Excel in Mathematics Book 10 Final_CTP (2080)_compressed (1)

Approved by Curriculum Development Centre, Sanothimi, Bhaktapur 351 Vedanta Excel in Mathematics - Book 10 Revision and Practice Time 21. y – 2 y2 – 2y + 4 + y + 2 y2 + 2y + 4 – 16 y4 + 4y2 + 16 22. 2x – y 4x2 – 2xy + y2 – 2x + y 4x2 + 2xy + y2 + 16x3 16x4 + 4x2 y2 + y4 23. 3a + 1 9a2 + 3a + 1 + 3a – 1 9a2 – 3a + 1 – 2 81a4 + 9a2 + 1 24. 1 1 + a + a2 – 1 1 – a + a2 + 2a 1 + a2 + a4 25. 1 1 + x + x2 – 1 1 – x + x2 + 2x 1 – x2 + x4 26. 2a a2 – 4b2 + 2a a2 + 4b2 + 4a3 a4 + 16b4 27. 2 1 – x2 – 2 1 + x2 + 4 1 – x4 Exponential expressions 1. Solve a) 2x – 2x – 2 = 6 b) 3x + 1 – 3x = 54 c) 3 x + 5 2 = 9 x +1 2 d) 2x = 16 8x e) 5x – 1 × 2x + 2 = 80 f) 33x .9x + 1 = 94x 3 g) 25x 42x+1 = 4x 2x h) 2 × 3x – 1 = 3 × 2x – 1 i) 75x – 4 . a4x – 3 = 72x – 3 . ax – 2 j) 32x – 10.3x + 9 = 0 k) 32x – 4.3x + 1 + 27 = 0 l) 4x – 3.2x + 2 + 32 = 0 m) 4x + 128 = 3.2x + 3 n) 5x – 1 + 5 5x = 5 1 5 o) 3x + 27 3x = 12 p) 2x + 32 2x = 12 q) 5x + 5 5x = 6 r) (3x – 1) (3x – 9) = 0 2. a) If a = xq +r . yp , b = xr + P . yq , c = xp + q . yr , show that aq–r br – pcp – q = 1 b) If x = (ab) 1 3 – (ab) – 1 3 , prove that x3 + 1 ab + 3x = ab. c) If a = xyp–1 , b = xyq – 1 and c = xyr –1 , prove that aq – r br – p cp – q = 1 d) If 2x =3y = 6 –z , show that 1 x + 1 y + 1 z = 0 e) If m = ax , n = ay and a2 = (my . nx ) z , show that xyz = 1 f) If xy = yx , proved that x y x y = x – 1 x y . g) If 2x = 3y = 6z , prove that z = xy x + y h) If 3x = 5y = 75z , show that z = xy 2x + y i) If a = 2x , b = 2y and ay bx = 4, proved that xy = 1

Vedanta Excel in Mathematics - Book 10 352 Approved by Curriculum Development Centre, Sanothimi, Bhaktapur Revision and Practice Time 3. a) If abc = 1, prove that: (1 + a + b–1) –1 + (1 + b + c–1) –1 + (1 + c + a–1) –1 = 1 b) If xyz = –1, prove that: (1 – x – y–1) –1 + (1 – y – z–1) –1 + (1 – z – x–1) –1 = 1 c) If p + q + r = 0, prove that: (1 + xp + x–q) –1 + (1 + xq + x–r) –1 + (1 + xr + x–p) –1 = 1 d) If a+b+c = k, show that x2a x2a + xk – b + xk – c + x2b x2b + xk – c + xk – a + x2c x2c + xk – a + xk – b = 1 4. a) If x2 – 2 = 22 3 + 2–2 3, prove that (i) x = 21 3 + 2–1 3 (ii) 2x(x2 – 3) = 5 b) If x2 + 2 = 32 3 + 3–2 3, prove that (i) x = 31 3 – 3–1 3 (ii) 3x(x2 + 3) = 8 5. a) Solve: 4x – 3 × 2x + 2 + 32 = 0. Also, use the value of x so obtained to verify the equation 5x + 53 – x = 30. b) The area of a window is 4x square meter. The curtain of size 3 m by 2x m is used in the window. If the area of the curtain is 2 square meters more than the area of window, find the possible areas of the window. Area of triangles and quadrilaterals 1. In the figure given alongside; PQRS is a rectangle, TQRU is a parallelogram and TA ⊥ RU. (a) What is the relation between the area of rectangle PQRS and the parallelogram? (b) If TQ = 12 cm and TA = 5 cm, find the area of rectangle PQRS. (c) Construct a parallelogram TQRU in which QR = 5 cm, TQ = 6 cm and diagonal TR = 6 cm. Construct rectangle equal in area to the parallelogram PQRS. 2. In the given parallelogram ABCD, base BC is produced to E such that BC = CE. (a) What is the relation between the area of triangles BCD and CDE? (b) If the area of parallelogram ABCD is 40 square centimeter, find the area of triangle BED. (c) Construct a parallelogram ABCD in which AB = 6 cm, BC = 4 cm and ∠BAD = 45° . Also, construct a triangle BEF having one angle 60° and equal in area with parallelogram ABCD. 3. In the given figure; PS // QR. (a) Which triangle is equal to the DPQR in area? (b) Prove that DPOQ and DROS have equal area. (c) Construct a triangle PQR having sides p = 6.4 cm, q = 6 cm and r = 5.6 cm. Also, construct another triangle SQR having one side 7 cm and equal in area to the ∆PQR. 4. In the given figure; PQRS is a square and S is the mid-point of base TR of triangle TUR. (a) If the diagonal PR = 6 cm, find the area of triangle TUR. P Q R U A S T A B C D E P Q R S O P Q S R U T

Approved by Curriculum Development Centre, Sanothimi, Bhaktapur 353 Vedanta Excel in Mathematics - Book 10 Revision and Practice Time (b) Prove that DTUR and square PQRS are equal in area. (c) Construct a triangle TUR having base TR = 7 cm, ∠T = 60°and ∠R = 75°. Also, construct rectangle PQRS equal in area to the ∆TUR. 5. In the given figure, ABCD is a quadrilateral. CE is drawn parallel to DB and it meets AB produced at E. (a) Write down the relation between the area of triangles BCD and BED. (b) Prove that: area of DADE = area of quad. ABCD. (c) Construct a quadrilateral ABCD in which AB = BC = 5.5 cm, CD = DA = 4.5 cm and ∠A = 60°. Also, construct ∆ADE equal in area to the quadrilateral ABCD. 6. Parallelograms PQRS and QRTU stand on the same base QR and between the same parallel lines PT and QR. Prove that: (i) ∆PQU ≅ ∆SRT (ii) Area of PQRS = Area of QRTU 7. Rectangle ABCD and parallelogram EBCF stand on the same base BC and between the same parallel lines AF and BC, prove that: (i) ∆ABE ≅ ∆DCF (ii) Area of rectangle ABCD = Area of EBCF 8. If XY//MN, P, Q and R are the points on XY such that PM//QN, prove that the area of triangle RMN is half of the area of quadrilateral PMNQ. 9. In the given figure, ABCD is a parallelogram in which diagonals AC and BD intersect at O. A line segment through O meets AB at P and DC at Q. Prove that: area of trap. APQD = 1 2 area of parm ABCD. 10. In the given quadrilateral ABCD, M is the mid-point of AC. Prove that: area of quad. ABMD = area of quad. DMBC. 11. ABCD is a parallelogram and X is any point within it. Prove that the sum of D XAB and D XCD is equal to half of the parallelogram. 12. ABCD is a parallelogram. X and Y are any points on CD and AD respectively. Prove that D AXB and D BYC are equal in area. 13. In DPQR, A and B are the mid-points of the sides PQ and PR respectively. D and C are two points of QR such that AD//BC. Prove that ABCD = 1 2 D PQR. 14. In the given trapezium PQRS, PQ // SR. M and N are the mid-points of diagonals PR and QS respectively. Prove that D PNR = D QMS. D C B A E D A B C Q O P D A B M C P Q C R D A B R M N S P Q

Vedanta Excel in Mathematics - Book 10 354 Approved by Curriculum Development Centre, Sanothimi, Bhaktapur Revision and Practice Time 15. In the given parallelogram PQRS, M is any point on the side PS. QM and RS are produced to meet at T. Prove that DQRT = quad. PQST. 16. In the given figure, PQRS and PABC are the parallelograms with equal area. Prove that SA // BR. 17. In the trapezium ABCD, AB // DC and P is the midpoint of BC. Prove that D APD = 1 2 trap. ABCD. 18. In the adjoining figure, it is given that PQ // RS and area of D PRS = area of D QRT. Prove that RQ // ST. 19. In the adjoining diagram, ABCD is a parallelogram. Prove that, Area of D APQ = Area of D PDC. 20. In the given D ABC, D, E, F and G are the mid-points of BC, AD, BE and CF respectively. Prove that D ABC = 8 D EFG. 21. In the figure, A, B and C are the mid-Points of PR, QA and QR respectively. D is any point of AR. Prove that, D PQR = 8 D BCD. P M T S Q P Q R A S C B R C P D A B P R S T Q A B C D P Q A B C O E G D F P Q B C A R D

Approved by Curriculum Development Centre, Sanothimi, Bhaktapur 355 Vedanta Excel in Mathematics - Book 10 Revision and Practice Time 22. In the adjoining figure, PRST is a parallelogram and PT is the median of D PQR. Prove that, D PQT = D STR. 23. In the figure alongside, PQRS is a parallelogram. X and Y are any points on QR and RS respectively such that XY // QS. Prove that, Area of D PQX = Area of D PSY. 24. In a parallelogram ABCD, P is any point on the diagonal AC. Prove that : (i) Area of ∆ABP = Area of ∆APD (ii) Area of ∆BPC = Area of ∆CPD 25. In parallelogram PQRS, QR is produced to T such that QR = RT. The line PT cuts RS at O. Prove that the triangle POQ is twice as large as the triangle SOT. Circle 1. In circle with centre O; the points A, B and C are on the circumference. Answer the following questions. (a) Draw two circles of different radii (not less than 3 cm), join B and C to the centre O and point C. Then explore experimentally the relationship between ∠BOC and ∠BAC. (b) If ∠BAC = 40o , find the measure of ∠BOC and ∠OBC. (c) If OB = BC, find the ratio of ∠BOC and ∠BAC. 2. In the circle with centre O; AB is a diameter and C is any point of the circumference. Answer the following questions. (a) Draw two circles of different radii (not less than 3 cm) and explore experimentally measure of ∠ACB. (b) If ∠BAC = 25o , find the measure of ∠ABC. (c) If ∠BAC : ∠ABC = 4: 5, find the value of ∠BAC. 3. P, Q, R and S are the concylcic points in a circle with centre O. Answer the following questions. (a) Draw two circles of different radii (at least 3 cm) and explore experimentally the relationship between ∠PSQ and ∠PRQ standing on the same arc PQ. (b) If PR is a diameter of the circle and ∠PRQ = 55o , find the measure of ∠QSR. (c) If PR is the diameter of the circle and ∠PQS = 50o , find the ratio of ∠SPR and ∠PRS. 4. In a cyclic quadrilateral ABCD, (a) Draw two circles of different radii (3 cm ≤ r ≤ 4 cm) and draw the cyclic quadrilateral ABCD in each circle. Then verify experimentally that: (i) ∠ABC + ∠ADC = 180o (ii) ∠BAD + ∠BCD = 180o P T Q S R P Q X R Y S B C A O B C A O B C D 130° A x O

Vedanta Excel in Mathematics - Book 10 356 Approved by Curriculum Development Centre, Sanothimi, Bhaktapur Revision and Practice Time (b) Find the value of x from the given figure. (c) AB = AD, ∠ABD = 43o and ∠DBC = 34o , find the value of ∠BAC. 5. Study the given figure and answer the following questions. (a) Which angle is equal to ∠BDE? (b) Find the value of x. (c) Arc CD = Arc AC, find the value of ∠DBC. 6. Given figure is a circle in which ∠ WAY = ∠ XBZ. Prove that, WZ // XY. T P Q R S U 7. In the adjoining figure, if PQ // RS, prove that, ∠ PTR = ∠ QUS. 8. In the given figure, O is the circumcentre of D ABC and OD ⊥ BC. Prove that ∠ BOD = ∠ BAC. 9. In the given figure, two chords AB and CD intersect at right angle at X. Prove that, chords (AC + BD) = chords (AD + BC) 10. In the adjoining figure, O is the centre of the circle. If ∠OCA = ∠ODB, prove that DO⊥AB. 11. In the given figure, P and Q are the mid-points of AB and AC respectively. Prove that AE = AF. B D 68° x C A E O Y W Z X A B A B C O D A C D B X A B O C D A E P Q F B C

Approved by Curriculum Development Centre, Sanothimi, Bhaktapur 357 Vedanta Excel in Mathematics - Book 10 Revision and Practice Time 12. In the adjoining figure, ABCD is a parallelogram. The inscribed circle cuts AB at E and CD at F. Prove that, ∠ EFD = ∠ ABC. 13. In the given diagram, AE is a diameter. If AD ⊥ BC, prove that D ABD ∼ D ACE. 14. In the given figure, APB = CQD. Prove that AC // BD. 15. In the figure given alongside, AB and CD are two parallel chords. Prove that AC = BD . 16. In the figure, O is the centre of the circle and the chords AB = BC = CD = DE. Prove that AD = BE. 17. In the given figure, NPS, MAN and RMS are straight lines. Prove that PQRS is a cyclic quadrilateral. 18. In the adjoining figure, PQ = RS. Prove that QT = ST and PT = RT. 19. In the given figure, PQSR is a cyclic quadrilateral. PR and QS are produced to meet at T. If PQ // RS. prove that TP = TQ. A E D F C B A E D B C A P Q C B D A C D B A E D O C B A N P Q R M S P R Q T S P Q S T R

