF : (x + y + z) LCM : (x + y + z) (x – y – z) (y – z – x) (z – x – y)
k) HCF : (3m + 2n + r) LCM : (3m + 2n + r) (3m – 2n – r) (r – 3m – 2n) (3m + r – 2n)

Vedanta Excel in Mathematics - Book 10 370 Approved by Curriculum Development Centre, Sanothimi, Bhaktapur

Answers

l) HCF : (3x + 2y + 2z) LCM : (3x + 2y + 2z) (3x – 2y – 2z) (2z – 2y – 3x) (3x – 2y + 2z)
m) HCF : 4x2 + 2x + 1 LCM : (8x3 – 1) (4x2 – 2x + 1) (4x2 – 2x – 1)
n) HCF : (1 + 2x2 + 4x2) LCM : (1 + 2x – 4x2) (1 – 64x6)
o) HCF : (9x2 + 3x + 1) LCM : (9x2 – 3x – 1) (729x6 – 1)
p) HCF : a – b + 1 LCM : (a + b) (a – b + 1) (a + b – 1) (a + b – 7)
q) HCF : 1 LCM : (x – 3) (x – y – 3) (x + y + 5)

Simplification of Rational Expressions

1. 1 2. 1 3. 6ab 4. 2 5. 1 6. 2 7. 2b
a2 + b2 x+1 x(x2 – 4) 4x2 – 1

8. 8x 9. (x 1 – 3) 10. 2 11. x2 – 10 12. 0
x4 – 1 –2) (x (x – 1) (x – 2) (x – 1)(x – 2) (x + 3)

13. 1 14. (a – 4 5) 15. 38 16. 0
(x – 3) (x – 1) 1) (a – (a + 3) (a + 4) (a – 6) 20. 0

7x – 25 18. 0 19. 1 21. 2(y – 2)
17. (x – 1) (x – 3) (x – 4) y2 – 2y + 4

22. 2(2x – y) 23. 2(3a – 1) 24. 0 25. 1 4x3 x8 26. 6
4x2 – 2xy + y2 (9a2 – 3a + 1) + x2 – a(a + 2) (a2 – 1)

27. x2 + 2 28. 6x 29. 2x2 30. 4a2
(x2 – 1) (4x2 – 1) x2 – y2 a2 – b2

31. 8a7 32. 4 33. x3 34. 1
a8 – 256b8 1 – x2 (x – y) (x3 + y3) (1 – a) (1 + a3)

35. 16a 36. 16a7x 37. 16y7 38. 0 39. 1
1 – a8 x8 – a8 y8 – 256 a–1

40. 1 41. 8a7b 42. 2m 43. 2(m2 + 1)
1–b a8 – b8 m+n m(m2 – 1)

Indices 1
a
1. a) 1 b) 3 c) 2 d) 1 e) 1 f) g) 25 h) 0.001
k) 1 16x2y2
1
i) 392 j) x x l) 4p4q3 m) 3x2 n) 2x2yz o) 1
2y2 y2

2. a) 1 b) 1 c) 1 d) 1 e) 1 f) 1 g) 1 h) (p – y)y

i) a j) x x+y k) b a–b l) 1 m) 1 1
b y d) 1 a f) 1
c) 3 n) 0, 2 p) 3, 2 n) 2x3 1
3. a) 3 b) 3 m) 3, 4 e) 2 g) –1 h) 2 i) 3 j) 0, 2
k) 1, 2 l) 2, 3 o) 1, 2 q) 0,41 r) 0, 2

7. a) 1, 2 b) 1 m2 or 4 m2

Surds

1. a) 3 5 b) 0 c) 11 3 d) 2 3 2 e) 2 f) – 7 g) 5 + 2 6 h) 0

i) 5 j) 5 k) 8 l) 1 2. a) 7 14 – 13 b) 2+ 6 + 10
3 3 11 4

c) 8 d) 8 e) 6 f) 6 g) – 3 5 h) 2x 1+x –2
x

i) 4 x2 – x j) 2x 3. a) 14 b) 1, 2 c) 1 d) 7 e) 3 f) 8
y j) 25 k) 5 n) 2
g) 3 h) 4 r) 4 s) 2a, a l) 36 m) 361
i) 81 5 63
2
o) a p) 196 q) 6 t) 16 4. 50
3 25

