SLC question Bank of MATH

probability of getting a prime numbered or even numbered card.

[Ans: 11/22] (b) Three children are born in a family. Calculate the probability of getting exactly two sons by drawing a 3 tree diagram.

[Ans: 8]

SET I Answer all the questions 1.

Group 'A' 1 1 (a) Simplify : 1 – ax – y + 1 – ay – x (b) Evaluate :

2.

5 1

(a) Solve :

[9 × (2 + 2) = 36] [Ans: 1]

1024

[Ans: 2] 25 [Ans: 16]

=2

3

3.

5.

2x – 3 (b) The product of the ages of a man 10 years before and 10 years hence is 300. Find his present age. [Ans: 20] (a) x – 1, 2x + 1, x + 5 and 3x + 1 are in ascending order. If its median is 18, find the value of x.

[Ans: 10] (b) Construct a cumulative frequency table represented by the given ogive.

[Ans:

120 100 80 60 40 20

0

4.

20 40 60 80 100 120 140

X

C.I. 0 – 20 20 – 40 40 – 60 60 – 80 80 – 100 100 – 120

f 0 10 20 30 50 10

S

6 cm

(b) Find the lateral surface area of the given prism [Ans: 140 cm2]

Y

140

P

Q

6.

160

(a) The area of the given parallelogram is 14 cm2 . If SR = 4 cm, QR = 7cm, find the value of ∠QRS. [Ans : 30°]

7.

(a) A number card is drawn at random from a group of number cards numbered from 2 to 13. Find the

8.

1

2

R

4 cm 10 cm

(a) The radius and height of a right circular cone are in the ratio 5 : 12 and its volume is 2512 cm3. Find the radius of its base.

[Ans: 10cm] (b) Find the circumference of the sphere whose volume is 1375 3 21 cm .

110   Ans: 7 cm   1 (a) A milkman bought 100 l of milk for Rs. 1500. 52 l of milk was lost by leakage. If he sold the remaining milk for Rs. 18 per litre, what was his gain or loss percentage?

[Ans: 13.4 %] (b) Find the compound interest on Rs. 11250 for 3 years if the rates of interest for the first, second and third year are 4%, 5% and 6% respectively. [Ans: Rs. 1772.10] (a) In the given figure if the area of ∆PQT is 50 cm2. Find the area of ∆PRS. [Ans: 50 cm2]

R

P

S

T

Q

(b) Find the value of x:

D

[Ans: 125°]

9.

A

C x 35° O

(a) In the adjoining figure, O is the centre of the circle. ∠OPQ = 50°. Calculate the value of x and y. [Ans: x = 100°, y = 130°]

B

S O x y R P

50° Q

1 2a 4a3 8a7 1 13. Simplify : a – b + a + b + a2 + b2 + a4 + b4 [Ans: a8 – b8 ] 14. The sum of the digits of a two digit number is 6. If 18 is subtracted from the number, the digits in the number are reversed, find the number.

[Ans: 42] 15. Calculate the lower quartile (Q1) from the following data [Ans: 41.67] Marks 20-40 406080-100 80 No of

B (b) In the adjoining figure, A and B are the points of x O contact of the tangents TA Q and TB. O is the centre of A the circle and ∠ATB = 50°. Calculate the value of x. [Ans: 65°]

50°

T

Group 'B' [16 × 4 = 64] 10. In a survey of a group of 120 people, 90 use Everest toothpaste, 72 use brighter toothpaste and 10 use neither of the past. (i) Construct a Venn-diagram to illustrate the above information. (ii) How many people use both the toothpaste? (iii) How many people use Everest toothpaste only? (iv) How many people use exactly one toothpaste?

[Ans: 52, 38, 58] 11. Find the H.C.F. of [Ans: x – 2] 2x3 – 16, x2 – 4x + 4, x3 – 3x2 + 2x 1 12. Solve: 5x – 5 + 54 – x = 15 [Ans: 4,5] 3

8 12 10 6 stud ents 16. The angle of elevation from the roof of a house to the top of a tree is found to be 45° . If the heights of the house and tree are 12 m and 25m respectively, find the distance between the house and the tree.

[Ans:13m] 17. Find the total surface area and A volume of the given solid 24cm O P object.

2 3 [Ans:6006cm , 1950.67cm ] A'

P

18. In the given figure, the total surface area of the given square based pyramid is 384cm2 and the side of the square base is 12 cm, find the slant height of the pyramid . [Ans: 10 cm]

D

A 12 cm

C

B

19. Santosh and Mandip can reap a field in 10 days . Mandip and Roshan can reap a field in 12 days. Roshan and Santosh can reap the same field in 15 days. (i) In how many days will they complete to reap the field if all of them reap together?

4

(ii) How many days will each of them take to reap the field 1 completely ?[Ans; (i) 8days, (ii) 24 days, 177 days , (iii) 40 days] 20. A merchant sells his goods marketing them 25% above the cost price.

If he allows a discount of 12% on selling the goods, what percent profit does he make?

[Ans:10%] 21. A person borrows Rs.10,000 for 1 year and 6 months at 10% p.a. compound interest payable yearly. But he immediately lends the sum for the same time and same rate of compound interest payable half yearly, How much does he gain in his transaction?

[Ans: Rs.781.25] 22 Prove that the triangles standing on the same base and between the same parallels are equal in area.

A D 23. In the given figure ABCD is a square and AE = AF Prove that BD // EF

SET II II Answer all the questions 1.

2.

3

40 35 30 25 20 15 10 5

C

4.

5.

5

3 4 (b) Evaluate: a6 b–2c3 ÷ a-8b-8c4 [Ans: a5 b4/3] x+5 = x +1 [Ans: 4] (a) (b) The product of two positive numbers which are in the ratio 2:3 is 96. Find the numbers.

[Ams: 8 & 12] (a) If –– x =50 and Σfx = 750, find the value of Σf. [Ans:15] (b) Write down the frequency table corresponding to the along side of frequency curve.

[Ans: Y

E

24. Verify experimentally that the angle in the same segment of a circle are equal. ( Two different figures are necessary but the radii of the circles must not be less than 3 cm) 25. Construct a triangle equal in area to the quadrilateral ABCD in which AB = 5cm, BC = 4.5cm, CD = 3.4cm, AD = 4.2cm, and diagonal AC = 6cm.