Vedanta Excel in Mathematics - Book 10 358 Approved by Curriculum Development Centre, Sanothimi, Bhaktapur Revision and Practice Time 20. In the adjoining figure, PQRS is a cyclic quadrilateral. PQ and SR are produced to meet at T. If QT = RT, prove that (i) PS // QR (ii) PR = QS. 21. In the given figure, O is the centre of the circle. Prove that ∠XOZ = 2 (∠XZY + ∠YXZ) 22. In the adjoining figure, AB = CD and BE = AD. Prove that ADBE is a parallelogram. 23. In the given figure, PS // QT and SR = ST. Prove that ∠QPS + ∠PST = 180°. 24. In the given figure, two circles intersect at the points A and D. If ABCD and AXYD are cyclic quadrilaterals, prove that BC // XY. 25. In the given figure, AP⊥BC, BR⊥AC, CQ⊥AB and O is the orthocenter of ∆ABC. Prove that ∠OPQ and ∠OPR are equal. 26. In the figure, if D, E and F are the mid-points of sides AB, AC and BC respectively and AG ⊥ BC. Prove that DEFG is a cyclic quadrilateral. 27. In the given figure; PQ = RT and SQ the bisector of ∠PQR. Prove that SQT is an isosceles triangle. P Q S T R X Z Y O A D E B C P Q R S T A B X D C Y A B C P Q R O A D B G F C E Q R S T P

Approved by Curriculum Development Centre, Sanothimi, Bhaktapur 359 Vedanta Excel in Mathematics - Book 10 Revision and Practice Time 28. a) If AC and BD are two equal chords on the opposite sides of diameter AB of a circle with centre O, prove that AC // BD. b) Two equal circles intersect each other at A and B. If a straight line PQ is drawn through A to touch the circumference of one circle at P and the other at Q, prove that BP = BQ. c) Two circles intersect at A and B. If AC and AD are the respective diameters of the circles, prove that C, B, D are collinear. d) Prove that any cyclic parallelogram is a rectangle. e) If two sides of a cyclic quadrilateral are parallel, prove that the remaining two sides are equal and the diagonals are equal. f) If two non parallel sides of a trapezium are equal, show that it is cyclic. g) Prove that the quadrilateral formed by angle bisectors of a cyclic quadrilateral ABCD is also cyclic, h) ABC is an isosceles triangle in which AB = AC. If D and E are the mid-points of AB and AC respectively, prove that the points B, C, D and E are concyclic. i) D and E are any two points on equal sides AB and AC of an isosceles triangle ABC such that AD = AE. Prove that B, C, D, E are concyclic. j) In an isosceles triangle PQR, PQ = PR. If the bisectors of ∠Q and ∠R meet PR at S and PQ at T, prove that the points Q, R, S, T are concyclic. k) Points P, Q, R and S are concyclic such that arc PQ = arc SR. If the chords PR and QS are intersecting at a point M, prove that: (i) area of DPQM = area of DSMR (ii) chord PR = chord QS l) PQRS is a cyclic quadrilateral. If the bisectors of ∠QPS and ∠QRS meet the circle at points A and B respectively, prove that AB is the diameter of the circle. Statistics 1. Mr. Chaudhary has a noodle factory. The monthly salary of the employees of his factory is given below. Salary (in Rs 000) 10-15 15-20 20-25 25-30 30-35 35-40 Number of workers 4 10 15 12 6 3 Answer the following questions. (a) How many workers are there in the factory? (b) Draw fm column. (c) Find the total amount for required for the salary in a month. (d) Calculate the average monthly salary. 2. The marks obtained by the students of class X in a Mock Test of mathematics are listed below. 22, 30, 58, 50, 38, 16, 40, 27, 35, 45, 56, 48, 42, 37, 41, 28, 18, 44, 36, 49, 62, 37, 29, 39, 32, 20, 43, 52, 40, 55 Answer the following questions. (a) What type of data is it?

Vedanta Excel in Mathematics - Book 10 360 Approved by Curriculum Development Centre, Sanothimi, Bhaktapur Revision and Practice Time (b) Construct a frequency table of class interval of 10 from the given data. (c) Calculate the average mark. (d) Are Σx and Σfm equal in this data? Give reason. 3. The age distribution of the patients admitted in a hospital during last month is given below. Age (years) 0-10 10-20 20-30 30-40 40-50 50-60 Number of patients 5 15 20 x 20 10 Answer the following questions. (a) Draw m and fm columns. (b) If the average age of the patients is 34 years, find the value of x. (c) Find the number of patients admitted in the last month. 5. The table given below shows the marks obtained by the students of class 10 of a school. Marks obtained 15-25 25-35 35-45 45-55 55-65 65-75 Number of students 2 3 9 8 7 6 Answer the following questions. (a) Construct the cumulative frequency table. (b) Find the class in which the median lies. (c) Compute the median. (d) Find the difference between the first quartile and the median. 6. The weights of teachers working in a school are given in the table below. Weight (in kg) 30-40 40-50 50-60 60-70 70-80 80-90 Number of people 1 4 20 10 3 2 Answer the following questions. (a) Construct the cumulative frequency table. (b) Find the class in which the Q1 lies. (c) Compute the first quartile. (d) Find the difference between the first and the third quartiles. 7. The people of a community organized the ‘Afforestation Program’ on March 21, the International Day of Forests. The heights of plants planted on the program are given below. Height of plants 20-25 25-30 30-35 35-40 40-45 45-50 Number of plants 6 15 24 p 12 15 Answer the following questions. (a) If the median height of the plants is 35 cm, find the class which includes the median height of the plants. (b) Draw the cumulative frequency table. (c) Find the value of p. (d) Find the difference between the median height and the third quartile height of the plants.

Approved by Curriculum Development Centre, Sanothimi, Bhaktapur 361 Vedanta Excel in Mathematics - Book 10 Revision and Practice Time 8. Based on the following data answer the questions. Wages (in Rs) 50-70 70-90 90-110 110-130 130-150 Number of workers 4 8 16 k 2 Answer the following questions. (a) If the upper quartile of the given data is Rs 114, find the class which contains the upper quartile. (b) Draw the cumulative frequency table. (c) Find the value of k. (d) Find the median wage. 9. The following data relates to the daily income of families in an urban area. Income (Rs) 500-600 600-700 700-800 800-900 900-1000 Number of families 7 12 18 16 6 Answer the following questions. (a) Find the modal class. (b) Compute the mode. (c) Compare among mean, median and mode. 10. The given table shows the pair of shoes against the shoes size sold this week in a shoes centre. The modal size is 33. Shoes size 0-10 10-20 20-30 30-40 40-50 Number of pair of shoes 25 30 37 m 33 Answer the following questions. (a) Find the modal class. (b) Find the value of m. (c) Compare among mean, median and mode. Probability 1. From a set of number cards numbered from 1 to 20, a card is drawn at random. (a) List out the cards numbered with the multiples of 4 and multiples of 7 superlatively. (b) Find the probabilities of getting a card numbered with multiple of 4 and multiple of 7 superlatively. (c) Sunayana tells that the events of getting the multiples of 4 and 7 are mutually exclusive. Is she right? Give reason. (d) Find the probability that the card is numbered with multiple of 4 or multiple of 7. 2. A card is drawn randomly from a well shuffled pack of number cards numbered from 10 to 30. (a) Make the sets of numbers numbered on the cards which are exactly divisible by 3 and exactly divisible by 8 separately.

Vedanta Excel in Mathematics - Book 10 362 Approved by Curriculum Development Centre, Sanothimi, Bhaktapur Revision and Practice Time (b) Find the separate probabilities of getting a card numbered with which is exactly divisible by 3 and divisible by 8. (c) Shashwat tells that the events of getting numbers which are exactly divisible by 3 and divisible by 8 are mutually exclusive. Is he right? Give reason. (d) Find the probability that the card having the number exactly divisible by 3 or 8. 3. A card is drawn randomly from a well shuffled pack of 52 playing cards. (a) Find the probability of getting a card of heart. (b) Find the probability of getting a card of diamond. (c) Find the probability of getting a card of heart or diamond. (d) Find the probability of getting a faced card or an ace. (e) Find the probability of getting a king card or a queen card. 4. A bag contains 5 red balls and 3 blue balls. A ball is drawn at random and replaced. After that another ball is drawn. (a) Find the probability that the first ball is blue. (b) Find the probability that the second ball is blue. (c) Are the events of getting blue balls in both draws independent events? Give reason. (d) Find the probability that both balls are blue. (e) Show the probabilities of possible outcome in tree diagram. 5. Two children are born from a married couple at the interval of 5 years, answer the following questions. (a) Draw a tree diagram to show the probabilities of possible outcomes. (b) Find the probability of getting two daughters. (c) Find the probability of getting at least one son. 6. A die is rolled and a coin is tossed together. (a) Show the probabilities of possible outcomes in a tree-diagram. (b) Find the probability of getting ‘5’ on die and head on coin. (c) Find the probability that a ‘square number’ on die and tail on coin. 7. There is one red, one blue and one white ball in a bag. A ball is drawn randomly and not replaced, and then another ball is drawn. (a) Write the sample space of the experiment using a tree diagram. (b) Find the probability of getting at least one red ball. 8. A bag contains 10 black and 6 white balls. Two balls are drawn randomly one by one without replacing the first one. (a) Draw a tree diagram to show the probabilities of possible events. (b) Find the probability that the first is black and the second is white. (c) Find the probability that both of them are of the different colour. 9. A pregnant woman is near to her delivery date. Find the probability of having (a) baby son on Wednesday of a week (b) baby daughter on Friday of a week.

Approved by Curriculum Development Centre, Sanothimi, Bhaktapur 363 Vedanta Excel in Mathematics - Book 10 Revision and Practice Time Trigonometry 1. A ladder reaches the top of a vertical wall making an angle of 60o with the ground. The foot of the ladder is at a distance of 4 feet from the base of the wall. Answer the following questions. (a) Find the height of the wall. (b) Find the length of the ladder. (c) If the ladder inclined to the wall at an angle of 45o , at what high would it touch the wall? 2. A vertical tree of height 18 m is broken by the wind so that it’s top has touched the ground by making an angle of 30o . Answer the following questions. (a) Find the height of unbroken part of the tree if the length of broken part is x metre. (b) Name the trigonometric ratio that represents the ratio of unbroken and broken parts of the tree. (c) Find the actual length of broken part of the tree. (d) At what distance has the top of the tree touched the ground from the foot of the tree? 3. A man, 1.5 m tall, observes the top of the Swoyambhu Mahachaitya Stupa of height 40 m and observes the angle of elevation of 30o . Answer the following questions. (a) Define angle of elevation. (b) Find the distance between the man and the centre of the basement of the stupa. (c) If the man moves a few meters towards the stupa, what change will be seen in the angle of elevation? 4. Based on the information given in the figure, answer the following questions. (a) Name the angle of elevation. (b) Find the height of the temple. (c) Find the length of the rope that required joining the top of the temple and the tree. 5. 7 m below from the top of the Dharahara 72 m high, a person observes the roof of the house 50 m away from the foot of the Dharahara and finds the angle of depression of 45o , answer the following questions. (a) Define angle of depression. (b) Find the value of ∠EDG. (c) Find the height of the house. (d) Calculate the length from the observation place to the roof of the house.

Vedanta Excel in Mathematics - Book 10 364 Approved by Curriculum Development Centre, Sanothimi, Bhaktapur Revision and Practice Time 6. a) A tower on the bank of a river is of height 40 m high and the angle of elevation of the top of the tower from the opposite bank is 300 . Find the width of the river. b) What will be the length of shadow of a tree 15 m high on the ground when the sun’s altitude is 450 ? Find. c) A poacher is targeting to a dove sitting on top of the 28 ft. tall pole which is situated in front of him. If the poacher fixes his catapult at the angle of 600 and does not miss his target, how far is the poacher from the foot of the pole? 7. a) The angle of elevation of the top of a tower from a point on the ground, which is 30 m away from the foot of the tower, is 300 . Find the height of the tower. b) A tree casts a shadow of length 8 3 m on the ground when sun’s elevation is 600 . Find the height of the tree. 8. a) The angle of elevation of the top of a tree from the roof of the house is 300 . If the heights of the house and the tree are 6m and 18m respectively, find the distance between the house and the tree. b) A man 5 ft. tall observes the top of a temple and finds the angle elevation 600 . If the height of the temple is 47 ft., find the distance between the man and the temple. c) A 1.5 m tall woman is standing in front of 41.5 m high tree. When observing the top of the tree, an angle of elevation of 450 is formed with the eyes. Find the distance between the tree and the woman. 9. a) A man 1.5 m tall observes the angle of elevation of the top of an electric pole and finds to be 300 . If the distance between the man and the pole is 12 m, find the height of the pole. b) From the roof of a house 6 m tall, the angle of elevation of a tower was observed and found to be 300 . If the distance between the house and tower was 14 3 m, find the height of the tower. c) A man of 2 meter height observes the angle of elevation of the top of the tree and finds to be 600 . If the distance between the man and the tree is 45m, find the height of the tree. d) A man observes the top of a pole of 51 m height, situated in front of him and finds the angle of elevation to be 300 . If the distance between man and the pole is 86 m, find the height of the man. e) A woman observes a bird sitting on the top of a tree in front her and finds the angle of elevation to be 600 . If the distance between woman and the tree is 30m and the height of tree is 53.76 m, find the height of the woman. 10. a) The angle of depression of a car parked on the road from the top of a 150 m high tower is 300 . Find the distance of the car from the foot of the tower. b) From the top of a temple 20 m high, the angle of depression of a pigeon sitting on the ground is observed and found to be 600 . How far is the pigeon from the basement of the temple?