Approved by Curriculum Development Centre, Sanothimi, Bhaktapur 371 Vedanta Excel in Mathematics - Book 10

Answers

Simultaneous equation

1. 2 lt., 3 lt 2. 4, 2 3. (i) Rs 300 (ii) 400 4. (i) Rs 5,000 (ii) Rs 150 5. 375, 25
9. 15 years, 21 years
6. 12 years, 33 years 7. 13 years, 16 years 8. 11 years, 36 years
2115yeayresa,r8s,1260yeyaerasrs 13. 10 years, 30 years
10. 11. 25 years, 55 years 12. 30 years, 70 years 17. 2,000, 2,010
14. 15. 7 years, 14 years 16. 1,992 21. 73
25. 28
18. 25 years, 15 years 19. 54 20. 24 30. 4 km/hr, 6 km/hr

22. 52 23. 57 24. 27

26. 27 27. 5, 8 28. 41 km/hr, 49 km/hr 29. 10 p.m.

31. 10 m, 8 m 32. 10 km/hr, 40 km/hr

Quadratic equation

1. a) 7 2. 8 3. 5 4. 6 5. 9 6. 6 7. 7 8. 11 9. 7, 8 10. 10
11. 8, 10 12. 15, 17 15. 4, 12 16. 6, 15 17.15, 20 18. 4, 6 19. 7, 5
20. 9, 6 21. 10 13. 10, 12 14. 9, 11 24. 16 years 25. 5 years26. 6 years 27. 12 years, 7 years

22. 4, 6 23. 15 years

28. 11 years, 7 years 29. 16 years, 10 years 30. 17 years, 11 years 31. 15 years, 10 years
32. 40 years, 10 years 33. 36 years, 9 years 34. 50 years, 30 years 35. 40 years, 10 years

36. 50 years, 30 years 37. 34 or 43 38. 64 39. 73 40. 45 41. 35 42. 94 43. 24
50. 25%
44. 24 45. 18 46. 16 47. 38 m 48. 15 m, 10 m 49. 14 m, 9 m

51. 20% 52. 40 km/hr 53. 300 km/hr 54. 10, 4 55. 20, Rs 50

Area of triangles and quadrilaterals

1. a) 60 cm2, b) 40 cm2 c) 3 cm d) 96 cm2 e) 42 cm2 f) 72 cm2

1. a) 40° b) 30° Circle d) 72°, 68° f) 34°
e) 40° f) 30°, 60° h) 40° l) 110°
i) 20°, 30° j) 55° , 125° c) 29°, 87° l) 76°
m) 22° n) 66° g) 38° p) 46°, 92°
q) 140° r) 150° k) 20° t) 90°
u) 98° v) 13° o) 130° x) 56°
y) 27° z) 65° s) 100° zb) 40°
zc) 60° zd) 30° w) 80° zf) 78°
b) 4 cm za) 20° d) 12 cm
2. a) 6 cm b) 64° ze) 35° d) 16° e) 31°, 59°
3. a) 30°, 90°, 15° h) 34° c) 6 cm j) 46° k) 30°
c) 61°
g) 20° i) 65°

Trigonometry

1. a) 40 3 m b) 15 m c) 16.17 ft d) 60 3 m 2. a) 10 3 m b) 24 m

3. a) 12 3 m b) 14 3 ft c) 40 m d) 20 3 m e) 24 m f) 20 3 m

4. a) 8.43 m b) 20 m c) 79.94 m d) 1.35 m e) 1.8 m f) 1.68 m

5. a) 150 3 m b) 11.55 m c) 20 3 m d) 500 m

6. a) 30 3 m b) 5 3 m c) 36 m

7. a) 20 ft b) 16.13 m c) 33.09 m d) 50 m 8. a) 24 m b) 11.55 m

9. a) 101.5 m b) 152 m c) 114.4 m d) 234 m 10. a) 16 m b) 21.44 m c) 34.14 m d) 51.21 m