[9 × (2 + 2) = 36] [Ans: (x2 - y2)3n]

F B

Group 'A' (a) Simplify: {(x-y) } ÷ {(x+y)n}–3 -3 -n

6

c.f. f 20 – 40 5 30 – 40 5 40 – 50 10 X 0 1020 30 40 50 60 70 Class Interval 50 – 60 7 60 – 70 8 (a) A coin is tossed and a dice is rolled. Find the probability of getting a head on the coin and a number 1 less than 3 on the dice.

[Ans: 6 ] (b) A bag contains 1 red ball, 1 white ball and 1 blue ball.

Two balls are drawn one after the other without replacement. Show all the possible outcomes and corresponding probabilities in a tree diagram. (a) Calculate the area of parallelogram PQRS if PS = 3 2 cm, SR = 8 cm and ∠PQR = 45°.

[Ans: 24 cm2]

6.

7.

8.

(b) The area of a parallelogram is 48 cm2. If the two adjacent sides are 8cm and 6 cm, find the length of its diagonal.

[Ans: 10cm] 2 (a) The surface area of a marble is 2π cm . What will be 2 the difference in the area if the radius is made 3 of its 10π original size?

[Ans: 9 cm2] (b) The volume of a rectangular pyramid is 210 cm3. If the area of its rectangular base is 105 cm2, find the height of the pyramid.

[Ans: 6 cm] (a) A fruit seller bought a basket containing 1 gross oranges for Rs. 432. But 14 oranges were rotten. He then sold the good oranges for Rs. 3.50 per orange.

Find his profit or loss.

[Ans: Rs. 23] (b) In what time will the compound interest compounded semi-annually on Rs. 4000 at 5% p.a. be Rs. 202.50?

[Ans: 1 year] (a) ABCD is a square. If the diagonal BD = 3 3 cm, find the area of ABCD. [Ans: 9 cm2] A

(b) Find the values of x and y [Ans: x = 35°, y = 55°]

9.

(a) In the adjoining figure, PQ is the diameter of the circle with centre O. If ∠ROS = 42°, find the value of ∠RTS. [Ans:69°]

(b) Find the values of x and y from the given figure, where O is the centre of the circle and TAN is the tangent at the point A. AP is the bisector of

O x 70° y C

B

P

R T 42° O

S

Q

O

T

A

x y

∠OAN. [Ans: x = 90°, y = 45°] Group 'B' [16 × 4 = 64] 10. In a class of 50 students, 25 students like to play football, 35 like to play cricket and 15 like to play both the games.

How many students donot like to play any games? Show the above information in a Venn-diagram.

[Ans: 5] 11. Find the L.C.M. of 8x3 + 1, 8x4 – x, 16x4 + 4x2 + 1 [Ans: x(8x3 – 1) (8x3 + 1)] 108 12. Solve: xx + xx = 31 [Ans: 2,3] 1+x 1–x 4x 8x3  2(1 + x) 13. Simplify : 1 – x + 1 + x + 1 + x2 + 1 – x4 Ans: 1 – x    14. 6 years ago, Ram was six times his son, 4 years hence, thrice his age will be equal to eight time his son's age. What are their present ages?

[Ans: 36 yrs, 11 yrs] 15. Calculate the upper quartile (Q3) from the given data [Ans: 61.43] Marks 20 – 50 – 60 30 – 60 – 40 -50 70 – obtained 30 40 70 80 No. of 5 10 6 7 8 4 students 16. A tree of 14m height is broken by the wind so that its top touches the ground and makes an angle of 60° with the ground. Find the length of the broken part of the tree.[Ans: 7.50 m] 17. Find the slant height of the cone if the 660 volume of the given solid is 7 cm3.

[Ans: 5 cm]

B O

3cm

A

C

18. Given figure is a square pyramid is which vertical height is 8 cm and length of base side

P

12cm

N

7

8

12cm

is 12cm. Find its total surface area and volume. [Ans: 384 cm2, 1152 cm3] 2 19. Deekshyanta can do 5 part of a work in 9 days. He calls Samir to finish the remaining work. They work together and finish it in 6 days. How many days will be taken by Samir to finish the work alone?

[Ans: 18 days] 20. The marked price of an article is 25% above its selling price and the cost price is 30% less than its marked price. Find 2 the discount percent and gain percent. [Ans: 20%, 147 %] 1 21. In what time will a sum of Rs. 1280 at 12 2 % p.a. compounded annually amount to Rs. 1620? [Ans: 2 years] R

22. In the given figure, P is the mid point of RC. Prove that area of ∆ RBC = area of //gm ABCD.

A

B

P

SET III Answer all the questions Group 'A' 1.

2.

3.

D

12 (a) Simplify : 4–1 + 3–1 (343)–2/3 (b) Evaluate: 5 (32)3

9

10

1 [Ans: 112 ]

(a) The average temperature from Sunday to Friday is 28°C and that of Sunday to Saturday is 30°C. Find the temperature on Saturday.

Y 40 [Ans: 42° C]

(b) From the ogive given alongside, find the median.

4.

[Ans: 1/7]

4 4 (a) Solve: 6x + 5 = x + 30 [Ans: 5] (b) The difference of the square of a number and 23 is 2.

FInd the number .

[Ans: ± 5]

C

23. Prove that a parallelogram inscribed in a circle is a rectangle.

24. Verify experimentally that the angles in the conjugate segments are supplementary, (Two different figures are necessary but the radii of the circles must not be less than 3cm) 25. Construct a triangle ABC in which BC = 7 cm, ∠ABC = 45° and AC = 8.5 cm. Also construct a triangle equal in area to the given ∆ ABC.

[9 × (2 + 2) = 36]

–1

35 30 25 20 15 10 5 0

50 54 58 62

[Ans: Height (inch)

X

55]

(a) The probability of solving a mathematical problem by 1 1 two students A and B is and 5 respectively. If the 2 problem is given to both the students find the probability of the problem being solved.

3 [Ans: 5 ] 2 (b) There are 30 students in a class of which 3 are boys.

Three students are chosen from the class at random, one after the other. Draw the probability tree diagram and

5.

6.

7.

8.

find the probability that there will be at least two boys 152 selected.

[Ans: 203 ] A (a) Find the area of the given quadrilateral ABCD in which AB = D BC, AD = DC = 3cm, BD = 5cm and B 2 C ∠ADB = 30°. [Ans: 7.5 cm ] (b) Find the area of ∆ABC in which AB = 105cm, BC = 91cm and AC = 98 cm.