Approved by Curriculum Development Centre, Sanothimi, Bhaktapur 365 Vedanta Excel in Mathematics - Book 10 Revision and Practice Time c) A dog sitting on the ground is 60m away from the house. If the angle of depression of the dog from the roof of the house is found to be 300 , find the height of the house. d) A pilot of an aeroplane finds the angle of depression to the top of radar tower to be 300 . At this time, if the horizontal distance of the aeroplane from the radar tower is 500 3 m, find the height of the plane. 11. a) From the top of a tower 40 m high, the angle of depression of the top of a temple 10 m high on the same level of ground was observed and found to be 300 . Find the distance between the tower and the temple. b) The heights of a house and a tree are 20 metre and 5 metre respectively. If a man observes the top of the tree from the roof of the house and finds the angle of depression to be 60°, find the distance between the house and the tree. c) From the top of a cliff 51 m high, the angle of depression of the top of a pole of height 15 m, situated in front of the cliff, was observed and found to be 450 . Find the distance between the cliff and the pole. 12. a) The angle of depression of the top of a tree as observed from the roof of the house 30 ft. high is found to be 30°. If the distance between the house and tree is 10 3 ft., find the height of the tree. b) The horizontal between two towers of different heights is 50 m. The angle of depression of the top of the first tower as seen from the top of the second tower is 300 . If the height of the second tower is 45 m, find the height of the first tower. c) From the top of a tower, the angle of depression of the roof of the house 10 m high and 40 m away from the tower was observed and found to be 300 . Find the height of the tower. d) From the roof of a house, the angle of depression of the top of the tree 20 ft. high was found to be 600 . If the distance between the house and the tree is 10 3 ft., find the height of the house. 13. a) A wire is tied at the top of an electric pole which is 12 m high. The wire is stretched and its other end is fastened on the ground. If the wire makes and angle of 300 with the ground, find the length of the wire from the ground to the top of the pole. b) A ladder, leaning against the wall of height 10 m, touches the top of the wall and makes an angle of 600 with the ground. Find the length of the ladder. 14. a) A boy who is 1.5 m tall is flying a kite. When the length of string of the kite is 200 m and it makes and angle of 300 with the horizon, find the height of the kite from the ground. b) The thread of a kite makes an angle of 600 with the horizon when a man of height 2 m flying a kite. If the length of thread is 100 3 m, what is the height of the kite from the ground? c) A girl of height 1.4 m is flying a kite from the roof of a house 33 m high. If the length of the string of the kite is 80 2 m and makes an angle of 450 with the horizon, find the height of the kite from the ground. d) On the roof of a house 10 m high, a 1.2 m tall girl is flying a kite and the kite is at a height of 128.2 m above the ground. If the string of the kite makes an angle of 30 0 with the horizon, find the length of the string. 15. a) A tree 24 m high is broken by the wind so that its top touches the ground and makes an angle of 300 with the ground. Find the length of broken part of the tree.

Vedanta Excel in Mathematics - Book 10 366 Approved by Curriculum Development Centre, Sanothimi, Bhaktapur Revision and Practice Time b) A tree of 40 m high is broken by the wind so that its top touches the ground and makes an angle of 600 with the ground. Find the length of broken part of the tree. c) If the top of a tree broken by the wind makes an angle of 450 with the ground at a distance of 10 2m from the foot of the tree, find the height of the tree before it was broken. d) A tree broken due to thunderstone forms a right angled triangle with the ground. The broken part of the tree makes an angle of 600 with ground. If the top of the tree is 15 m far from its foot, how tall was the tree before it was broken? 16. a) A man observes the top of tower of 50 3 m height from 150 m far from the foot of the tower. Find the angle of elevation of the top of the tower. b) Find the angle of elevation of the sun when the height of a tree and length of its shadow are 10 m and 10 m respectively. c) A man of height 5 ft. tall observes a bird sitting on the top of a tree which is situated in front of him. If the height of the tree is 55 ft. and the distance between the man and the tree is 50 ft., find the angel of elevation. d) The diameter of a circular pond is 48 m and a pillar of height 30 3 m is fixed at the centre of the pond. If the length of the pillar inside the water surface is 5 3 m, what will be the angle elevation when a person of 3 m tall observes the top of the pillar from the bank of the pond? 17. a) A man observes the top of a tree of height 7 m from the roof of a house 22 m high. If the distance between the tree and the house is 15m, find the angle of depression made by the man. b) A boy, on the top of 30 m high view tower, observes a 2 m tall girl standing on ground. If the girl is 48.49 m far from the foot of the tower, find the angle of depression of the girl from the eyes of the boy. 18. a) A man is 1.6 m tall and the length of his shadow is 80 cm. Find the length of shadow of a building 35 m tall at the same time of the day. b) The length of shadow of a house 30 m high is 30 3m at 3:00 p.m., find the length of shadow of the tree 20 m tall at the same time. 19. a) The shadow of a tree on the ground is found to be 20 m longer when the sun’s altitude is 450 than it is 600 . Find the height of the tree. b) Find the height of a house if the angles of elevation of its top changes from 300 to 600 as the observer advances 50 3m towards its base. c) From an aeroplane flying vertically over a straight road, the angles of depression of two consecutive kilometer stones on the same sides are 300 and 450 . At what height is the aeroplane from the ground? 20. a) A house is 28 m high. The angle of elevation of the top of a tower just in front of it from the top of the house is 300 and from the foot of the house is 600 . Find the height of the tower and the distance between the house and tower. b) From the top of a building 40 m high, the angle of elevation and angle of depression of the top and bottom of a tower are observed to be 450 and 600 respectively. Find the height of the tower.

Approved by Curriculum Development Centre, Sanothimi, Bhaktapur 367 Vedanta Excel in Mathematics - Book 10 Answers 1. Sets Exercise : 1.1 1. a) (i) 11 (ii) 5 (iii) 6 (iv) 9 (v) 2 (vi) 3 (vii) 4 (viii) 2 b) Show to your teacher. 2. a) (i) 40 (ii) 18 (iii) 8 (iv) 12 (v) 10 (vi) 48 b) (i) 20 (ii) 15 (iii) 65 (iv) 35 3. a) (i) 42 (ii) 8 (iii) 15 (iv) 17 b) (i) 15 (ii) 5 (iii) 15 (iv) 25 c) 40 5 30 15 P Q (i) 75 (ii) 5 (iii) 40 (iv) 30 d) (i) 80 (ii) 65 (iii) 0 (iv) 15 e) (i) 34 (ii) 7 (iii) 19 (iv) 22 4. a) (i) 40, 50 (ii) 0, 90 b) (i) 10, 15 (ii) 0, 25 c) (i) 100 (ii) 30 5. a) (i) 40 25 10 50 L P b) (i) 250 350 250 550 B M (ii) 115 (iii) 10 (iv) 40 (ii) 1150 (iii) 250 (iv) 550 c) (i) 30 30 20 20 B S d) 25 30 15 30 D T (ii) 600 (iii) 1500 (iv) 3750 (i) 85% (ii) 15% (iii) 25% (iv) 55% 6. a) (i) 380 (ii) 50 (iii) 330 (iv) 130 50 120 200 S G 7. a) (i) 18 x 7 25 M E b) (i) 20 x 5 65 C W (ii) 4 (iii) 22 (iv) 7 (ii) 10% (iii) 75% (iv) 70% U U U U U b) (i) 45 (ii) 5 (iii) 40 (iv) 16 5 24 A M U U U U

Vedanta Excel in Mathematics - Book 10 368 Approved by Curriculum Development Centre, Sanothimi, Bhaktapur Answers 8. a) (i) 3000 x 600 1800 M S b) (i) 20 x 15 10 E M (ii) 600 (iii) 2400 (iv) 2:3 (ii) 5 (iii) 25 (iv) 5:3 9. a) (65 – x x 10 (55 – x) F M (i) 90% (ii) 1200 (iii) 300 10. a) (i) 32 33 5 30 C A b) (i) 20 60 10 10 E M (ii) 3000 (iii) 990 (iv) 1860 (ii) 450 (iii) 135 (iv) 135 11. a) (i) 2x – 10 10 3x – 10 P H b) (i) 4x – 25 25 35 5x – 25 Y J (ii) 34 (iii) 41 (iv)32% (ii) 50 (iii) 15 (iv) 25% 12. a) 2x 50 40 x M S b) 200 x 2x 150 S W (i) 70 (ii) 60 (iii) 30 (i) 250 (iii) 200 (iv) 450 13. a) (i) 12000 1000 2000 10000 H S U b) (i) 376 (ii) 135 (iii) 326 (iv) 135 50 24 191 A O U (ii) 23000 (iii) 2000 (iv) 22000 14. a) (i) 1200 (ii) 320 (iii) 230 b) (i) 20 (ii) 180 15. a) (i) 15 (ii) 105 (iii) 60 (iv) 60 15 80 45 A B U b) (i) 20 (ii) 60 (iii) 80 c) (i) Rs 3,00,000 (ii) Rs 5,00,000 (iii) Rs 25,50,000 (iv) 40 U U b) (70 – x) x 20 (60 – x) R W (i) 50% (ii) 900 (iii) 180 U U c) 45 25 5 25 S E 800 c) (i) 45 (ii) 35 (iii) 70 (iv) 20 25 15 10 M S U U U U U U U U

Approved by Curriculum Development Centre, Sanothimi, Bhaktapur 369 Vedanta Excel in Mathematics - Book 10 Answers Exercise : 1.2 1. a) (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 (xv) 20 b) (i) 15 (ii) 10 (iii) 45 (iv) 20 (v) 75 (vi) 5 c) 2. a) 75, 25 A 10 15 10 5 10 20 5 B C b) (i) 18 (ii) 3 (iii) 15 (iv) 59 P 17 10 18 3 8 20 15 59 Q R 3. a) S 19 13 7 11 5 15 12 D A b) (i) E 20 20 10 15 30 15 5 35 M N c) S 75 60 30 15 30 30 45 G F U (i) 82 (ii) 15 (iii) 12 (iv) 46 (ii) 35 (iii) 20 (iv) 40 (i) 15 (ii) 150 (iii) 60 4. a) (i) 800 (ii) 60 (iii) T 200 140 60 50 40 60 250 100 R S (iv) 230 b) (i) 80 (ii) 5 (iii) 45 5. a) (i) N 20 15 5 20 10 15 5 E S 10 (ii) 500 (iii) 225 b) (i) F 12 25 10 15 20 5 8 T I 5 (ii) 600 (iii) 120 6. a) (i) E 7 5 2 6 3 8 10 H S (ii) 2 (iii) 41 b) (i) B 12 10 4 4 6 15 11 S F (ii) 4 (iii) 62 7. a) (i) 14 (ii) 9 (iii) C 2 9 5 4 8 3 1 F B b) (i) C 16 10 25 19 15 20 11 P S (ii) 70 (iii) 20 2. Compound Interest Exercise - 2.1 1. a) (i) CA = P T 1 + R 100 (ii) CI = P 1 + R 100 T – 1 (iii) CA = P 2T 1 + R 200 (iv) CI = P 2T 1 + R 200 – 1 (v) CA = P 4T 1 + R 400 (vi) CI = P 4T 1 + R 400 – 1 b) CA = P T 1 + R 100 . 1 + MR 1200 c) CI = P T 1 + R 100 . 1 + MR 1200 – 1 8 A 6 4 3 5 2 12 10 B C 25 34 U U U U U U U U U U U U

Vedanta Excel in Mathematics - Book 10 370 Approved by Curriculum Development Centre, Sanothimi, Bhaktapur Answers d) CA = P 1 + R1 100 1 + R2 100 1 + R3 100 2. a) Rs 408 b) Rs 4,965 3. a) Rs 100, Rs 100 b) (i) Rs 4,410 (ii) Rs 9,408 (iii) Rs 12,974.40 (iv) Rs 3,510 c) (i) Rs 1,261 (ii) Rs 3,360 (iii) Rs 1,623 (iv) Rs 385 d) (i) Rs 5,202 (ii) Rs 18,522 e) (i) Rs 2040 (ii) Rs 6,305 f) (i) Rs 22,510.18 (ii) Rs 16,810 g) (i) Rs 3,765.26 (ii) Rs 5,766.80 4. a) (i) Rs 71,500 (ii)Rs 71,662.50 (iii) Rs 71,747.84 b) (i) Rs 53,000 (ii) Rs 53,045 (iii) Rs 53,068.18 c) (i) Rs 6,800 (ii) Rs 6,936 (iii) Rs 7,006.73 5. a) Rs 1,550 b) Rs 275.40 6. a) Rs 10,692 b) Rs 16,844 c) Rs 19,091 7. a) Rs 486 b) Rs 6,305 8. a) (i) Rs 12,000 (ii) Rs 1,996.80 b) (i) Rs 30,000 (ii) Rs 5,643 c) Rs 32,000 d) Rs 24,000 9. a) 2 years b) 3 years c) 2 years 10. a) 4% p.a. b) 10% p.a. 11. a) (i) 10% p.a (ii) Rs 9,680 (iii) Rs 10,648 b) (i) 4% p.a. (ii) Rs 50,700 (iii) Rs 52,728 12. a) (i) 5% p.a. (ii) Rs 16,000 b) (i) 10% p.a. (ii) Rs 5,000 c) 12% p.a. Rs 1,25,000 13. a) 10% p.a., Rs 4,500 b) 7% p.a., Rs 5,000 14. a) (i) Rs 50,000 (ii) Rs 56,375 (iii) Less by Rs 1,375 b) (i) Rs 10,506 (ii) Rs 11,986.84 (iii) Less by Rs 182.30 15. a) (i) Rs 1,92,500 (ii) Rs 42,500 (iii) More by Rs 10,000 b) (i) Rs 1,52,320 (ii) Rs 52,320 (iii) More by Rs 24,000 16. a) 10% p.a. Rs 4,000 b) 10% p.a. Rs 12,000 17. a) Rs 3,000, Rs 7,000 b) Rs 5,000, Rs 4,000 18. a) In account Y because it gives more interest. b)) 12.75% c) 11.14% less interest 3. Population Growth and Compound Depreciation Exercise - 3.1 1. a) P T 1 + R 100 b) P 1 + R 100 T – 1 c) P 1 + R1 100 1 + R2 100 1 + R3 100 2. a) 34,020 b) 10% p.a. c) 2.1 % p.a. 3. a) 36,300 b) 3,70,440 c) 18,522 d) 32,000 e) 1,56,250 4. a) 2 years b) 2 years c) 5% p.a. d) 10% p.a. 5. a) 3,95,808 b) 24,000 c) 20,000 d) 10,000 e) 1,14,444 f) 35,937 6. a) 1,94,922 b) 27,360 7. a) 8,505 b) 7,96,875 8. a) 23.15 cm b) 2 × 102 c) Rs 21,296 d) Rs 5,12,000 Exercise - 3.2 1. P T 1 – R 100 b) P 1 – 1 – R 100 T c) P 1 – R1 100 1 – R2 100 1 – R3 100 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 7. a) 5% p.a. b) 10% p.a. c) 20% p.a. d) 12% p.a. 8. a) Rs 31,464 b) Rs 5,12,244 9. a) 10% p.a., Rs 50,000 b) 5% p.a., Rs 48,00,000 4. Currency Exchange Exercise - 4.1 1. a) Nepal Rastra Bank b) Buying rate c) EUR ( ) 1 = Rs 133.75 2. a) and b) Answer the questions yourself and show to your teacher.