11. a) 30° b) 45° c) 45° d) 60° 12. a) 45° b) 30° 13. a) 17.5 m b) 20 3 m
b) 94.64 m
14. a) 47.32 m b) 75 m c) 1.366 km 15. a) 42 m, 14 3 m

16. a) 18 cm2 b) 105 cm2 c) 68 3 cm2 d) 64 cm2 e) 10 cm f) 8 cm g) 60° h) 45°

17. a) 72 3 cm2 b) 9.24 cm c) 20 cm d) 4 2 cm e) 16 cm f) 30° g) 60°

18. a) 30 cm2 b) 48 cm2 c) 27 3 cm2 d) 45 cm2 e) 48 cm2 f) 12 3 cm2, 3 3 cm2 g) 8 2 cm
19. a) 18 cm b) 8 cm c) 30°, 6 cm2

Vedanta Excel in Mathematics - Book 10 372 Approved by Curriculum Development Centre, Sanothimi, Bhaktapur

Answers

Statistics

1. a) 28.75 b) 70.75 c) 38.6 d) 42.5 2. a) 24.06 b) 54.68
3. a) 33.3
5. a) 180 b) 415.22 4. a) 39.33 b) 30.83
6. a) 53.29
7. a) 39.17 b) 9 c) 10 d) 9, 10
9. a) 15.63
10. a) 69.67 b) 24.58 c) 60 d) 78.33 e) 36 f) 132.5
11. a) 7
b) 37.14 8. a) 6 b) 10 c) 23, 21

b) 24.44 c) 37.5 d) 8 e) 20.87 f) 137.5

b) 90.75 c) 22.78 d) 350 e) 56.25 f) 39

b) 10 12. a) 31.11 b) 70

1. a) 5 b) 7 c) 5 Probability
6 15 6
d) 7
2. a) 2 b) (i) 11 (ii) 2 15 (iv) 1 (v) 11 (vi) 1
13 13 13 13 13 26
(iii) 2
c) (i) 8 (ii) 4 (iii) 7 13 b) 5 c) 5 d) 3
13 13 13 26 6 8
3. a) 12
e) (i) 17 (ii) 11 (iii) 1 37 b) 7 c) 4
20 20 2 11 11
4. a) 4
5. a) 7 b) 2 6. a) 3 15 c) 3
10 3 8 4
b) 1
7. a) 0.65 b) 0.45 c) 1 3 (iv) 13
2 24
8. a) 11 (iii) 11
12 b) (i) 5 (ii) 1 24
12 4
9. a) 4 d) 2
9 b) 1 c) 1 13
12 12
10. a) 0.97
b) 0.88
11. a)
P(B2) = 184 P(B1B2) = 16
49

184 8B 12
49
P(B ) = 6W P(W ) = 164 P(B1W2) =
2
1

8B

6W P(W ) 8B P(B2) = 184 12
2 49
= 146 P(W1B2) =

6W (i) 25 (ii) 24
49 49
P(W ) = 164 P (W1W2) = 9
2 49

Approved by Curriculum Development Centre, Sanothimi, Bhaktapur 373 Vedanta Excel in Mathematics - Book 10

Answers

b) P(F2) = 1522 P(F1F2) = 9
169

P(F1) = 1522 12F P(NF2) = 5428 P(F1NF2) = 36
48NF 169

12F P(F2) = 1522

48NF P(NF 36
2 169
) = 5428 12F P(NF1F2) =
48NF

P(NF ) = 5428 P (NF1NF2) = 144
2 169

Probability of first face card and second non face card = 36
169

12. a) P(S2) = 1 P(S1S2) = 1
2 4

1 S 1
P(S 1) = 2 4
D P(D ) = 1 P(S1D2) =
2 2

S

D P(D ) P(S 2) = 1 1
2 2 4
= 1 S P(D1S2) =
2
D

P(D ) = 1 P (D1D2) = 1
2 2 4

Probability of no son= 1
4

b)