[Ans: 4116 cm3] (a) A solid metallic sphere of radius 7cm is out into two halves. Find the total surface area of each hemisphere so formed [Ans: 462 cm2] (b) If the volume and height of a right circular cone are 1887 cm3 and 37 cm respectively. Find the area of its base.

[Ans: 153 cm2] (a) An electrician bought 50 balls at Rs. 15 per bulb. If 7 bulbs were defective and he has to make a profit of Rs. 67 on the total outlay, find the selling price of one bulb.[Ans: Rs. 19] (b) Find the rate of compound interest when Rs. 5120 amounts to Rs. 7290 in 1 year 6 months, if the interest is compounded half yearly?

[Ans: 25 %] (a) In adjoining figure NMRP is a N M quadrilateral in which MN // PR. R ∠NMR = ∠PRM = 90°, MR = 8cm P 18 cm and PN = 10cm. Find the area of quadrilateral NMRP. [Ans: 120 cm2] (b) Find the values of x and y: [Ans: x = 130°, y = 115°]

C y x O 65°

D

B

A

O

A

C 11 B

9.

(a) If O is the centre of the circle, Calculate all the angle of the rhombus OABC. [Ans: ∠A = ∠C= 60°, ∠B = ∠O = 120°]

(b) PA and PB are the tangents from an external point P to the circle with centre at O. Calculate the values of x and y if ∠BAE = 106°. [Ans: x = 32°, y = 148°]

D B

P

y O

x

106° A E

Group 'B'

[16 × 4 = 64]

10. In a class of 75 students, 28 like football but not cricket and 32 liked cricket but not football. If 7 students did not like both games, find (i) how many students liked both the games? (ii) how many students liked football? (iii) how many students liked cricket? (iv) illustrate the above information in Venn-diagram. [Ans: 8, 36, 40] 11. Find the H.C.F. of [Ans: x(x – 2)] 2x3 – 5x2 + 2x, 3x3 – 8x2 + 4x, 2x4 – 16x 5x – 1 5x – 1 9 12. Solve: =1+ [Ans: 2 5] 5x + 1 1 2 1 2 54x 13. Simplify: x – 3 – 2x + 3 + x + 3 – 2x – 3 [Ans: 4x4 + 5x2 + 81 ] 14. A number of two digits is equal to four times the sum of its digits. If 18 is added to the number, the digits are reserved.

Find the number.

[Ans: 24] 15. Compute the arithmetic mean of the following data:[Ans: 57.75] 12

Marks 25 – 65 – 75 75 – 35 – 45 – 85 – 55 – obtained 35 85 45 55 95 65 No. of 3 5 4 5 9 2 12 students 16. An observer finds an angle of depression of 60° when he observes a car on the road from the roof of his house. If the car is at a distance of 50m from the foot of the house, find the height of the house.

[Ans: 86.6m] 17. The volume of a cone is equal to the volume of cylinder whose height is 9 cm and diameter 40cm. If the height of the cone is 108 cm then find its radius of circular base.[Ans: 10cm] 18. Find the total surface area of the solid object given in the figure. [Ans: 92.5m2]

23. In the given figure, CD is the angular bisector of ∠BDE of a cyclic quad. ABCD. Prove that ∆ABC is an isosceles triangle.

D

B

C

E

24. Verify experimentally that the angle at the centre of a circle is double of the angle at the circumference standing on the ame arc (Two different figures are necessary but the radii of the circles must not be less than 3cm) 25. Construct a trapezium ABCD in which AD//BC, AB = 4.6 cm, BC = 2.5cm, ∠DAB = 60° and ∠BCD = 90°. Also construct a triangle equal in area to the trapezium.

2.5m

19. Praful can do as much work in 4 days as Safal can do it in 5 days. If they work together, they can finish it in 20 days.

What time will each take to finish the work? [Ans: 45 days, 36 days] 20. If a tourist paid Rs. 5610 for a carved window made of wood with a discount of 15% including 10% VAT, what is the marked price of the window?

[Ans: Rs. 6000] 21. Deepa has invested a certain sum of money at compound interest added annually. She gets an interest of Rs. 225 added in her investment at the end of second year. Find the sum invested and the rate of compound interest.[Ans: Rs. 3750, 6%] 22. In the given figure, rectangle ABCD A D E F and parallelogram EBCF are on the same base BC and between the same parallels AF and BC. Prove that B C (i) ∆ABE ≅ ∆DCF (ii) Area of the rectangle ABCD = Area of the parallelogram EBCF.

13

A

14

SET IV Answer all the questions 1.

Group 'A' 5m + 3n x ÷ x3m – 2n (a) Simplify : 2m + n x

2.

3.

4.

[Ans: x4n]

30 cm

20 (b) Evaluate:

10 5

a

a–51

5

a5

5 (a) Solve: x + 9 = 1 [Ans: –8] (b) If 11 is added to the square of a number the result is 47. Find the number.

[Ans: 6] (a) If the lower quartile class is 20 – 30, cumulative frequency of pre-lower quartile class is 6, the frequency of quartile class is 14 and the total number of data is 30 then find the value of lower quartile.

[Ans: 31.7] (b) Find the value of p and q in the following table: C.I. f c.f.

0–4 5 5 4–8 7 12 8 – 12 p 20 12 – 16 10 q [Ans: p = 8, q = 30] (a) Two coins are tossed at the same time. Find the

(a) In the given figure, find the length AB if the area of ∆ABC is 27 cm2 [Ans: 9 cm]

6.

(a) The height and radius of base of a cylinder are in the ratio 3 : 1. If its volume is 1029π cm3, find its height.

[Ans: 7 cm] (b) Find the total surface area of the solid cone obtained by revolving the given right angles ∆ABC about BC. [Ans: A 942 cm2]

7.

(a) A watch is priced at Rs. 1530 including 1 12 % VAT. Calculate the price of the B 5 cm C 2 watch without VAT. [Ans: Rs. 1360] (b) The share of a bank depreciates every year by 2.5%. If the amount depreciation of the share this year is Rs. 15, find the present value of the share.