Approved by Curriculum Development Centre, Sanothimi, Bhaktapur 371 Vedanta Excel in Mathematics - Book 10 Answers 3. a) (i) NRs 28,080 (ii) NRs 1,31,135.40 (iii) NRs 1,00,724.40 (iv) NRs 1,14,274.80 (v) NRs 1,04,457.60 (vi) NRs 5,030 (vii) NRs 72,668.40 (viii) NRs 1,08,190.80 b) (i) INR ( ) 1,12,500 (ii) USD ($) 1,867.22 (iii) GBP (£) 1,125.84 (iv) JPY 1,81,451.61 4. a) (i) GBP (£) 4,000 (ii) CAD ($) 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 ($) 6,180 5. a) NPR 58,820 b) (i) NPR 1,52,354.40 (ii) NPR 6,09,417.60 6. a) (i) NPR 1,05,488 (ii) USD ($) 5,000 b) (i) NPR 3,36,144 (ii) EUR ( ) 2,400 7. a) GBP (£) 2,500 b) CAD($) 10,000 8. a) NPR 5,37,544 b) NPR 10,62,432 9. a) $ 520 b) £ 60 c) 13,800 Yen d) $ 130.09 e) $ 64.04 f) QAR 1,653.44 g) $ 24.78 10. a) Nepal b) New York 11. a) (i) $ 4,500 (ii) $ 1 = NPR 126 (iii) Gain NPR 27,000 (iv) Gain NPR 15,882.35 b) (i) GBP (£) 4,125 (ii) £ 1 = NPR 144 (iii) Loss NPR 66,000 (iv) Loss NPR 71,881.19 12. a) (i) NPR 8,22,900 (ii) NPR 9,87,480 (iii) NPR 11,15,852.40 b) (i) NPR 14,17,500 (ii) 62.96% profit 13. a) (i) $ 7,830 (ii) $ 8,700 (iii) $ 8,613 b) (i) CNY 25,20,000 (ii) CNY 25,83,000 (iii) CNY 25,44,255 14. a) (i) NPR 1,05,600 (ii) NPR 1,49,160 (iii) NPR 53,697.60 (iv) NPR 30,204.90 more b) (i) £ 140 (ii) £ 184.80 (iii) £ 166.782 (iv) £ 17.094 less 5. Mensuration (I): Pyramid Exercise - 5.1 1. a) (i) a2 (ii) 2al (iii) a2 + 2al (iv) 1 3 a2 h b) 2xy sq. units c) (p2 + 2pq) sq. units d) 1 3 m2 n cu. units 2. a) (i) 60 cm2 (ii) 260 cm2 (iii) 700 cm2 (iv) 1040 cm2 b) 1020 cm2 c) 504 cm2 3. a) (i) 384 cm3(ii) 1568 cm3 (iii) 98 cu. ft. (iv) 378 cu. ft. b) 486 m3 c) 384 cm3 d) 2000 cu. ft. 4. a) 14 cm b) 21 cm 5. a) (i) 10 cm (ii) 15 cm (iii) 24 cm (iv) 8 cm b) (i) 10 cm (ii) 30 cm (iii) 8 cm (iv) 15 cm 6. a) 126 cm2 , 175 cm2 b) 240 cm2 , 340 cm2 c) 420 cm2 , 616 cm2 7. a) 60 cm2 , 96 cm2 b) 240 cm2 , 384 cm2 c) 544 cm2 , 800 cm2 d) 720 cm2 , 1296 cm2 e) 672 cm2 , 868 cm2 f) 432 cm2 , 756 cm2 8. a) 512 cm3 b) 400 cm3 c) 1280 cm3 d) 4320 cm3 9. a) (i) 24 cm (ii) 25 cm (iii) 700 cm2 b) (i) 8 cm (ii) 10 cm (iii) 384 cm2 10. a) (i) 5 cm (ii) 4 cm (iii) 48 cm3 b) (i ) 10 cm (ii) 12 cm (iii) 400 cm3 11. a) 1568 cm3 b) 1296 cm3 12. a) (i) 91445760 cu. ft. (ii) 923786.64 sq. ft. b) (i) 84 cu. ft. (ii) 65.76 sq. ft. 13. a) (i) 624 m2 (ii) Rs 74,880 b) (i) 12 ft. (ii) Rs 5,40,000 Exercise - 5.2 1. a) (i) 2pr (ii) pr2 (iii) prl (iv) pr(r + l) (v) 1 3 pr2 h (vi) r2 + h2 = l 2 b) pab c) px(x + y) d) 1 3 px2 y 2. a) (i) 550 cm2 (ii) 440 cm2 (iii) 2200 cm2 (iv) 990 cm2 b) 330 cm2 c) 1496 cm2 d) 3036 cm2 3. a) (i) 264 cm3 (ii) 1232 cm3 (iii) 8250 cm3 (iv) 17600 cm3 b) 770 cm3 c) 5544 cm3 d) 38.5 cu. ft. 4. a) 10 cm b) 7 cm c) 5 cm 5. a) 550 cm2 , 704 cm2 b) 1822.86 cm2 , 3080 cm2 c) 2310 cm2 , 3696 cm2 d) 6741.43 cm2 , 10164 cm2

Vedanta Excel in Mathematics - Book 10 372 Approved by Curriculum Development Centre, Sanothimi, Bhaktapur Answers 6. a) 1232 cm3 b) 5280 cm3 c) 1005.71 cm3 d) 12936 cm3 7. a) (i) 13 cm (ii) 12 cm (iii) 314.29 cm3 b) (i) 40 cm (ii) 50 cm (iii) 7542.86 cm2 c) (i) 14 cm (ii) 48 cm (iii) 9856 cm3 8. a) (i)7 cm (ii) 550 cm2 (iii) 1232 cm3 b) (i) 10.5 inch (ii) 452.1 sq. inch(iii) 1016.4 cu. inch 9. a) (i) 45 (ii) Rs 319 b) (i) 308000 m2 (ii) Rs 1,15,500 6. Mensuration (I): Combined Solids Exercise - 6.1 1. a) (i) a2 (ii) 4a (iii) 2al (iv) 4ah2 (v) 2al + 4ah2 (vi) a2 + 2al + 4ah2 vii) 1 3 a2 h1 (viii) a2 h2 (ix) a2 ( 1 3 h1 +h2 ) b) (i) 2al1 (ii) 2al2 (iii) 2a(l1 + l2 ) (iv) 1 3 a2 h1 (v) 1 3 a2 h2 (vi) 1 3 a2 (h1 + h2 ) 2. a) (i) 720 cm3 (ii) 864 cm3 (iii) 1584 cm3 b) (i) 270 cm3 (ii) 486 cm3 (iii) 756 cm3 c) (i) 512 cm3 (ii) 4096 cm3 (iii) 4608 cm3 3. a) 36 cm3 b) 320 cm3 4. a) 504 cm2 b) 154 cm2 5. a) (i) 60 cm2 (ii) 240 cm2 (iii) 336 cm2 b) (i) 240 cm2 (ii) 480 cm2 (iii) 864 cm2 c) (i) 260 cm2 (ii) 400 cm2 (iii) 760 cm2 6. a) 5 cm b) 1,584 cm2 c) 264 cm3 d) 1,824 cm3 7. a) Rs 4,920 b) Rs 21,600 Exercise - 6.2 1. a) (i) pr2 (ii) 2prh (iii) 2pr2 (iv) 2pr(r + h) (v) pr(3r + 2h) (vi) pr2 h (vii) 2 3 pr3 (viii) pr2 ( 2 3 r + h) b) (i) pr2 (ii) 2prh1 (iii) prl (iv) pr(2h1 + l) (v) pr(r + 2h1 + l) (vi) pr2 h1 (vii) 1 3 pr2 h2 (viii) pr2 ( h1 + 1 3 h2 ) c) (i) 2pr2 (ii) prl (iii) pr(2r + l) (iv) 1 3 pr2 h (v) 2 3 pr3 (vi) 1 3 pr2 (2r + h) 2. a) 16285.5 cm3 b) 30389.33 cm3 c) 1642.67 cm3 d) 1056 cm3 e) 5852 cm3 f) 1659.43 cm3 g) 1990.67 cm3 h) 754.29 cm3 i) 12936 cm3 j) 2200 cm3 k) 2112 cm3 l) 2310 cm3 3. a) 73.92 cm2 b) 2640 cm2 c) 198 cm2 d) 1430 cm2 4. a) (i) 15 ft (ii) 17 ft. (iii) 880 sq. ft b) (i) 33.5 m (ii) 38.03 m (iii) 2886.84 cm2 5. a) 8888 cm2 b) 3344 cm2 c) 5104 cm2 d) 1056 cm2 e) 3318.86 cm2 f) 2851.2 cm2 g) 214.5 cm2 h) 858 cm2 6. a) (i) 7 cm (ii) 1232 cm2 b) (i) 10.5 cm (ii) 4158 cm3 7. a) (i) 7 cm (ii) 718.67 cm3 b) (i) 14.5 cm (ii) 2233 cm3 8. a) 9 cm b) 7 cm 9. a) (i) 2.53 m (ii) 23.84 m3 (iii) Rs 11,918.91 b) (i) 0.7 m (ii) 5.801 m3 (iii) Rs 2,320.27 10. a) (i) 26.2944 m2 (ii) Rs 13,147.20 b) Rs 30,140 Exercise - 6.3 1. Show to your teacher 2. Show to your teacher 3. a) Rs 3,150 b) Rs 3,000 c) Rs 30,600 4. a) 10,000 l b) 6,000 l c) 9,240 l d) 11,000 l 5. a) Rs 16,500 b) Rs 52,500 6. a) (i) Rs 7,800 (ii) Rs 27,300 b) Rs 27,170 7. Rs 1,58,625 8. (i) 65 m2 (ii) 325000 l (iii) Rs 1,625 (iv) 13 days 7. Sequence and Series Exercise - 7.1 1. Answer the questions yourself and show to your teacher. 2. a) d = b – a n + 1 b) 5 3. a) 7 b) 10 c)13 d) a + nd 4. a) 10 b) 18 c) 0 d) –44 e) 4 f) 25 12 g) a2 h) a2 + b2 5. a) 50 b) –30 6. a) 14 b) 3 c) 14 d) –24 7. a) 9 b) 15 c) –9 8. a) 2 b) 25 c) 12, 16 d) 10, 30 e) 12 m, 18 m 9. a) 10, 14, 18 b) 13, 16, 19, 21 c) 3, 9, 15, 21, 27 d) –17, –27, –37, –47, –57, –67 10. a) (i) 5 (ii) 18, 23 b) (i) –9 (ii) 87, 78 c) (i) 7 (ii) 14, 21, 28 d) (i) 17 (ii) 15, 32, 49 11. a) (i) 4(ii) 4 (iii) 11, 19, 23