) = 12 P(S1S2S3) = 1
P(S1S2D3) = 8
S P(S 3 1
D 8
=12 P(D3) = 1
P(S ) S 2
D
2

S P(S3) = 1 P(S1D2S3) = 1
2 P(S1D2D3) = 8
D 1
P(D ) = 1 8
1 2 2 2
=
P(S ) P(D ) = 21
3
1

S 1 P(D1S2S3) = 1
8
D P(S ) = 2

P(D S 3
1 D
) =21 P(S2) = 1 P(D ) 1 P(D1S2D3) = 1
2 3 2 8
S =

D P(D 1
2 2
) = 21 P(S3) = P(D1D2S3) = 1
8
S
D P(D
3
) = 21 P(D1D2D3) = 1
8

Probability of at least a son = 7
8

Vedanta Excel in Mathematics - Book 10 374 Approved by Curriculum Development Centre, Sanothimi, Bhaktapur

Answers

c) P(S1S2S3) = 1
8
12
P(S ) =

S 3
D
=12 P(D3) = 1 P(S1S2D3) = 1
S 2 8
) D
P(S
2 S
D
S P(S3) = 1 P(S1D2S3) = 1
S 2 P(S1D2D3) = 8
D D 1
P(D2) = 1 8
=12 2
) P(D
P(S 3 ) = 21
1

S 1 1
8
D P(S ) = 2 P(D1S2S3) =

P(D 3
1
) =21 P(S2) = 1 P(D3) 1 P(D1S2D3) = 1
2 2 8
S =

D P(D 1
2 2
) =21 P(S3) = 1
8
P(D1D2S3) =

Probability of at least two daughters = 1 P(D ) = 1
2 3 2

P(D1D2D3) = 1
8

P(W2) = 1 P(W1W2) = 5 × 1 = 5
2 9 2 18

5 4W 5 1 5
9 9 2 18
13. a) P(W 1) = 4B P(B2) = 1 P(W1B2) = × =
b) 2
5W
5W P(W2) = 58
4B P(B ) = 4 P(B1W2) = 4 × 5 = 5
1 9 9 8 18

3B P(B 4 3 1
2 9 8 6
) = 3 P (B1B2) = × =
8
5
P(W1 , W2)= 18

) = 12 P(R1B2) = 1
6
P(B 2

=13 1B 1 P(R1G2) =1
1G 2
P(G2) = 6
1R
P(R ) 1G 1 P(B1R2) =1
2
1 6

1R P(B1) = 1 P(R2) =
1B 3
1G
P(G ) = 21 P(B1G2) = 1
P(G 2 6
1
) =31 1R 1 =1
1B 2
P(R2) = P(G1R2) 6

P(B ) =21 P(G1B2) = 1
2 6

Sample space {R1B2 ,R1G2 , BR2, B1 G2, G1 R2, G1B2}

Approved by Curriculum Development Centre, Sanothimi, Bhaktapur 375 Vedanta Excel in Mathematics - Book 10

Answers

c) 1 P(B1Y2) =1
P(Y 2) = 2
6

1Y 1 P(B1W2) = 1
1W 2 6
=13 P(W2) =
P(B ) 1B
1W 1 P(Y1B2) =1
1 2
6
1B P(Y1) = 1 P(B2) =
1Y 3

1W P(W ) = 21 P(Y1W2) =1
2
P(W 6

1 ) =31 1B P(B2) = 1 1
1Y 2 6
P(W1B2) =

P(Y ) =21 P(W1Y2) =1
2
6

Probability of at least a black = 2
3

d) = 25 P(R1 W2) = 1
15
)
P(W
2

2W

1 3B P(B ) = 3 P(R1 B2) = 1
2 5 10
6

=

) 1
15
P(R ) =15 P(W1 R2) =
1 2P(W2)