[Ans: Rs. 600] (a) The area of the rhombus ABCD is 36 cm2 and the diagonal AC = 8cm. Find the length of the diagonal BD. [Ans: 9 cm]

[Ans: 1]

1 probability of getting the same event in both the toss.[Ans: ] 2 (b) There are 9 white and 11 black balls of the same shape and size in a bag. If two balls are drawn randomly in succession without replacement from the bag. Show the probability of all the possible outcomes in a tree diagram.

5.

(b) Find the total surface area of the given triangular prism. [Ans: 768 cm2]

[9 × (2 + 2) = 36]

8.

C x O

(b) O is the centre of the circle. Find the value of x if ∠OBA = 35° [Ans: 55]

9.

{= (a) Find the values of x and y if BC { and ∠DCE = 90° CD [Ans: x = 42°, y = 45°]

35°

B

A

D

A

x 48° y

B

E

C

B C

30° 12 cm

15 A

16

T

C P

32° yx

60° Q

(b) Find the value of x and y where O is the centre of the circle and PQ is the tangent. [Ans: x = 62°, y = 59°]

10.

11.

12.

13.

14.

15.

Group 'B' [16 × 4 = 64] In a group of 150 music lovers, it was found that 90 people liked folk songs, 70 people liked modern songs and 30 did not like both songs. (i) How many liked both songs? (ii) Show the above information in a Venn-diagram.[Ans: 40] Find the H.C.F. and L.C.M. of M (x3 + 1) (x – 1) and (x4 + x2 + 1) (x2 – 3x + 2) [Ans: H.C.F. = (x –1) (x2 – x + 1), L.C.M. =(x – 2) (x3 + 1) (x3 – 1)] 28 Solve : x + 7 + x = [Ans: 9] x+7 Simplify : 1 1 1 1 + xb – a + x c – a + 1 + xc – b + x a – b + 1 + xa – c + x b – c [Ans: 1] One year ago, the father was 8 times as old as his son. Now, his age is equal to the square of his son's age, find their present ages.

[Anrs: 49 yrs, 7 yrs] If the mean of the data is 30.75, find the value of x. [Ans: 7]

Class

0-10 10 - 20

20 – 30 6

30 – 40 9

40 – 50 8

50 – 60 5

No. of 5 x students 16. From the top of the 40m hight house, the angles of depression to the two points on the same side of the house observed are 60° and 45° respectively. Find the distance between two points. [Ans: 16.9 m] 17. Find the surface area and volume of given cylinder with a hemisphere at one end.

[Ans: 555.5cm2, 859.83 cm3]

20 cm

17

4cm

18. Find the total surface area and volume of the given solid. [Ans: 289.98 cm2, 384 cm3] 6cm

5 19. 4 boys and 6 girls can do a piece of work in 2 days. 8 boys and 3 girls can do the same work in 2 days. In how many days will 1 boy and 1 girl do the work separately? [Ans: 20 days, 30 days] 20. The marked price of an electric heater is R. 3200. If the shopkeeper allows a certain discount and a customer bought it for Rs. 2640 including 10% VAT, what is the discount percent?

[Ans: 25%] 21. A man borrowed a sum of money and paid back in 2 years in two equal installments. If the rate of compound interest was 4% p.a. and if he paid back Rs. 676 annually, what sum did he borrow?

[Ans: Rs. 1275] A Q D 22. In the given parallelogram ABCD, P and Q are the mid points of AB and AD respectively. Prove that area of fig. P 7 C PQDCB = (area of //gm ABCD) B 8

23. In the adjoining figure, O is the centre of the circle and AB is a diameter. If arc BC = arc CD, prove that AD // OC.

C

D A

O

B

24. In the cyclic quadrilateral ABCD, Verify experimentally that ∠ABC + ∠ADC = 180° and ∠BAD + ∠BCD = 180° 18

(Two different figures are necessary but the radii of the circles must not be less than 3cm) 25. Construct a triangle ABC in which AB = 5.7 cm, BC = 5.3cm and CA = 6.2 cm. Also construct a parallelogram equal in area to the ∆ABC if one side of the parallelogram is 7.5 cm.

(b) Find the volume of given prism.

[Ans: 124.70 cm3]

P

6.

SET V

(a) Find the volume of the following square based pyramid. [Ans: 384 cm3]

D

C

Answer all the questions 1.

Group 'A' n+2 6 + 7 × 6n (a) Simplify : n + 1 6 × 8 – 5 × 6n 4

2.

3.

3

4

3

[Ans: 4a ] (b) Evaluate: 128 a ÷ 2 a (a) Solve: 5x – 1 = 2 x + 3 [Ans: 13] (b) Divide 81 into two parts whose product is 1260.[Ans: 60,21]

(b) From the given ogive, find the median [Ans: 12]

20 10 12 8 4 X

8.

(a) What is the probability that a leap year will have 53 Tuesdays?

5.

7.

Y

O 4 8 12 16 20 Marks obtained

4.

B

12 cm

[Ans: 1]

–1 –9

(a) The mean of a,b,c,d is 9 and the mean of a,b,c,d,e, f is 12. Find the mean of e and f.[Ans: 18]

A

[9 × (2 + 2) = 36]

2 [Ans: 7 ]

(b) Two cards are drawn from a well-suffled deck of 52 cards. Drawing a tree diagram find the probability that 1 both the cards are knaves.

[Ans: 221 ] (a) The area of ∆ABC is 12 cm2. If AC = 6 cm and AB = 8cm, find the value of ∠BAC. [Ans: 30°] 19

(b) The circumference of the base of a cylinder is 132 cm and the area of its curved surface is 1584 cm2. Find its height.

[Ans: 12 cm] (a) The VAT on a crarte of beer is Rs. 90. If VAT was levied at 10%, find the cost of the crate of beer including VAT. [Ans: Rs.990] (b) Calculate the population of a town three years ago if the present population is 83,65,427 and the annual growth rate is 10%.

[Ans: 62,85,069] (a) In the given figure ABCD is a square and EBCF is a parallelogram. If AB = 4cm, calculate the area of parallelogram EBCF. [Ans: 16 cm2]

A

D

B

C

(b) O is the centre of the circle and OA // BC. If reflex ∠AOC = 230°, find the values of x and y. [Ans: x = y = 50°]

E

C B

y O x 230° A

20

F

9.

(a) In the figure alongside, ABCD is a cyclic quadrilateral in which ∠ADE = 88°, ∠ABD = 26° and DC = BC. Find the values of x and y.