Approved by Curriculum Development Centre, Sanothimi, Bhaktapur 373 Vedanta Excel in Mathematics - Book 10 Answers b) (i) 8 (ii) 4 (iii) 32, 40, 48 12. a) (i) 3 (ii) 5 (iii) 4, 7, 10, 13, 16 b) (i) 5 (ii) 11 (iii) 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75 c) (i) 5 (ii) 5 (iii) 80, 85, 90, 95, 100 13. a) (i) 2, 20 (ii) 8, 14, 17 b) (i) –1, 27 (ii) 7, 11, 19,23 14. a) (i) 15 (ii) 25, 40, 55, 70, 85 b) (i) –20 (ii) 480, 460, 440, 420 Exercise - 7.2 1. a) Sn = n 2 (a + l) b) Sn = n 2 [2a + (n – 1)d] c) Sn = n 2 (n + 1) d) Sn = n2 e) Sn = n(n + 1) 2. a) 210 b) 795 c) 522 d) –1250 e) 656 f) 68 3. a) 210 b) 5050 c) 100 d) 900 e) 1640 f) 3080 4. a) 900 b) 1150 c) –600 d) –690 5. a) 540 b) 1050 c) 3500 d) 164 e) 2325 6. a) 50 b) 32 c) 200 d) –55 7. a) 65 b) 210 c) 120 d) 120 8. a) (i) –30 (ii) 8, 11 (ii) t9 + t10 + t11 = 0 b) (i) 285 (ii) 14, 15 (iii) t15 = 0 9. a) (i) a = 10, d = 5 (ii) 1885 b) (i) a = –1, d = 4 (ii) 1645 10. a) (i) a = 5, b = 5 (ii) 275 b) (i) a = 1 2 , d = 1 (ii) 200 11. a) (i) a = –19, d = 7 (ii) 1625 b) (i) a = 2, d = 3 (ii) 610 c) (i) a = –1, d = 9 4 (ii) 650 12. a) (i) Rs 4,80,000, Rs 4,85,000, Rs 4,90,000, ...(ii) Rs 24,50,000 b) (i) 200 kg, 250 kg, 300 kg, ... (ii) 24.5 quintal 13. a) (i) 2000 (ii) 500 (iii) 42500 b) (i) 10000 (ii) 2000 (iii) 360000 14. a) (i) 77 (ii) 8 b) (i) Rs 52,250 (ii) 12 Exercise - 7.3 1. a) Answer the questions yourself and show to your teacher. b) ab c) 9 2. a) r = 1 b n+1 a b) 2 3. a) 7 b) 9 c) 1 4 d) mn = arn 4. a) 4 b) 6 c) 10 d) 18 e) 20 f) 4 9 g) 2 h) 3 5. a) 10 b) 18 6. a) 12 b) 15 7. a) 6 b) 22 8. a) 2 b) 45 c) 24, 15 d) 250, 130 9. a) 6, 18, 54 b) 6, 12, 24, 48 c) 4, 2, 1, 1 2 , 1 4 d) 3 2 , 1, 2 3 10. a) (i) 3 2 (ii) 12, 18 b) (i) – 1 5 (ii) –25, 5 c) (i) 2 (ii) 12, 24, 48 d) (i) 2 (ii) 1 4, 1 2 , 1 11. a) (i) 2 (ii) 3 (iii) 8, 16 b) (i) 1 2 (ii) 3 (iii) 24, 6 12. a) (i) 2 (ii) 5 (iii) 2, 4, 8, 16, 32 b) (i) 2 (ii) 4 (iii) 30, 60, 120, 240 13. a) (i) a = 5, b = 3125 (ii) 125 b. (i) a = 4, b = 972 (ii) 36, 108 14. a) 2, 8 or 8, 2 b) 8, 18 or 18, 8 15. a) (i) R = 1.1 (ii) Rs 11,000, Rs 12,100, Rs 13,310 b) (i) 1.2 (ii) Rs 60,000, Rs 72,000, Rs 86,400 Exercise - 7.4 1. a) Sn = a(rn – 1) r – 1 b) Sn = lr – a r – 1 2. a) 63 b) 765 c) 1094 d) 1705 e) 211 f) 16,808 3. a) 1020 b) 4004 4. a) 252 b) 1820 c) 126 d) 364 5. a) 364 b) 765 c) 728 d) 555.555 6. a) (i) 5 (ii) 7 b) (i) 2 (ii) 6 c) (i) 144 (ii) 5 7. a) (i) 5 (ii) 400 b) (i) 5 (ii) 324 8. a) (i) a = 2, r = 2 (ii) 256 (iii) 2046 b) (i) a = 96, r = 1 2 (ii) 12 (iii) 189 9. a) (i) 51150 (ii) 204750 b) (i) 30 cm (ii) 31 cm 10. a) (i) 5 (ii) 2560 b) (i) Rs 300 (ii) Rs 9,600 11. a) (i) 315 (ii) 381 (iii) Shop-II sold 66 more mobile sets b) (i) Rs 11,500 (ii) Rs 10,230 (iii) Option-I, Rs 1,270 more

Vedanta Excel in Mathematics - Book 10 374 Approved by Curriculum Development Centre, Sanothimi, Bhaktapur Answers 8. Quadratic Equation Exercise : 8.1 1. Answer the questions yourself and show to your teacher. 2. a) ±1 b) –2, 3 c) 3, – 1 2 d) 5 2 , 2 5 e) 0, 1 2 f) 0, 4 3 3. a) ±3 b) ±2 c) ±4 3 d) ±5 2 e) ±6 f) ±9 g) ±8 5 h) ±10 7 i) ±3 j) ±4 3 k) ±5 6 l) ±7 8 4. a) x2 – 8x + 15 = 0 b) x2 – x – 6 = 0 c) x2 + 6x + 8 = 0 d) x2 – x – 12 = 0 5. a) 0, 4 b) 0, 5 c) 0, 4 d) –1, –2 e) –3, –4 f) 1, 2 g) 3, 5 h) –3, 4 i) 1, 1 2 j) 4, – 2 3 k) –3, 7 5 l) 7, 3 2 6. a) – 1 2 , – 2 3 b) 3 , 1 3 c) 5 2 3 , 3 2 7. a) 4, 3 b) 3, 2 c) 0, 2 d) 2, 1 3 e) 5, –1 f) 0, 4 g) 0, 5 h) 4, 11 2 8. a) ±4, b) ± 5 c) –1, 2 d) –1, 2 e) 5, 5 2 f) 0, 4 9. Do yourself and show to your teacher. 10. a) 10 b) 10 Exercise : 8.2 1. a) 1, –3 b) 1, –7 c) 9, –1 d) 14, –4 e) 1 6 , – 7 6 f) 1, 1 5 2. a) 2, –3 b) 3, 4 c) –2, 5 d) 3, 7 e) 5, –4 f) –8, 3 3. a) 2, 1 b) 2, –4 c) 2, –5 d) 3, –1 e) 3, 4 f) –7, 4 g) 1 2 , 3 h) –2, 1 3 i) – 2 3 , 3 2 j) 3, 1 3 k) –7 5 , 3 l) –a 5 , a 3 m) 2, 4 n) 1 3 , 1 3 o) –1, 5 p) 4, 11 2 q) 6, 40 13 r) 1, – 1 4 Exercise : 8.3 1. Answer the questions yourself and discuss in the class. Then show to your teacher. 2. a) –1, –2 b) –2, –3 c) 2, –3 d) 2, 1 2 e) 2, 4 3 f) 3 2 , 5 3. a) ±2 b) ±3 c) ±4 d) ±2 5 e) 0, 1 f) 0, 3 g) 0, – 1 2 h) 0, – 2 3 4. a) 1, 2 b) 2, 3 c) 1, –3 d) 2, –4 e) 0, 5 f) 0, –14 g) –1, – 1 2 h) 3, – 7 3 i) –2, – 5 3 j) 5, – 5 2 k) 1, 6 l) 9 10 , – 5 6 5. a) 4, 4 3 b) 9 ± 33 2 c) 2, –3 d) ±9 e) 5, 5 2 f) 3, 4 3 g) 0, 4 h) 0, 1 2 6. a) (i) 80 (ii) Rs 155 b) (i) 2 hours (ii) 55 km/hr 7. Complete your project work in a group or individually. Discuss the outcomes in the class. Exercise : 8.4 1. a) 3 b) 5 c) 8 2. a) 8 b) 3 c) 4 d) 6 e) 6 f) 8 g) 2 3. a) 5 b) 4 c) 7, 8 d) 8, 10 e) 7, 9 4. a) 10 b) 3, 7 5. a) 30

Approved by Curriculum Development Centre, Sanothimi, Bhaktapur 375 Vedanta Excel in Mathematics - Book 10 Answers years b) 20 years, 10 years 6. a) 6, 4 b) 14, 4 c) 8, 5 d) 8, 3 7. a) 8, 2 b) 7, 3 c) 6, 8 d) 5, 7 8. a) 63 or 36 b) 43 or 34 c) 54 d) 38 e) 92 f) 24 g) 24h) 36 i) 64 j) 35 9. a) 2 years b) 6 years 10. a) 17 years , 12 years b) 9 years, 7 years c) 16 years, 9 years d) 17 years, 13 years e) 9 years, 4 years. f) 12 years, 6 years g) 10 years, 6 years h) 15 years, 10 years i) 29 years, 5 years j) 25 years, 4 years 11. a) 9 m, 7 m b) 56 m c) 9 m, 7 m d) 19 m, 13 m e) 3m f) 8 m, 5 m 12. a) 6 cm, 8 cm, 10 cm b) 3 cm, 4 cm c) 6 cm, 8 cm d) 15 cm, 20 cm, 25 cm 13. a) (i) 12 years (ii) 75 % b) (i) 24 years (ii) 75% 14. a) (i) 10 m (ii) 100%b) (i) 30 m × 24 m (ii) 20% 15. a) (i) Rs 60 (ii) 33 1 3 % b) (i) Rs 40 (ii) 25% 16. a) (i) 20 (ii) 4% b) (i) 10 (ii) 25% c) (i) 40 km/hr (ii) 1 hr more 9. Simplification of Rational Expressions Exercise - 9.1 1. a) 0 b) 1 c) 1 – x 1 + x d) a3 a2 – 1 e) x2 (x + y)2 f) a (a – x)2 2. a) 2a3 a2 – b2 b) 2q3 p2 – q2 c) b2 – a2 (x + b) (x – a) d) 20 (x + 6) (x + 4) e) 8m m2 – 4 f) 8y 25 – y2 3. a) 1 ab b) x + y xy c) p + 2 2p d) c2 + cd + d2 cd e) n2 + 7n + 49 7n f) 1 (x – y) (y – z) 5. a) 0 b) 9 (x + 2) (x – 3) (x – 4) c) 5 (a – 3)(a – 4) (a – 5) d) x + 4 (x + 2) (2x – 1) 6. a) 2 (1 – x) (x – 2) b) 2 (1 – a) (a – 2) c) 3x – 7 (x – 2) (x – 3) d) 5 (a – 3) (a – 4) (a – 5) 7. a) 2x x + 2 b) 4 a + b c) 8xy3 x4 – y4 d) 2ab a2 – b2 e) 2 x2 – 1 f) 8x2 y2 x4 – y4 8. a) – 4x (1 + x2 + x4 ) b) 2(x – 3) (x2 – 3x + 9) c) 2(x – y) x2 – xy + y2 d) 4 1 + a2 + a4 e) 2(2a – b) 4a2 – 2ab + b2 f) 2(3x – 1) 9x2 – 3x + 1 9. a) 1 b) 1 10. a) 3 x 1 – x b) 2 y x – y c) a 2(1 – a) d) x 2(x – 1) 12. Do yourself and show to your teacher. 10. Exponentiation Equations Exercise - 10.1 1. a) x = m + n b) x = p + q – r c) y = m – n + p d) m = n n – 1 2. a) 2 b) 2 c) 0 d) 3 3. a) –3 b) 7 c) 4 d) 5 4. a) 8 b) 3 2 c) 2 d) 5 e) –2 f) 2 g) 3 h) –2 i) 7 2 j) –2 k) – 2 5 l) – 1 3 5. a) 3 b) 5 c) –3 d) 8 e) 4 f) 5 g) – 1 2 h) 2 6. a) 3 b) 3 c) 0 d) 1 e) 0 f) –2 g) 1 h) 2 i) –4

Vedanta Excel in Mathematics - Book 10 376 Approved by Curriculum Development Centre, Sanothimi, Bhaktapur Answers j) –3 k) 1 l) 1 m) –2 n) 3 o) 2 7. a) –2 b) 1 c) 5 d) 0 e) 3 2 f) 1 3 8. a) ± 2 b) ±2 c) ±2 d) ±1 e) 1, 3 f) 1, 2 g) 0, –3 h) ±1 9. a) 2, 3 b) 1, 2 c) 1, 2 d) 1, 2 e) 1, 2 f) ±2 g) 0, 1 h) 1, 2 i) –1, 2 10. a) 2 years b) 3 years 11. a) (i) 1, 2 b) (i) 0, 1 12. a) (i) 5 × 2x = 4x + 4 (ii) 0, 2 (iii) 1 m2 or 16 m2 (iv) 5 m2 or 20 m2 b) (i) 42 – x + 4x – 1 = 5 (ii) 1, 2 (iii) 1 aana or 4 aana (iv) 4 aana or 1 aana c) (i) 30 (ii) 4 Exercise - 10.2 4. a) x = 1, y = 2 or x = 2, y = 1 b) m = 1, n = 3 or m = 3, n = 1 11. Geometry: Area of triangles and quadrilaterals Exercise - 11.1 1. Answer the questions yourself and show to your teacher. 2. a) 112 cm2 b) 32 cm2 c) 240 cm2 d) 270 cm2 3. a) 45 cm2 b) 8 cm2 c) 9 cm2 d) 40 cm2 e) 20 cm2 f) 20 cm2 g) 25 cm2 h) 54 cm2 4. a) 50 cm2 b) 50 cm2 c) 35 cm2 12. Geometry: Construction Exercise - 12.1 Show to your teacher. 13. Geometry: Circle Exercise - 13.1 1. to 4. Answer the questions yourself and show to your teacher. 5. a) (i) 60° (ii) 300° b) (i) 150° (ii) 210° 6. a) (i) 80° (ii) 40° c) (i) 68° (ii) 34° 7. a) 20° b) 42° c) 65° d) 41° Exercise - 13.2 1. and 2. Answer the questions yourself and show to your teacher. 3. a) 75°, 75° b) 140° c) 110° d) 62° e) 55° f) 60° g) 50° h) 140° i) 75° j) 30° k) 78°, 39° l) 52°, 104° m) 40° n) 18°, 42° o) 35°, 55° p) 25°, 25° 4. a) 50° b) 110° c) 122° d) 120° 5. a) 158°, 101° b) 60° c) 110° d) 108° e) 48° f) 90° g) 60° h) 70° i) 38°, 49° j) 110° k) 36° l) 85°, 35° 6. a) 75°, 30° b) (i) 140 (ii) 80° (iii) 140° c) 65° d) 20° 14. Statistics Exercise - 14.1 1. a) 30 b) 40 2. a) 37 b) 125 cm 3. a) 5 b) 5 4. a) 13 b) 20 5. a) 30 b) 18 6. a) 5 b) 11 7. a) 250 b) 480 8. a) 10 b) 12 c) 5 9. a) 40, 50 b) 5, 35 10. a) 24 b) 43 c) 75 d) 50.64 11. a) 28.6 b) 45 12. a) 10 b) 20 c) 12 Exercise - 14.2 1. and 2. Answer the questions yourself and show to your teacher. 3. a) 26 b) 42.5 c) 41.67 d) 40 4. a) (30 – 40) b) (25 – 35) c) (65 – 80) d) (60 – 70) 5. a) (ii) 30 - 40 (iii)35 b) (ii) 60 - 70 (iii) 70 c) (ii) 90 - 120, (iii) 93.6 d) (ii) 20 - 30 (iii) 26 6. a) (ii) 30 - 40 (iii) 33.5 b) (ii) 25 - 35 (iii) 34