1R P(B1) = 2 1R P(R = 1 1
2W 6 1W 5 15
3B P(W1 W2) =
3B
P(B
P(Y 2 ) = 53 1
5
) P(W1 B2) =

1

3 2W1R
= 1B

5 1
5
P(R2) = P(B1 R2) = 3
25
P(W
2 ) = 2
5
P(B
P(B1 W2) = 6
) 25

2

=

25

P(B1 B2) = 6
25
6
P(B1B2) = 25

Vedanta Excel in Mathematics - Book 10 376 Approved by Curriculum Development Centre, Sanothimi, Bhaktapur

Ministry of Education
Curriculum Development Centre, Sanothimi, Bhaktapur

Syllabus of Compulsory Mathematics - Class 10

S.N. Subject Matters Estimated
periods
1. Set
• Verbal problem solving of the problems involving maximum 8

three sets by using Venn-diagrams
• Union, intersection and difference of sets by using

Venn-diagrams
• Identification in real life situations related to the relation between

sets and problem solving by using mathematical relation

2. Arithmetic 20
• Tax and money exchange: Problems related to VAT and money 24
exchange (including mark price, discount and VAT) 36
• Compound interest (maximum 2 years for half yearly and 3
years for yearly compound interest)
• Population growth and depreciation (only yearly)
• Project work related to profit, loss, population growth, etc.

3. Mensuration

• Area of triangle (Right angled triangle, equilateral triangle,
isosceles triangle, scalene triangle)

• Lateral surface area, total surface area and volume of
triangular prism,

• Curved surface area, total surface area and volume of
cylinder, sphere, hemisphere, cone, and the solid formed due
to the combination of any two different solids,

• Total surface area and volume of pyramid
• Problems related to calculation of quantity, estimation of cost

by using the properties of geometrical bodies.
4. Algebra

• H.C.F. and L.C.M. (Maximum three expressions by

factorisation method only)

• Simplification of radicals and surds related to four

fundamental operations

• Additional problems of indices and exponential equation (in

the quadratic form)

• Simplification of rational expressions (Maximum four

fractional terms)

• Word problems of simultaneous equation

• Word problems of quadratic equation

• Related example by using mathematical model

Approved by Curriculum Development Centre, Sanothimi, Bhaktapur 377 Vedanta Excel in Mathematics - Book 10

5. Geometry 44

Theorems related to area of triangle and quadrilateral 10
17
• The area of parallelograms standing on the same base and 11
between the same parallels are equal.

• The area of triangle is half of the area of the parallelogram
standing on the same base and between the same parallels.

• The area of triangles standing on the same base and between
the same parallels are equal.

Construction

• Construction of triangle and quadrilateral of equal area.

Circle
• The arcs of a circle that subtend equal angle at the centre of the

circle are equal.
• Equal arcs of a circle subtend equal angle at the centre of the

circle.
• Equal chords of a circle form equal arcs in the circle.
• If the arcs formed by chords of a circle are equal, the chords

are equal.
• The angle at the centre of a circle is twice the angle at its

circumference standing on the same arc.
• The angle in the circumference of a semi-circle is one right

angle.
• The angles in the same segment of a circle are equal.
• The opposite angles of a cyclic quadrilateral are

supplementary
• A tangent to a circle and radius drawn at the point of contact

are perpendicular to each other.
• Logical and diagrammatic discussion about the

interrelationship between various geometrical properties.