[Ans: x = 56°, y = 124°]

B

A y 26° 88° E

x D

C

(b) Find the length of OP where PA and PB are the B tangents to the points A and B respectively, OA = 2 cm and BP = O P 5 cm. [Ans: 7 cm] A

Group 'B' [16 × 4 = 64] 10. In an examination, 48% of students passed in English only and 35% passed in Nepali only. If 12% of the students were failed in both subjects. (i) what percent of students passed in both subjects? (ii) what percent of students passed in English? (iii) represent the above information in a Venn-diagram.[Ans:5%, 53%] 11. Find the H.C.F. and L.C.M. of (a + c) (a – c) + b(2a + b), (b + a) (b – a) + c(2b + c) and (c + b) (c – b) + a(2c + a) [Ans: HCF = (a + b + c), LCM = (a + b + c) (a + b – c) (a + c – b) (b + c –a) ] [Ans: 1, –2] 12. Solve: 52x + 2 – 126 . 5x + 5 = 0  1  1  1  1  1  1       13. Simplify : xa – ba – c.xb – cb – a . xc – ac – b [Ans: 1] 14. A number consists of two digits whose product is 12. If 9 is subtracted from the number, the digits interchange their places. Find the number.

21

[Ans: 43] 15. Calculate the value of x if the median of the given data is 24 [Ans: 10] 20 – 30 – 40 – Class0 - 10 10 – 20 30 40 50 interval Frequency 4 12 x 9 5 16. On a windy day, a boy of height 1.1m was flying his kite when the length of the string of the kite was 33m, it makes an angle of 30° with the horizon. At what height was the kite above the ground?

[Ans: 17.6m] 17. A metal object is made from a hemisphere and a cone with base radius 12cm. If the total height of the solid is 28cm, find the volume and surface area of the solid.[Ans: 1920πcm3, 528 cm2]

18. In the given figure the total surface area of the given square based pyramid is 96 cm2 and the slant height of the pyramid is 5cm, find the measure of the side of square base.[Ans: 6 cm]

A

B

E P

C

D

19. Shyam can do a piece of work in 20 days. Ram is found to be 20% less efficient than Shyam. Find in how many days will Ram do the same work.

[Ans:25 days] 20. The labelled price of an article is Rs. 1800 and the shopkeeper allows 20% discount. After imposing VAT, the sale price of an article becomes Rs. 1620, find the rate of VAT. [Ans: 12.5%] 21. The compound interest of a certain sum for 2 years is Rs. 8034 and the simple interest of the same sum for the same duration of time at the same rate of interest is Rs. 7800.

Find the sum and the rate of interest [Ans: Rs. 65000, 6%] E D F 22. ABCD and EBCF are two A parallelograms standing on the same base BC and between same parallels 22

B

C

AF and BC. Prove that area of //gm ABCD = area of //gm EBCF.

misread as 43 instead of 34, find the correct mean.[Ans: 46.50] (b) From the given ogive, find the modal class. [Ans: 60 – 80]

A

23. In a circle with centre O, chords AB and CD intersect outside the circle at E. Prove that ∠AOC – ∠BOD = 2∠AEC.

4.

B E

O D

C

24. Verify experimentally that the inscribed angle is half of the angle at the centre standing on the same arc. (Two different figures are necessary but the radii of the circles must not be less than 3cm)

5.

(a) The odds in favour of an event is 2 : 3. Find the probability of occurance of this event. [Ans: 2/5] (b) A bag contains 5 blue and x yellow balls. A ball is taken out and without replacing the first ball another ball is taken out. Draw a probability tree diagram and find the value of x, if the probability getting both 3 [Ans: 3] yellow balls is 28 (a) Find ∠BAD of a rhombus ABCD with sides 12cm and [Ans: 30°] area 72 cm2

25. Construct a parallelogram ABCD with AB = 3.6 cm, ∠A = 60° and AD = 4.4 cm. Also construct a triangle with one side = 5.5 cm and making its area equal to the area of the parallelogram. (b) Find the volume of the given solid. [Ans: 1400 cm3]

SET VI Answer all the questions

5cm

Group 'A'

1.

(a) (b)

2.

(a) (b)

3.

(a)

[9 × (2 + 2) = 36] a + b  Simplify :(a – b) × (b–2 – a–2) Ans: a2b2    4 3 5 3 × 27 × 9 1  Evaluate: 816 × 33 Ans: 81   Solve: 2a + 1 + a = 5.

[Ans: 4] 10 pencil and 2 eraser cost Rs. 40 and 25 pencils and 4 erasers cost Rs. 90. Find the cost of a pencil and an eraser.

[Ans: Rs. 2 and Rs. 10] Y The mean of 6 observations is 50 48 but one of the data was 40

16 cm

30 20 10 O 20 40 60 80 100 Marks

23 X

6.

(a) If the surface area of a marble is volume

1 cm2, find its 4π 1  3 Ans: 2cm  48π  

(b) Find the curved surface area of the given 7cm cone.

[Ans: 137.5 cm2]

7.

24

(a) Find the percentage discount if an article labelled at Rs. 4200 is sold for Rs. 3822. [Ans: 9%]

8.

(b) The population of a place was 2000. Within a year the population increased 3% by brith rate and 2% by migration. Find the present population. [Ans: 2100] (a) In the figure alongside PQRS is a P S parallelogram, PX and PY are the X altitudes. If QR = 12cm, SR = 10cm and area of PQRS = 96 Q R Y cm2, calculate PX and PY .[Ans: 9.6 cm, 8 cm]

(b) Find the values of a, b, and c. [Ans: a = 22°, b = c = 68°]

A 22°

O

a b

C

c B

9.

(a) In the given figure, if ∠DAB = 80°, ∠EDF = 15° and DF // BC, find the value of ∠ABC. [Ans: 115°]

D

A

E

15°

F

80° B C

B

b) Find the values of a, b and c.