Approved by Curriculum Development Centre, Sanothimi, Bhaktapur 377 Vedanta Excel in Mathematics - Book 10 Answers 7. a) (ii) 20-30 (iii) 10 (iv) 65% b) (ii) 30-40 (iii) 4 (iv) 57.14 8. a) (ii) 20-30 (iii) 28.5 b) (ii) 65-80 (iii) 67.5 c) (ii) 200-300 (iii) 294.4 d) (ii) 30-40 (iii) 32.5 9. a) (ii) 40-50 (ii) 47.92 b) (ii) 45-60 (iii) 55 c) (ii) 52-56 (iii) 53.75 e) (ii) 60 - 80 (iii) 70 10. a) Rs 14.17 b) 36 c) 45 11. a) (ii) 20-30 (iii) 6 (iv) 78.26% b) (ii) 20-30 (iii) 5 (iv) 50% Exercise - 14.3 1. Answer the questions yourself and show to your teacher. 2. a) 70 - 80 b) 30 - 45 c) 160 - 165 3. a) 60 b) 50 c) 2 4. a) 37 b) 13.5 c) 26.5 d) 34.5 e) 26.33 f) 45.33 5. a) (i) 10-12 (ii) 11 years b) (i) 20-30 (ii) 28 c) (i) 400-600 (ii) Rs 520 6. a) 24 b) 47 7. a) (i) 40 - 60 (ii) 12 (iii) 22 b) (i) 45 - 60 (ii) 15 (iii) 5.36 % 15. Probability Exercise - 15.1 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 ∩ B) 3. a) 5 6 b) 2 3 c) 3 13 d) 0.5 e) (i) 4 5 (ii) 1 5 4. a) 1 2 b) 7 25 c) 3 8 d) 0.45 5. a) 2 13 b) 1 13 c) 2 13 d) 11 13 e) 1 13 f) 3 4 g) 1 2 h) 3 26 i) 11 13 j) 12 13 6. a) (i) 1 3 (ii) 1 2 (iii) 2 3 (iv) 2 3 (v) 2 3 b) 13 36 7. a) (i) 1 3 (ii) 3 10 (iii) 7 30 (iv) 8 15 b) 11 34 c) 16 21 8. a) (i) 2 3 (ii) 5 9 (iii) 2 9 b) 7 10 9. a) 8 13 b) 4 13 c) 7 13 d) 4 13 10. a) (i) 2 5 (ii) 1 3 (iii) 1 2 (iv) 4 5 b) 6 11 c) 7 11 d) 1 3 e) 4 9 Exercise - 15.2 1. b P(A ∩ B) = P(A) × P(B) c) P(X ∩ Y ∩ Z) = P (X) × P(Y) × P(Z) d) Independent 2. a (i) 1 4 ii) 1 4 iii) 3 4 iv) 3 4 b) 1 12 c) 3 65 d) 10 13 3. a) 1 169 b) 1 676 (ii) 144 169 (iii) 1 169 (iv) 12 169 (v) 1 2 4. a) (i) 9 25 (ii) 4 25 (iii) 6 25 (iv) 4 25 (v) 9 25 b) (i) 35 256 (ii) 1 16 (iii) 45 128 (iv) 5 64 (v) 121 256 c) 14 27 5. a) 0.98 b) 3 5 Exercise - 15.3 Possible out comes = {H1 H2 , H1 T2 , T1 H2 , T1 T2 } 1. a) H T H P(T1 H2 )= 1 2 × 1 2 = 1 4 P(H1 T2 )= 1 2 × 1 2 = 1 4 P(H1 H2 )= 1 2 × 1 2 = 1 4 P (T1 T2 ) = 1 2 × 1 2 = 1 4 T H T P(H1 ) = 1 2 P(H1 ) = 1 2 P(H2 ) = 1 2 P(T2 ) = 1 2 P(H2 ) = 1 2 P(T2 ) = 1 2

Vedanta Excel in Mathematics - Book 10 378 Approved by Curriculum Development Centre, Sanothimi, Bhaktapur Answers (i) 3 4 2. a) S D S P(D1 S2 ) = 1 4 P(S1 D2 ) = 1 4 P(S1 S2 ) = 1 4 P (D1 D2 ) = 1 4 D S D P(S1 ) = 1 2 P(D1 ) = 1 2 P(S2 ) = 1 2 P(D2 ) = 1 2 P(S2 ) = 1 2 P(D2 ) = 1 2 P(H1 H2 H3 ) = 1 8 P(H1 H2 T3 ) = 1 8 P(H1 T2 H3 ) = 1 8 P(H1 T2 T3 ) = 1 8 P(T1 H2 H3 ) = 1 8 P(T1 H2 T3 ) = 1 8 P(T1 T2 H3 ) = 1 8 P(T1 T2 T3 ) = 1 8 H T H T H T H T H T H T H T P(H1 ) = 1 2 P(T1 ) = 1 2 P(T2 ) = 1 2 P(T2 ) = 1 2 P(T3 ) = 1 2 P(T3 ) = 1 2 P(T3 ) = 1 2 P(T3 ) = 1 2 P(H2 ) = 1 2 P(H2 ) = 1 2 P(H3 ) = 1 2 P(H3 ) = 1 2 P(H3 ) = 1 2 P(H3 ) = 1 2 b) (i) 1 8 (ii) 3 8 (iii) 1 2 (iv) 1 2 v) 3 8 (i) 1 4 b) S D S P(D1 S2 ) = 1 4 P(S1 D2 ) = 1 4 P(S1 S2 ) = 1 4 P (D1 D2 ) = 1 4 D S D P(S1 ) = 1 2 P(D1 ) = 1 2 P(S2 ) = 1 2 P(D2 ) = 1 2 P(S2 ) = 1 2 P(D2 ) = 1 2

Approved by Curriculum Development Centre, Sanothimi, Bhaktapur 379 Vedanta Excel in Mathematics - Book 10 Answers c) S D S P(D1 S2 ) = 1 4 P(S1 D2 ) = 1 4 P(S1 S2 ) = 1 4 P (D1 D2 ) = 1 4 D S D P(S1 ) = 1 2 P(D1 ) = 1 2 P(S2 ) = 1 2 P(D2 ) = 1 2 P(S2 ) = 1 2 P(D2 ) = 1 (i) 2 1 4 d) P(S1 S2 S3 ) = 1 8 P(S1 S2 D3 ) = 1 8 P(S1 D2 S3 ) = 1 8 P(S1 D2 D3 ) = 1 8 P(D1 S2 S3 ) = 1 8 P(D1 S2 D3 ) = 1 8 P(D1 D2 S3 )= 1 8 P(D1 D2 D3 ) = 1 8 S D S D S D S D S D S D S D P(S1 ) = 1 2 P(D1 ) = 1 2 P(D2 ) = 1 2 P(D2 ) = 1 2 P(D3 ) = 1 2 P(D3 ) = 1 2 P(D3 ) = 1 2 P(D3 ) = 1 2 P(S2 ) = 1 2 P(S2 ) = 1 2 P(S3 ) = 1 2 P(S3 ) = 1 2 P(S3 ) = 1 2 P(S3 ) = 1 2 (i) 7 8 e) (i) 1 2 (ii) 1 8 (iii) 7 8 P(S1 S2 S3 ) = 1 8 P(S1 S2 D3 ) = 1 8 P(S1 D2 S3 ) = 1 8 P(S1 D2 D3 ) = 1 8 P(D1 S2 S3 ) = 1 8 P(D1 S2 D3 ) = 1 8 P(D1 D2 S3 ) = 1 8 P(D1 D2 D3 ) = 1 8 S D S D S D S D S D S D S D P(S1 ) = 1 2 P(D1 ) = 1 2 P(D2 ) = 1 2 P(D2 ) = 1 2 P(D3 ) = 1 2 P(D3 ) = 1 2 P(D3 ) = 1 2 P(D3 ) = 1 2 P(S2 ) = 1 2 P(S2 ) = 1 2 P(S3 ) = 1 2 P(S3 ) = 1 2 P(S3 ) = 1 2 P(S3 ) = 1 2

Vedanta Excel in Mathematics - Book 10 380 Approved by Curriculum Development Centre, Sanothimi, Bhaktapur Answers 3. a) 3R 5W 3R P(W1 R2 ) = 15 64 P(R1 W2 ) = 15 64 P(R1 R2 ) = 9 64 P (W1 W2 ) = 25 64 5W 3R 5W P(R1 ) = 3 8 P(W1 ) = 5 8 P(R2 ) = 3 8 P(W2 ) = 5 8 P(R2 ) = 3 8 P(W2 ) = 5 8 b) 6B 4W 6B P(W1 B2 ) = 6 25 P(B1 W2 ) = 6 25 P(B1 B2 ) = 9 25 P (W1 W2 ) = 4 25 4W 6B 4W P(B1 ) = 6 10 P(W1 ) = 4 10 P(B2 ) = 6 10 P(W2 ) = 4 10 P(B2 ) = 6 10 P(W2 ) = 4 10 (i) 13 25 (ii) 12 25 P(R1 W2 ) + P(W1 R2 ) = 15 32 c) 4K 4K P(K1 K2 ) = 12 169 P(K1K2 ) = 12 169 P(K1 K2 ) = 1 169 P (K1 K2 ) = 144 169 4K P(K1 ) = 4 52 P(K2 ) = 4 52 P(K2 ) = 4 52 (i) 1 169 48K P(K1 ) = 48 52 P(K2 ) = 48 52 P(K2 ) = 48 52 48K 48K 4. Show to your teacher. 5. a) Sample space {B1 B2 , B1 W2 , W1 B2 , W1 W2 } 8B 5W 7B P(W1 B2 ) = 10 39 P(B1 W2 ) = 10 39 P(B1 B2 ) = 14 39 P (W1 W2 ) = 5 38 5W 8B 4B P(B1 ) = 8 13 P(W1 ) = 5 13 P(B2 ) = 7 12 P(W2 ) = 5 12 P(B2 ) = 8 12 P(W2 ) = 4 12

Approved by Curriculum Development Centre, Sanothimi, Bhaktapur 381 Vedanta Excel in Mathematics - Book 10 Answers b) 3R 4B 2R P(B1 R2 ) = 2 7 P(R1 B2 ) = 2 7 P(R1 R2 ) = 1 7 P (B1 B2 ) = 2 7 4B 3R 3B P(R1 ) = 3 7 P(B1 ) = 4 7 P(R2 ) = 2 6 P(B2 ) = 4 6 P(R2 ) = 3 6 P(B2 ) = 3 6 6. a) (i) 35 132 (ii) 15 22 (iii) 35 66 (iv) 31 66 7B 5W 6B P(W1 B2 ) = 35 132 P(B1 W2 ) = 35 132 P(B1 B2 ) = 7 22 P (W1 W2 ) = 5 33 5W 7B 4W P(B1 ) = 7 12 P(W1 ) = 5 12 P(B2 ) = 6 11 P(W2 ) = 5 11 P(B2 ) = 7 11 P(W2 ) = 4 11 b) (i) 2 9 (ii) 7 15 (iii) 17 45 (iv) 1 15 (v) 14 45 7. a) (i) 3 95 (ii) 35 38 b) (i) 1 221 (ii) 11 221 (iii) 95 663 (iv) 1 663 c) 38 85 P(R1 ) = 3 10 P(B1 ) = 5 10 P(Y1 Y2 ) = 1 45 P(Y1 B2 ) = 1 9 P(Y1 ) = 2 10 P(Y2 ) = 1 9 P(Y2 ) = 2 9 P(B2 ) = 4 9 P(R2 ) = 3 9 P(B2 ) = 5 9 P(R2 ) = 3 9 3R 4B 2Y P(R2 ) = 2 9 P(R2 ) = 5 9 P(Y2 ) = 2 9 3R 5B 2Y 3R 5B 1Y 2R 5B 2Y P(Y1 R2 ) = 1 15 P(B1 Y2 ) = 1 9 P(B1 B2 ) = 2 9 P(B1 R2 ) = 1 6 P(R1 Y2 ) = 1 15 P(R1 B2 ) = 1 6 P(R1 R2 ) = 1 15