6. Trigonometry
• Area of triangles and quadrilateral by using trigonometric
formulae
• Problems of height and distance (containing only one angle)
• Project work and problem related to real life situations

7. Statistics
• Conversion of raw data into grouped and continuous data
• Mean, median and quartiles of grouped data
• Analysis and conclusion of statistics by using central
tendencies

8. Probability
• Problems related to addition and multiplication laws of
mutually exclusive events
• Problems related to the addition and multiplication laws of
probability of independent and dependent events
• Problems related to the probability tree-diagram (two steps for
three events and three steps for two events)

Vedanta Excel in Mathematics - Book 10 378 Approved by Curriculum Development Centre, Sanothimi, Bhaktapur

Approved by Curriculum Development Centre, Sanothimi, Bhaktapur 379 Subject: Compulsory Mathematics Specification grid (Written Exam) Time: 3 hours
Secondary Level (Class 9-10)

Full Marks: 100

Cognitive Units K CA HA Total Remarks
domain

Subject area

1 Set 1 Set - - 1×4 - 4
1×5 At lest 2 marks
2 Tax and money exchange
14 questions are asked
2 Arithmetic 3 Compound Interest 1×1 2×2 1×4 from each unit.

4 Population growth and
compound depreciation

5 Plane surface At lest 3 marks
16 questions are asked
3 Mensuration 6 Cylinder and sphere 1×1 3×2 1×4 1×5
7 Prism and Pyramid from each unit.

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

9 Surd At lest 3 marks
24 questions are asked
4 Algebra 10 Indices 1×1 5×2 2×4 1×5
from each unit.
11 Rational expressions

Vedanta Excel in Mathematics - Book 10 12 Equations

5 Geometry 13 Area of triangles and 2×1 3×2 3×4 1×5 At lest 4 marks
quadrilaterals 25 questions are asked

14 Construction from each unit.

15 Circle

6 Trigonometry 16 Trigonometry - 1×2 1×4 -6

7 Statistics 17 Statistics 1×1 1×2 1×4 -7
8 Probability 18 Probability - 2×2 - -4
6 10 4 37
Total no. of question 6 17 40 20 100
Total marks 34

Model Questions

Model Question
SEE Examination 2075 RE-109'CP'

Subject: Compulsory Mathematics

Attempt all the questions.

Group 'A' [3 × (1 + 1) = 6]

1. a) If initial population of any place is X0 and annual rate of population growth is R%
per annum, what is the population of that place after Y years?

b) Write the area of an isosceles triangle having length of equal sides 'm' cm and third
side is 'n' cm.

2. a) What is the value of (9m)0? Write it?

b) Write the name of the quartile which divides the continuous data below 25%.

3. a) Write down the relation between in the area of rectangle and a triangle standing on
b) the same base MN and between the same parallel lines MN and AB.

Write the relation between the opposite angles of a cyclic quadrilateral.

Group 'B' [4 × (2 + 2) + 3 × (2 + 2 + 2) = 34]

4. a) What is the price of a bag costing Rs 1,800 after levying 13% Value Added Tax? Find
it.

b) The present price of a car is Rs 20,00,000. If its price reduces by 10% annually, after

how many years it's price will be Rs 14,58,000? Find it. M 7cm 8cm
5. a) In the given figure, find the area of 'MNO. 24cm

N 25cm O

b) If the volume of a hemisphere is 486S cubic cm then find its radius. Q'

3cm
c) In the figure, the area of rectangular surfaces of the prism is 180 sq. cm, P' R'

³PQR = 90°m, PR = 5 cm and P'Q' = 3 cm. Find the length of PP'. Q

6. a) Prove that: 4a + 2 + 4a =1 PR
b) 17 × 4a
3+ 2
Rationalise the denominator of:
3– 2
7. a) Find the L. C. M. of:

p2 – q2, (p + q)2

b) Solve: w + 4 = 3 64

c) If the sum of two consecutive even numbers is 34, find the numbers.

8. a) In the given figure, WXYZ is a parallelogram. If ³XAY = 90°, WA Z
AY = 8 cm and the area of parallelogram WXYZ is 64 sq. cm, find Y
the length of AX.

X

Vedanta Excel in Mathematics - Book 10 380 Approved by Curriculum Development Centre, Sanothimi, Bhaktapur

Model Questions

b) In the given figure, M is the centre of the circle. If ³GEF = 2x° and E M G
³EGF = 3x°, find the value of ³FHG. 2x° 3x°

H?
F

B

c) In the given figure, X is the centre of the circle. AB and AC are two A ?
tangents. If ³BXC = 105°, find the value of ³BAC.
6 cm X
105°
C

9. a) In 'DEF, DE = 12 3 cm, ³DEF = 60° and the area of 'DEF is 36 sq. cm, find the
measurement of EF.

b) In a continuous series, the average marks of some students is 40 and the sum of
their marks (∑fm) is 1,200. Find the number of students.