[Ans: a = 65°, b = 130°, c = 25°]

a O c b A 65° E

C

D

Group 'B' [16 × 4 = 64] 10. A college awarded 38 medals in football, 15 in basketball and 20 in cricket. If these medals went to a total of 58 men and only three men got medals in all three games, how many received medals in exactly two of the three games. [Ans: 9] 25

11. Find the H.C.F. of: 8a3 – 27, 8a3 – 18a and 16a2 – 16a – 12 12. Solve : x+2– x–2 1 = x+2 + x–2 2

[Ans: (2a – 3)] 5  Ans: 2  

13. Simplify: x–3 54 2(x –3)  x+3  + – Ans:  2 2 4 2 2 x + 3x + 9 x – 3x + 9 x + 9x + 81  x – 3x + 9 14. Rs. 200 is divided equally among a certain number of children. If there were 25 children more, each would have received 40 paisa less, find the number of children.[Ans: 100] 15. Calculate the value of 'a' from the following data, if the upper quartile (Q3) is 74 [Ans: a = 10] Marks 20 – 40 – 60 – 80 – 40 60 80 100 No. of 8 12 a 6 students 16. A ladder 16m long leans against the wall of a house. If the foot of the ladder is 8m from the house, (i) at what height did the top of the ladder lean against the house from its foot? (ii) find the angle made by the ladder with the ground.

[Ans: 8 3 m, 60°]

17. A cone is placed on a cylinder as shown in the figure. The area of the base of the cylinder is 125 cm2 and height of the cylinder is 3cm. If the volume of the whole solid is 625 cm3, find the height of the solid. [Ans: 9 cm]

18. The given figure is a solid object made of a pyramid and a prism. Find the 26

10 cm 19 cm

volume of the solid object. [Ans: 148 cm3]

SET VII Answer all the questions

19. A man undertakes to do a cerain job in 40 days. He hires 15men for the job. At the end of 10 days, only one-fifth of the work was completed. How many extra men must be employed in order to complete the work in time?[Ans: 5 men] 20. A shopkeeper sold his goods for Rs. 16950 allowing 25% discount and then levied 13% VAT. Find the amount of discount.

[Ans: Rs. 5000] 21. The compound amount of a sum of money in 2 years is Rs. 8820 and in 3 years is Rs. 9261. Find the sum and the rate of interest [Ans: Rs. 8000, 5%] A

22. On the given figure, AE // CD, AB //EC//FD and CB //DA//FE. Prove that area of //gm ABCG = area of //gm EGDF.

C

2.

3.

E G

B

1.

F D

23. O is the centre of the circle in which inscribed angle ABC and central angle AOC are standing on the same arc. AC. Prove that ∠AOC = 2∠ABC. 24. Verify experimentally that the inscribed angles standing on the same arc are equal (Two different figures are necessary but the radii of the circles must not be less than 3cm) 25. Construct a parallelogram ABCD in which AB = 3.2 cm, BC = 5cm and AC = 3.5cm. Also, construct a parallelogram equal in area to the parallelogram ABCD whose one angle is 60°.

4.

5.

27

28

Group 'A' [9 × (2 + 2) = 36] –1 –2 –2 (a) Simplify :(x + y ) ÷ (x – y ) × (x –1 – y–1) [Ans: 1] 23 × 84 × 64–2 (b) Evaluate : 43 × 16–4 [Ans: 8192] –1

(a) Solve: x – 3 = 2 x [Ans: 9] (b) Find the two numbers such that 5 times the larger plus 3 times the smaller is 47 and 4 times the larger minus twice the smaller is 20.

[Ans: 7, 4] (a) The mean of a continuous series Y which has 80 terms is 40. When 30 25 class 5 – 15 is included in the 20 series, the new mean is 30. Find 15 the frequency of the class 10 5 interval 5 – 15. [Ans: 10] X O 10 20 30 40 5060 (b) Give the Q3 class from the Class Interval adjoining figure. [Ans: 30 – 40]

(a) What is probability of giving a child birth by a pregnant lady on a Tuesday?

[Ans: 1/7] (b) A coin is biased so that the probability that it lands 2 showing heads up is . The coin is tossed three times.

3 Draw a tree diagram to show the possible outcomes and find the probability that more heads than tails are D 20C obtained.

[Ans: ] 27 (a) In the given figure, ABCD is a 30° parallelogram. If BC = 5cm, and B A ∠DAB = 30°. Find the length of AB if the area of ∆ABC = 15 cm2.

6.

quadrilateral where BC is produced to E. If AB = AD and ∠ADB = 48° find the value of ∠DCE. [Ans: 84°]

[Ans: 6cm] (b) The perimeter of a triangular field is 540 m and its sides are in the ratio 25 : 17 : 12. Find the area of the P triangle.

[Ans: 9000 cm2] (a) Find the area of the triangular faces of the given pyramid if the C height of the pyramid is 5cm and the base is a square of side 24 cm .

A B [Ans: 312 cm2] 24 cm

(b) From the given figure, find the values of a, b and c. [Ans: a= b = c= 45°]

10.

7.

8.

(b) If the circumference of great circle of a sphere is πcm, π   find its volume. Ans: 6 cm3   (a) Hari sold three bags for Rs. 645 bearing a loss of Rs. 51. At what rate did he buy the bags.

[Ans: Rs. 232] (b) What is the rate of compound depreciation of a machine worth Rs. 1,00,000 which is sold after 2 years for Rs. 81,000.

[Ans: 10%] 1   (a) Calculate the area of the given quadrilateral.Ans: 2 h(a + b)  

11.

12.

13.

b h

14.

a

A

D

a (b) Find the values of a and b. [Ans: a = b = 60°]

15.

b O

30°

C

B

9.

(a) In the given figure, O is the centre of the circle and ABCD is a cyclic

A D B

O C

29 E

30

c a 2a O b

Group 'B' [16 × 4 = 64] In a survey of a group of students, it was found that 40% of the students like folk songs, 30% like modern songs and 20% like both songs. If 90 students like neither folk nor modern songs, find the number of students in the school and the number of students who like only folk songs.

[Ans: 180, 36] Find the LCM of 1 + 4a + 4a2 – 16a4 and 1 + 2a – 8a3 – 16a4.

[Ans: (1 + 2a)(1 – 2a) (1 + 2a – 4a2) (1 + 2a + 4a2)] 1 Solve: 4x + 4–x = 1616 [Ans: 2, –2] a–1 3 1 + (a + 2) (a – 1) – (1 – a)(1 – 2a) Simplify: (2a –1)(a + 2) a+4   Ans: (a + 2) (2a – 1)   A year hence a father will be 5 times as old as his son. Two years ago the father was 3 times as old as his son will be 4years hence. Find their present ages. [Ans: 29 yrs, 5 yrs] Calculate the median from the given data: [Ans: 11.83] Marks 0 – 5 – 10 10 – 15 – 20 – 25 – 30 – obtained 5 15 20 25 30 35 No. of 11 6 15 6 8 5 4 students

16. A man 1.6 m tall is 30m away from a tower and he observers the angle of elevation of the top of the tower to be 30°. What is the height of the tower?