Vedanta Excel in Mathematics - Book 10 382 Approved by Curriculum Development Centre, Sanothimi, Bhaktapur Answers 16. Trigonometry Exercise - 16.1 1. and 2. Answer the questions yourself and show to your teacher. 3. 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 4. a) 60° b) 30° c) 45° d) 60° 5. a) (i) Angle of elevation (ii) 30 3 m (iii) ∠ACB becomes larger (iv) ∠ACB becomes smaller b) (i) Angle of depression (ii) 30° (iii) 20 3 m (iv) ∠DAC becomes larger 6. a) (i) ∠CAE (ii) 30 ft, 3 ft (iii) 33 ft (iv) ∠CAE becomes larger b) (i) ∠CAE (ii) 42 m (iii) 14 3 m 7. a) 60 m b) 36 3 m c) 40 3 m d) 20 3 m e) 12.5 m f) 15 3 m g) 150 2 m h) (i) 6.5 m (ii) 3.75m 8. a) 10 3 m b) 60 3 m c) 20.2m 9. a) 8 3 m b) 174.8m c) 2.35m d) 53 m e) 45 3 m 10. a) 17.6m b) 95m 11. a) 71.7 m b) 80.2 m 12. a) 30° b) 30° c) 45° 13. a) 21.73m b) 6.5m c) 12m 14. a) 109.28m b) 400m Revision and Practice Time Set 1. a) n(U) = 2000, n(P) = 1125, n(J) = 750, n(P ∪ J) = 250 b) 1750 c) 1000 125 250 625 P J , 1000 d) 1875 2. a) 40 b) 60 c) 15, 30 10 25 15 C B d) 3 : 4 3. a) 90% b) 70% c) 20% , 40% 20% 30% 10% M S d) 80% U U U

Approved by Curriculum Development Centre, Sanothimi, Bhaktapur 383 Vedanta Excel in Mathematics - Book 10 Answers 16. Trigonometry Exercise - 16.1 1. and 2. Answer the questions yourself and show to your teacher. 3. 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 4. a) 60° b) 30° c) 45° d) 60° 5. a) (i) Angle of elevation (ii) 30 3 m (iii) ∠ACB becomes larger (iv) ∠ACB becomes smaller b) (i) Angle of depression (ii) 30° (iii) 20 3 m (iv) ∠DAC becomes larger 6. a) (i) ∠CAE (ii) 30 ft, 3 ft (iii) 33 ft (iv) ∠CAE becomes larger b) (i) ∠CAE (ii) 42 m (iii) 14 3 m 7. a) 60 m b) 36 3 m c) 40 3 m d) 20 3 m e) 12.5 m f) 15 3 m g) 150 2 m h) (i) 6.5 m (ii) 3.75m 8. a) 10 3 m b) 60 3 m c) 20.2m 9. a) 8 3 m b) 174.8m c) 2.35m d) 53 m e) 45 3 m 10. a) 17.6m b) 95m 11. a) 71.7 m b) 80.2 m 12. a) 30° b) 30° c) 45° 13. a) 21.73m b) 6.5m c) 12m 14. a) 109.28m b) 400m Revision and Practice Time Set 1. a) n(U) = 2000, n(P) = 1125, n(J) = 750, n(P ∪ J) = 250 b) 1750 c) 1000 125 250 625 P J , 1000 d) 1875 2. a) 40 b) 60 c) 15, 30 10 25 15 C B d) 3 : 4 3. a) 90% b) 70% c) 20% , 40% 20% 30% 10% M S d) 80% 4. a) 375 b) 450 c) 175, 275 100 75 50 C V d) 325 5. a) 80 b) 40 c) 40 20 20 120 T I , 60 d) 2 : 1 6. a) 24 b) 16 c) 56 d) 5: 7 7. a) 30 50 10 4 E M b) 40 c) 16 d) 16 8. a) 40 20 30 F M 10 b) 90% c) 750 d) 225 9. a) 150 b) 30 c) 110 30 40 N J 10. 10 30 20 80 E N , 80, 10 11. 100 5 30 W S a) 5 b) 35 c) 105 d) 130 12. (i) 8 (ii) 256 (iii) 256 U 24 8 12 Q D 13. a) 210 b) 75, 45 75 75 15 T C c) 120 14. 30 10 40 15 M S a) 30 b) 40 c) 70 d) 85 15. a) 24 b) 16 c) 26 d) 10 14 16 M S 16. a) 33 b) 42 c) 45 d) 27 15 18 S M 17. a) 110 b) 30 20 50 10 M S 18. a) 180 b) 25% 20% 30% 25% F B 19. 30 15 5 10 Z G , 15 20. 36 U U U U U U U U U U U U U U

Vedanta Excel in Mathematics - Book 10 384 Approved by Curriculum Development Centre, Sanothimi, Bhaktapur Answers 21. a) 50 b) 80 22. a) 70 b) 30 23. a) 100 b)180 c) 50 100 130 20 A B 24. a) 38 b)32 c) 18 20 12 10 C F 25. a) 30 20 4 6 M S b) 60 c) 20 d) 50 26. a) 20 b) 60 27. a) 5 b) M 20 5 5 10 15 20 25 S H c) 65 d) 30 28. M 35 60 12 18 22 10 5 13 P C a) 153 b) 108 c) 27 d) 22 29. a) E 80 60 5 10 20 10 15 70 J K b) 230 c) 260 d) 40 Compound interest 1. a) Rs 1,60,000 b) Rs 1,68,000 c) Rs 1,72,405 d) 5% more 2. a) Rs 77,500 b) Rs 78,812.50 c) Rs 79,846.71 d) 3.03% more 3. a) Rs 1,60,000 b) Rs 1,600 c) Rs 881 d) Bina made Rs 719 more profit than Mina 4. a) Rs 55,000 b) Rs 14,850 c) Rs 18,205 d) 22.59% 5. a) Rs 12,000 b) Rs 5,280 c) Rs 5,569.20 d) 5.19% 6. a) Rs 45,000 b) Rs 55,000 c) Rs 10,800 d) Rs 66,550 7. a) 10% b) Rs 20,000 c) Rs 6,620 8. a) 10% b) Rs 1,60,000 c) Rs 24,800 9. a) Rs 2,000 b) Rs 400 c) 4.76% 10. a) Rs 22,000 b) 2.2 years 11. a) Rs 30,750 b) Rs 34,336.11 c) Rs 2,086.11 12. b) Rs 45,900 c) Rs 5,900 d) Rs 2,500 more 13. a) Rs 30,000 b) Rs 33,300 14. a) Rs 12,750 b) 4% 15. a) Rs 50,000 b) Rs 1,575 more Population Growth and Depreciation 1. a) 50000 b) 73205 2. a) 113300 b) 116699 3. 10,000 4. a) 6500 b) 6760 c) 6490 (approx.) 5. a) 4 % b) 16900 c) 19845 6. a) Rs 3,24,000 b) 20% p.a. 7. a) 20% b) Rs 60,000 c) 4 yrs 8. a) Rs 4,750 b) Rs 6,709.38 c) Rs 4,294 d) Rs 1,140.59 Money Exchange 1. a) selling rate b) $ 2500 c) $ 33000 d) Rs 5,17,524 2. a) ¤ 4400 b) NPR 128.75 c) Rs 16,500 d) Rs 31,025.64 3. a) 260000 ¥ b) 260000 ¥ c) 257425.74 ¥ 4. a) NPR 60,000 b) NPR 7,50,000 c) NPR 9,00,000 d) NPR 10,17,000 Mensuration 1. a)260 cm2 b) 360 cm2 c) 12 cm d) 400 cm3 2. a) 512 cm3 b) 10 cm c) 320 cm2 d) 80% 3. a) 24 cm b) 868 cm2 c) 22.96 cm d) 1500.05 cm3 4. 864 cm2 5. 384 cm3 6. 1568 cm3 7. 384 cm2 , 384 cm3 8. 6000 cm3 9. a) 6.24 m2 , 1.104 m3 b) 2112 cm3 c) 216 cm2 10. a) 12 ft. b) 8 ft. c) 1200 sq. ft. d) Rs 4,80,000 11. a) 2464 cm2 , 7392 cm3 b) 858 cm2 , 1950.67 cm3 c) 880 cm2 , 1913.19 cm3 12. Rs 2,860 U U U U U U U U

Approved by Curriculum Development Centre, Sanothimi, Bhaktapur 385 Vedanta Excel in Mathematics - Book 10 Answers 13. Rs 9,900 14. Rs 2,006.46 15. a) 6050 cm2 b) Rs 75,625 16. a) 4065.6 m2 b) Rs 1,20,120 Sequence and Series 1. d = 3, m1 = 8, m2 = 11, m3 = 14, m4 = 17 2. a) –4 b) 3 c) 4, 0 3. a) 51 b) 3 c) 45, 33, 27, 21, 15 4. a) Rs 500 b) Rs 4,000 5. a) 580 b) 2 c) 190 6. a) 25 b) 3, 8 c) t4 + t5 + ... + t8 = 0 7. a) Rs 55,000 b) Rs 5,000 8. a) Rs 1,350 b) 10 9. Rs 1,35,000 10. a) 25 b) 13 years 11. r = 3, g1 = 6, g2 = 18, g3 = 54, g4 = 162 12. a) 3 b) 4 c) 137 13. a) 1 3 b) 2 c) 18, 6 14. 8, 32 15. a) 6 b) 512 16. a) Rs 300 b) Rs 38,400 Quadratic equation 1. a) ±4 b) 4, – 2 9 c) 14, 23 2 d) 2(1± 3 ) e) –2 f) –10, – 1 3 g) 0, – p + q 2 h) –a, –b 2. a) (37 – x) years, (8 – x) years b) 5 years c) 21 years 3. a) (40 + x) years, (16 + x) years b) 2 years c) 4 years 4. a) x + y = 15, xy = 54 b) 9 years, 6 years c) 21 years 5. a) x = (y + 1)2 , y = x – 21 b) 25 years, 4 years c) 26 years 6. a) xy = 400, y = 3x – 110 b) 40 years, 10 years c) 15 years 7. a) 30 years, 10 years b) 5 years 8. a) 40 m, 30 m b) 25% 9. a) 48 b) Rs 1,375 10. a) 40 km/hr b) 1 hr more 11. 64 12. 37 13. 94 14. 36 Simplification of Rational Expressions 1. 1 2. 1 3. 6ab a2 + b2 4. 2 x + 1 5. 1 6. 2 x(x2 – 4) 7. 2b 4x2 – 1 8. 8x x4 – 1 9. 1 (x –2) (x – 3) 10. 2 (x – 1) (x – 2) 11. x2 – 10 (x – 1)(x – 2) (x + 3) 12. 0 13. 1 (x – 3) (x – 1) 14. 4 (a – 1) (a – 5) 15. 38 (a + 3) (a + 4) (a – 6) 16. 0 17. 7x – 25 (x – 1) (x – 3) (x – 4) 18. 0 19. 1 20. 0 21. 2(y – 2) y2 – 2y + 4 22. 2(2x – y) 4x2 – 2xy + y2 23. 2(3a – 1) (9a2 – 3a + 1) 24. 0 25. 4x3 1 + x2 – x8 26. 8a7 a8 – 256b8 27. 4 1 – x2 Exponential Equation 1. a) 3 b) 3 c) 3 d) 1 e) 2 f) 1 g) –1 4 h) 2 i) 1 3 j) 0, 2 k) 1, 2 l) 2, 3 m) 3, 4 n) 0, 2 o) 1, 2 p) 3, 2 q) 0, 1 r) 0, 2 5. a) 1, 2 b) 1 m2 or 4 m2 Area of triangles and quadrilaterals 1. a) equal b) 60 cm2 2. a) Area of triangle BCD = Area of triangle CDE b) 40 cm2 3. a) DSQR 4. a) 18 cm2 5. a) Area of triangle BCD = Area of triangle BED Circle 1. b) 80°, 50° c) 2 : 1 2. b) 65° c) 40° 3. b) 35° c) 40°, 50° 4. b) 40° c) 60° 5. a) ∠ BAC b) 22° c) 136° Statistics 1. a) 50 c) Rs 12,00,000 d) Rs 24,000 2. a) Individual data c) 39.33 d) ∑x = 1169, ∑fm = 1180, ∑x and ∑fm are not equal. 3. b) 55 c) 125 5. b) (45 – 55) c) 49.375 d) 10.21 6. b) (50 - 60) c) 57.5 kg d) 7.5 kg 7. a) (35 – 40) c) 18 d) 6.875 cm

Vedanta Excel in Mathematics - Book 10 386 Approved by Curriculum Development Centre, Sanothimi, Bhaktapur Answers 8. a) (110 - 130) c) 10 d) Rs 100 9. a) (700 - 800) b) Rs 760 c) Mean < Median < Mode 10. a) (30 - 40) b) 40 c) Mean < Median < Mode Probability 1. a) M4 = {4, 8, 12, 16, 20}, M7 = {7, 14} b) P(M4 ) = 1 4 , P(M7 ) = 1 10 c) Yes d) 7 20 2. a) D3 = {12, 15, 18, 21, 24, 27, 30}, D8 = {16, 24} b) P(D3 ) = 1 3 , P(D8 ) = 2 21 c) Yes d) 3 7 3. a) 1 4 b) 1 4 c) 1 2 d) 4 13 e) 2 13 4. a) 3 8 b) 3 8 c) Yes d) 9 64 e) 5R 3B 4R 3B 5R 2B P(B1 R2 ) = 3 8 × 5 7 = 15 56 P(R1 B2 ) = 5 8 × 3 7 = 15 56 P(R1 R2 ) = 5 8 × 4 7 = 5 14 P (B1 B2 ) = 3 8 × 2 7 = 3 28 P(R1 ) = 5 8 P(B1 ) = 3 8 P(R2 ) = 4 7 P(B2 ) = 3 7 P(R2 ) = 5 7 P(B2 ) = 2 7 5. a) S S S D D D P(D1 S2 ) = 1 4 P(S1 D2 ) = 1 4 P(S1 S2 ) = 1 4 P (D1 D2 ) = 1 4 P(S1 ) = 1 2 P(D2 ) = 1 2 P(S2 ) = 1 2 P(D2 ) = 1 2 P(S2 ) = 1 2 P(D2 ) = 1 2 b) 1 4 c) 3 4 6. a) H H H T T T P(T1 H2 ) = 1 4 P(H1 T2 ) = 1 4 P(H1 H2 ) = 1 4 P (T1 T2 ) = 1 4 P(H1 ) = 1 2 P(D2 ) = 1 2 P(H2 ) = 1 2 P(T2 ) = 1 2 P(H2 ) = 1 2 P(T2 ) = 1 2 b) 1 12 c) 1 6