10. a) If a dice is rolled and a coin is tossed at the same time, find the probability of
occurring odd number on dice and head on the coin.

b) Two cards are drawn randomly from a well shuffled deck of 52 cards in succession
without replacement. Show the probabilities of possible outcomes of getting Ace
and not getting Ace card in a tree diagram.

Group C [10 × 4 = 40]

11. In a survey of people of a community, it was found that 70% liked curd, 60% liked milk,
20% don't like both curd and milk and 550 liked both curd and milk then,

(i) draw a Venn-diagram to illustrate the above information.

(ii) find the total number of people participated in the survey.

(iii) find the number of people who like curd only.

12. A businessman exchanged Nepali currency Rs 6,60,000 into US dollar at the rate of
$1 = NRs 110. After four days, Nepali currency is revaluated by 10% and he exchanged
the dollars into Nepali currency again. What is his gain or loss? Find it.

13. The given figure is a combined solid made up of a cylinder 116 cm
and a cone. The diameter of the base of the object is 6 cm, 120cm
length of the cylindrical part is 116 cm and the total length
of the solid object is 120 cm. Find the total surface area of the
solid object.

14. Find the H.C.F. of: p2 + 4pq + 4q2, p4 + 8pq3 and 3p4 – 10p2q2 + p3q

15. Simplify: t: 1 – 1 – 2p
1 – p + p2 1 + p + p2 1 – p2 + p4

Approved by Curriculum Development Centre, Sanothimi, Bhaktapur 381 Vedanta Excel in Mathematics - Book 10

Model Questions

E HJ I

16. In the given figure, EF // GH, EI // FG and FJ // GI then prove
that:

(i) 'EFJ # 'HGI FG
(ii) Area of parallelogram EFGH = Area of parallelogram FGIJ.

17. Construct a quadrilateral MNOP in which NO = MN = 4.2 cm, OP = PM = 5.2 cm and
³NOP = 75°. Also construct the 'PQO which is equal in area to the quadrilateral MNOP.

18. Verify experimentally that the circumference angle BED is half of the central angle
BCD standing on the same arc BD of a circle. (Two circles having radii at least 3 cm are
necessary.)

19. The heights of a house and a temple are 13 m and 25 m respectively. If a man observes
the roof of the house from the roof of the temple he finds the angle of depression 45°,
find the distance between the house and temple.

20. Find the median from the data given below.

Class interval 40 - 50 50 - 60 60 - 70 70 - 80 80 - 90
Frequency 7 8 6 5 4

Group D [4 × 5 = 20]

21. A person deposited Rs 55,000 in bank 'P' for two years at the rate of 10% per annum
compounded annually. But after one year, bank has changed the policy and decided to
pay semi-annual compound interest at the same rate. What is the percentage difference
between the compound interest of the first year and second year? Give reason with
calculation.

22. Two pillars of height 8 feet each with four faces shown, of the gate of a stadium have
one-one pyramid of height 4 feet each having the same base on their tops. The base
of each pillar is 6 ft × 6 ft. If the pillars with pyramid are painted at the rate of 75 per
square feet, what will be the total cost? Find it.

23. The area of a rectangular field is 3000 sq. meters and perimeter is 220 metre. Out of
length or breadth, which one is to be decreased by what percentage to make it a square?
Find it.

24. Points K, L, M and N are concyclic such that arc KL = arc NM. If the chords KM and
LN are intersected at a point P, then prove that:

(i) Area of 'KPL = Area of 'NPM

(ii) chord KM = chord LN

Vedanta Excel in Mathematics - Book 10 382 Approved by Curriculum Development Centre, Sanothimi, Bhaktapur