[Ans: 18 .92m]

17. Find the volume of the given solid made up of cone on both sides.[Ans: 2310 cm3]

O

B

M D

8 cm

D

P C

23. In the cyclic quadrilateral ABCD, Prove that i) ∠BAD + ∠BCD = 180° and (ii) ∠ABC + ∠ADC = 180°.

24. Verify experimentally that the angle in the semi-circle a right angle. (Two different figures are necessary but the radii of the circles must not be less than 3cm) 25. Construct a quadrilateral ABCD in which AB = BC = 6cm, AC = AD = 6.5 cm and ∠BAD = 60°. Also construct a triangle equal in area to the quadrilateral ABCD.

P

A

A

B

14 cm

18. In the given solid, the upper part has a pyramid of slant height 5cm and the lower part is a prism of side 8cm. If the volume of the solid figure is 448 cm3, find the height of the prism.

[Ans: 6 cm]

22. In the given tranpezium ABCD, AD // BC and AP = PB. Prove that 1 ∆PCD = 2 trap. ABCD.

C

19. Amit and Ankit can do a piece of work in 16 days and 24 days respectively. Amit worked alone for 4 days and Ankit worked alone for 6 days. In how many days will the 4   remaining work be finished if they work together?Ans: 45 days   20. A shopkeeper allows a discount of 10% and still makes a profit of 15% on selling an article. If the marked price of the article is Rs. 15000, find its selling price, cost price and profit.

[Ans: Rs. 13500, Rs.11739.13, Rs. 1760.87] 21. The difference between the compound interest and the simple interest on a sum of money for 2 years at a rate of 10% interest per annum is Rs. 20. Find the sum.[Ans: Rs. 2000]

31

32

side QP = 6 cm and the side PS = 9 cm, determine the measure of the ∠SRT. [Ans: 60°]

SET VIII S.L.C. Question 2065 CDR 2065 (2009) Attempt all the questions.

Group'A' [9×(2+2)]=36 132x+1 + 5 × 169x 1= (a) Simplify : [Ans: 2] 9 × 169x (b) Evaluate:

4

216a9b5 ÷

4

6–1a–3 b

(b) Given figure is a triangular prism whose volume is 1,800 cubic cm.

If AB = 15 cm, BC = 8 cm and ∠ABC = 90o, find the length of the prism. [Ans: 30 cm]

[Ans: 6a3b]

2= (a) Solve : 9x2 – 20 = 3x – 2 [Ans: 2] (b) If 6 is added to the square of a number, the result is 31.

Find the number.

[Ans: +5, –5] 3. (a) The mean weight of some men is 56 kg and the sum of their weight is 392 kg, find Y the number of men. [Ans: 7] 250 (b) From the given graph, find 200 the third qnartile class. [Ans: 150 100 40 – 60]

6.

A

A'

B'

B C'

C

(a) Obtain the total surface area of a hemisphere having the diameter 21 cm.

[Ans: 1039.50 cm2]

(b) The curved surface area of the given cone is 8,800 sq. cm. If the slant height is 100 cm, determine the height PO of the cone. [ Ans: 96 cm2]

P

Q

O

R

50

4.

O 20 40 60 80 100

cubed number.

5.

X

(a) A number card is drawn Marks obtained randomly from the set of numbered cards, numbered from 6 to 39. Find the probability that the card may be a prime number or a

7.

5 [Ans: 7 ]

(b) An urn contains 7 green and 9 black balls of the same shape and size. Two balls are drawn at random one after the other without replacement. Draw a tree diagram showing all the probabilities and also find the 3 probability of getting both black balls.

[Ans: ] 10 (a) In the given figure, PQRS is a S P parallelogram in which QR is produced to the point T. If the area of Q the parallelogram is 27 3 sq. cm, the T R

8.

(a) At 18% loss the selling price article of an article is Rs. 164. Calculate the cost price of the article. [Ans: 200] (b) A radio costing Rs. 6,000 is depreciated per year and 2 years later its price becomes to Rs. 5,415. Find the rate of depreciation in percent.

A D E [An: 15%] (a) In the given figure, ABCD is a rhombus in which the B C diagonal AC = 20 cm and the diagonal BD = 28 cm. If AD is produced to E, find the area of the ∆BCE. [Ans: 140 cm2] (b) In the given figure O is the centre of the circle. If ∠QOR = 110o, calculate the value of the ∠PSQ. [Ans: 35°]

P

S

Q O 110° R

33

34

B

A

9.

F

10°

E

92°

(a) In the given figure, ABCD is a cyclic quadrilateral in which AB is produced to F. If DC || BE, ∠DAB = 92o and ∠FBE = 10o, evaluate the ∠ADC. [Ans: 98°]

D C

P

(b) In the given figure, PT is a tangent in which T is the point of contant. If ∠PTQ= 75° and ∠STQ = 35°, calculate the ∠QST. [ Ans: 105°]

Group 'B'

S 35°

75° T

Q

[16 × 4 = 64]

10. If n(A) = 48, n(B) = 51, n(C) = 40, n(A∩B) = 11, n(B∩C) = 10, n(C∩A) = 9, n(A∩B∩C) = 4 and n(U) = 120, find the –––––– . Present the above values of n(A∪B∪C) and n (A∪B∪C) information in a Venn diagram.

[Ans: 113,7] 11. Find the H.C. F. of: 9x2 – 4y2 – 8yz – 4z2, 4z2 – 4y2 – 9x2 – 12xy and 9x2 + 12xz + 4z2 – 4y2 [Ans: 3x + 2y + 2z] 343 12. Solve : 7x + 7x = 56 [Ans: 1,2] x+3 x–3 54 13. Simplify: x2 + 3x + 9 + x2 – 3x + 9 – x4 + 9x2 + 81 [Ans: 2(x – 3) 2 x – 3x + 9 ] 35

14. A number consists of two digits whose sum is 9. It three times the number is equal to eight times the number formed by interchanging the digits, find the number. [Ans: 72] 15. Compute the median from the table given below: [Ans: 49.16] Marks obtained 25– 35– 45– 55– 65– 75–85 35 45 55 65 75 No. of students 5 10 12 8 3 2 16. From the roof of a house of 6m tall, the angle of elevation of the top of a tower was observed and found to be 30°. If the distance between the house and the tower was 19 3 m, determine the height of the tower.