Approved by Curriculum Development Centre, Sanothimi, Bhaktapur 387 Vedanta Excel in Mathematics - Book 10 Answers 7. a) P(R1 B2 ) = 1 6 P(R1 G2 ) = 1 6 P(B1 R2 ) = 1 6 P(B1 G2 ) = 1 6 P(G1 R2 ) = 1 6 P(G1 B2 ) = 1 6 1R 1G 1B 1G 1R 1B P(R1 ) = 1 3 P(B1 ) = 1 3 P(G1 ) = 1 3 P(B2 ) = 1 2 P(R2 ) = 1 2 P(G2 ) = 1 2 P(R2 ) = 1 2 P(G2 ) = 1 2 P(B2 ) = 1 2 1R 1B 1G Sample space {R1 B2 ,R1 G2 , BR2 , B1 G2 , G1 R2 , G1 B2 } b) 2 3 8. a) 8B 6W 8B P(W1 B2 ) = 12 49 P(B1 W2 ) = 12 49 P(B1 B2 ) = 16 49 P (W1 W2 ) = 9 49 6W 8B 6W P(B1 ) = 8 14 P(W2 ) = 6 14 P(B2 ) = 8 14 P(W2 ) = 6 14 P(B2 ) = 8 14 P(W2 ) = 6 14 b) 12 49 c) 24 49 9. a) 1 14 b) 1 14 Trigonometry 1. a) 4 3 m b) 8 m c) 4 2 m 2. a) (18 – x) m b) sine c) 12 m d) 6 3 m 3. a) ∠EDA b) 66.68 m c) Angle of elevation will be increased 4. b) 33.87 m c) 57.74 m 5. b) 45° c) 15 m d) 50 2 m 6. a) 40 3 m b) 15 m c) 16.17 ft 7. a) 10 3 m b) 24 m 8. a) 12 3 m b) 14 3 ft c) 40 m 9. a) 8.43 m b) 20 m c) 79.94 m d) 1.35 m e) 1.8 m 10. a) 150 3 m b) 11.55 m c) 20 3 m d) 500 m 11. a) 30 3 m b) 5 3 m c) 36 m 12. a) 20 ft b) 16.13 m c) 33.09 m d) 50 m 13. a) 24 m b) 11.55 m 14. a) 101.5 m b) 152 m c) 114.4 m d) 234 m 15. a) 16 m b) 21.44 m c) 34.14 m d) 51.21 m 16. a) 30° b) 45° c) 45° d) 60° 17. a) 45° b) 30° 18. a) 17.5 m b) 20 3 m 19. a) 47.32 m b) 75 m c) 1.366 km 20. a) 42 m, 14 3 m b) 94.64 m

Vedanta Excel in Mathematics - Book 10 388 Approved by Curriculum Development Centre, Sanothimi, Bhaktapur Students’ Evaluation System (Class 10) (a) Internal (Formative) Evaluation Students’ individual portfolio should be managed with the marks under the following headings. S.N. Area of evaluation Weightage 1. Participation: attendance and participation in classroom activities 3 2. Terminal examinations (Obtained marks from each of 2 terminal exams should be converted in to 3) 6 3. Practical/Project work (at least 1 project work from each area should be prepared and presented in class) 16 Total 25 (b) External (Summative) Evaluation Summative evaluation covers 75% of the entire weightage of the course intended by the curriculum. The items should be chosen from all the chapters of the course of a session for the test paper prepared to the external evaluation. The test should contain knowledge, skill, application and higher ability based items by following specification grid. Specification Grid for External Evaluation F.M.: 75 Time: 3 hours S.N. Area Working hours Knowledge (16%) Understanding (24%) Application (40%) Higher ability (20%) Total no. of items Total no. of questions Total Marks No. of items Marks No. of items Marks No. of items Marks No. of items Marks 1. Set 12 1 1 1 1 1 3 1 1 4 1 6 2. Arithmetic 28 2 2 2 3 3 5 2 3 9 3 13 3. Mensuration 28 2 2 2 3 2 5 2 3 8 3 13 4. Algebra 32 2 2 2 4 3 7 1 2 8 3 15 5. Geometry 28 2 2 2 3 2 5 2 3 8 3 13 6. Statistics and Probability 24 2 2 2 3 2 4 2 2 8 2 11 7. Trigonometry 8 1 1 1 1 1 1 1 1 4 1 4 Total 160 12 12 12 18 14 30 11 15 49 16 75

Approved by Curriculum Development Centre, Sanothimi, Bhaktapur 389 Vedanta Excel in Mathematics - Book 10 Model Question Set-2080 Class: X Subject: C. Mathematics Time: 3 hours F.M. : 75 Attempt all the questions. 1. A survey was conducted among 80 students of a school regarding their achievements of Mathematics and Science in a Mock Test. The results of the survey are as follows: • The ratio of number of students who passed in Mathematics to the number of students who passed in Science is 2:3 • 30 students passed both the subjects • 10 students failed in both the subjects Based on this information, answer the following questions. (a) How many students passed in either Mathematics or Science? [1] (b) Represent the above data in a Venn-diagram. [1] (c) Find the number of students who passed in Mathematics. [3] (d) By how many times is the number of students who passed in Science only more than the number of students who passed in Mathematics only? Find. [1] 2. Saroj deposited Rs 5,00,000 in a commercial bank for 2 years at 10% p.a. compounded half yearly. But after 1 year the bank changed its policy and decided to give compound interest compounded quarterly at the same rate. The bank charges 5% tax on the interest as per government’s rule. (a) What is the formula to calculate the compound interest compounded half-yearly on P at R% p.a. for T year? [1] (i) C.I. = P 1 + R 100 T –1 (ii) C.I. = P 1 + R 200 2T –1 (iii) C.I. = P 1 + R 300 3T –1 (iv) P 1 + R 400 4T –1 (b) How much net interest did he get the first year? [2] (c) What is the percentage difference between the interest of the first year and second year after paying tax? [2] 3. The population of a municipality increases every year by 5%. 1025 people migrated to other places from there at the end of B.S. 2079 and the population of the municipality remained 10,000. Answer the following questions based on the given information. (a) What was the population of the municipality at the end of B.S. 2079 with migrated number of people? [1] (b) What was the population of the place in the beginning of B.S. 2078? [1] (c) How many more or less number of people would be there in the municipality if the population was increased by 4% in B.S. 2078 and 6% in B.S. 2079? [2]

Vedanta Excel in Mathematics - Book 10 390 Approved by Curriculum Development Centre, Sanothimi, Bhaktapur 4. Mr. Shakya imports i-phone sets from U.S.A. and sells in Nepal. He imports each i-phone for US$ 740 with custom duty charge. He makes 40% profit and sells each i-Phone with 13% value added tax. (US$ 1 = NPR 125) (a) How much Nepali rupee does he pay for each i-phone? [1] (b) If Mrs. Rai buys an i-phone set from Mr. Shakya, how much should she pay for it? [1] (c) If Mrs. Rai used i-phone for 2 years and sold it at the rate of 20% p.a. compound depreciation, by what amount would its cost be devaluated? [2] 5. A rural municipality built a temple in a village. The roof of the temple is in the shape of square-based pyramid. The length of side side of the roof is 24 ft. and the height of each of the triangular face of the roof is 20 ft. The roof of the temple is covered with zinc sheet. (a) What is the formula to calculate the volume of a square based pyramid with side length of base ‘a’, height ‘h’ and slant height ‘l’? [1] (i) a2 h (ii) 1 3 a2 h (iii) 2al (iv) a2 + 2al (b) If the size of each rectangular zinc roofing sheet is 15 ft × 4 ft, what would be the cost for the covering the roof of the temple with zinc sheet at the rate of Rs. 2,500 per piece? [3] 6. Once a group of people went for a picnic at a hill side. Due to peak season, they did not get a proper accommodation there. The weather was fine so they decided to make a conical tent in a park. They went to a tent house near by the picnic sport and brought the canvas in rent that is enough to make the tent with base radius 11.2 m and height 6.6 m. Answer the following questions based on the given information. (a) Write the formula to find the curved surface area of a right circular cone. [1] (b) Calculate the area of base of the tent. [1] (c) How many people were there in the group if each person required 8.96 square meter of space on the ground for the accommodation? [1] (d) What is the rent of the canvas brought to make the tent at Rs. 5 per sq. m? [2] 7. A shopkeeper sells the water tanks made up of plastic materials and formed with the combination of a cylinder and a hemisphere. For the use of own house, a person bought a water tank having the base radius 1.05 m and height 3.5 m. (a) What is the volume of each tank? [2] (b) If the volume of the material contained in the tank for making it is 5% of the volume of the tank, what is the cost of filling up the tank completely at the rate of 25 paisa per litre? [2] 8. The monthly commission amounts of received by Ankit, an employee, working in a real estate company for 5 months are as follows. Month Baishakh Jestha Asar Shrawan Bhadra Commission Rs 2,000 Rs 5,000 Rs 8,000 Rs 11,000 Rs 14,000 Model Question Set - 2080

Approved by Curriculum Development Centre, Sanothimi, Bhaktapur 391 Vedanta Excel in Mathematics - Book 10 Look at the table above and write the answers to the questions below. (a) What is the formula to calculate the arithmetic mean between the number ‘a’ and ‘b’? [1] (i) A.M. = a + b 2 (ii) A.M. = a – b 2 (ii) A.M. = ab (iv) A.M. = 2(a + b) (b) What is the mean value of commission amount of Baisakh and Asar received by him? Find it. [1] (c) What is the total commission amount received by Ankit at the end of Bhadra? Calculate using the formula. [2] 9. Answer the following questions. (a) Simplify: 1 x2 – 5x + 6 + 1 x2 – 3x + 2 + 2 x2 – 8x + 15 [3] (b) Solve: 2x + 16 2x = 10 [3] 10. Prabin and Rakshya are brother and sister. Prabin’s present age is 20 years and Rakshya’s present age is 15 years. (a) How old were Prabin and Rakshya before x years? [1] (b) What is the value of x if the product of their ages before x years was 234? [2] (c) After how many years later, will 2 times of Prabins age become 3 times of Rakshya’s age? [2] 11. In the adjoining figure, AD // BE and BA // CD. Answer the following questions. (a) What is the relation between the area of ∆ABD and ∆AED? [1] (i) Area of ∆ABD = 2 × Area of ∆AED (ii) Area of ∆ABD = 1 2 Area of ∆AED (iii) Area of ∆ABD = Area of ∆AED (iv) Area of ∆ABD > Area of ∆AED (b) If the area of trapezium ABED is 100 sq. cm and the area of ∆CDE is 40 sq. cm; what is the area of ∆ADE? [1] (c) Construct a triangle PQR in which PQ = 5.2 cm, QR = 6 cm and ∠Q = 60°. Construct another triangle SPQ which is equal in area to the ∆PQR and having side PS = 8.5 cm. [2] 12. Answer the following questions. (a) Draw two circles with centre O and radii at least 3 cm. Take any three points A, B and C on the circumference in each circle. Then, explore experimentally the relation between ∠AOB and ∠ACB. [3] (b) If AB were a diameter of the circle and ∠CAB = 30o , what would the ratio of ∠CAB and ∠ABC? [2] A B C E D Model Question Set - 2080

Vedanta Excel in Mathematics - Book 10 392 Approved by Curriculum Development Centre, Sanothimi, Bhaktapur 13. In the given figure, O is the centre of the circle, AE = BE, ∠BAE = 70o , ∠DCE = x and ∠CDE = y. Answer the following questions. (a) Write down the relation between ∠ABC and ∠ADC. [1] (b) Find the values of x and y. [2] (c) Is arc AD equal to arc BC? Give reason. [1] 14. The given table represents the marks obtained by the students of class 10 in the second terminal examination in mathematics subject. Marks obtained 0-15 15-30 30-45 45-60 60-75 No. of students 3 4 8 10 5 Answer the following questions by looking at the data. (a) Construct the cumulative frequency table. [1] (b) Find the median class. [1] (c) Calculate the median mark. [2] (d) What percent of students obtained more than median mark? [2] 15. Akriti rolls a dice and then he tosses a coin. (a) Draw a tree diagram to show the probability of all the possible outcomes. [1] (b) Find the probability of getting an even number on dice and head on coin. [2] (c) Bimal tells that the events occurring from the dice and the coin are dependent events, is he right? Give your reason. [2] 16. In the figure given alongside, the height of the house is 60 ft and the height of tree is 25 ft. From right top of the roof of the house, a man observes the top of the tree. Based on this information, answer the following questions. (a) Name the angle of depression. [1] (b) Find the length of AE part of the house. [1] (c) Find the distance between the house and the tree. [1] (d) If the tree were 35 ft away from the house, what would be the angle of depression of the top of the tree from the right top of the house? [1] A B C E D 70° O x y 30° D A B C B E Model Question Set - 2080