[Ans: 63 m] 17. Given figure is s solid composed of a cylinder with hemisphere at one end. If the total surface area and the height of solid are 770 sq cm. and 14 cm respectively. Find the height of the cylinder.[Ans: 7cm]

18. Given figure is a square based pyramid. If the slant height of the pyramid is 17cm and the side of the base 16 cm, determine the volume of the pyramid.

[Ans: 1280 cm]

16cm

19. A man undertook a contract to finish a piece of work in 32 days and he immediately employed 28 labourers to do the work. After 24 days only two third of the work was finished. How many labours should be added to finish the work in time?

[Ans: 14] 36

20. After allowing 16% discount on the marked price of an article and levying 13% value added tax, then the price of the article becomes to Rs. 9,492. Find the value added tax.

[Ans: Rs. 1092] 21. A person took a loan of Rs. 46,875. If the rate of compound interest is 4 paisa per rupee per year, in how many years will the compound interest be Rs. 5,853.

[Ans 3 yrs] 22. Prove that the centre angle MCN at the center C of a circle is twice the angle MPN at the circumference standing on the same arc MN. 23. In the given figure, ABCD is a parallelogram. If M and N are any points on CD and DA respectively, prove that ∆AMB = ∆CDN + ∆ANB.

D

M

C

N A

SET IX Send-Up Test: 2009 SEDIPS Answer all the questions x+2

1.

2.

3.

(a) Simplify : (b) (a) (b) (a)

5

Group 'A' – 45.5x – 1 16.5x

[9 × (2 + 2) = 36] [Ans: 1]

3 3 Evaluate: 24a7b11 ÷ 3a4b5 [Ans: 2ab2] [Ans: 9] Solve: x + 16 = x + 2 Divide 25 into two parts such their product is 156.[Ans: 12, 13] Find arithmetic mean from given data: [Ans: 2.94]

B

x 1 2 3 4 5 f 2 4 6 5 1 (b) Find the class and frequency of first quartile from the following graph.

[Ans: 2 – 4, 20]

24. Verify experimentally that the sum of the opposite angles of a cyclic quadrilateral is two right angles (Two circles of radii not less than 3cm are necessary).

25. Construct a quadrilateral PQRS having PQ = 4.4 cm, QR = 4.9cm, RS = 4.2 cm, SP = 2.8 cm and SQ = 6.6 cm. Draw a ∆PST equal in area to the quadrilateral.

Y 140 120 100 80 60 40 20 0

2 4 6 8 10 12

X

Marks

4.

37

38

(a) A card is drawn at a random from a well shuffled pack of 52 cards. Find the probability that it is a king or red 7 card.

[Ans: 13 ] (b) A bag contains 10 white and 15 black balls. Two balls are drawn randomly one by one without replacement.

By drawing tree diagram, show all S R the probabilities with possible outcomes.

P

Q

5.

= 130°. Find the value of ∠ QOS [Ans: 100°]

(a) The area of rhombus PQRS is 18 3 sq cm and side of rhombus is 6cm. Find ∠SPQ. [Ans: 60°]

D

6.

7.

8.

(b) Find the lateral surface area of A E F 12cm given triangular prism.

2 [Ans: 720 cm ] B 9cm C (a) The total surface area of a hemisphere is 1848 sq cm, find its radius.

[Ans: 14 cm] (b) If the area of the curved surface of a circular prism of radius 5cm is 660 cm2, find its volume. [Ans: 1650 cm3] (a) A fruit seller bought 1200 oranges at Rs. 1.50 each . If he sold them at Rs. 21.60 per dozen, find his profit or loss percent.

[Ans: 20%] (b) The cost of a motorbike after 3 years becomes Rs. 92583 at the rate of depreciation of 10% per annum.

Calculate the original price of the motorbike.[Ans: 127000] (a) In the adjoining figure, AB = 4cm, AC = 5cm and ∠ABC = 90°, find the area of parallelogram ABDE. [Ans: 12 cm2] (b) In the given figure, AB is the diameter of a circle with center O and ∠BOD = 120°, find the value of x. [Ans: 30°]

D

E

A

C

(b) In the given figure, ABE is a tangent where B is the point of contact. If AB = BC and ∠CBE = 50°, find ∠DBC. [Ans: 105°]D A

11.

B

13.

D

14.

x O C

120° B

15.

P

9.

(a) In the given circle, O is the centre of the circle. If ∠QRS

O Q

S R 39

B

C E

Group 'B' [16 × 4 = 64] 10. In a class X, 20% students passed in all three subjects, 46% failed in Maths, 57% failed in English, 42% failed in Science, 35% failed in Math and English, 25% failed in English and Science, 15% failed in Science and Maths. (a) Find the percentage of students who failed in all three subjects.

12.

A

O

40

(b) Draw a Venn -diagram to show the above information. [Ans: 10%] Find the HCF of : [Ans: 2a – 1] 8a3– 1, 4a3 – 2a2 + 2a – 1 and 6a2 + 11a – 7 26 Solve: 51 – x + 5x – 1 = [Ans: 2, 0] 5 1 2 1 2  54x  Simplify : x – 3 – 2x + 3 + x + 3 – 2x – 3 Ans: (x2 – 9)(4x2 – 9)   The sum of the digits of a two digits number is 13. If the digits are reversed, the new number is 9 less than the original number. Find the number.

[Ans: 76] Find the median from the table given below: [Ans: 60] Marks 35 – 45 – 55 – 65 – 75 – obtained 45 55 65 75 85 No. of 7 8 10 9 6 students

AE = arc BF, Prove that 16. The upper part of the tree broken down by the wind makes an angle of 30° with the ground and the distance from the ∠ACE = ∠BDF. foot to the point where the top of the tree touches the ground is 50m. What was the original height of the tree?[Ans: 86.6 = 50 3 m] 24. Verify experimentally that the opposite angles of a cyclic 17. Find the volume of the given solid: quadrilateral are supplementary. (Two figures with radii of 3 circle more than 3 cm are necessary) [Ans: 718.66 + 3080 + 616 = 4414.66 cm ] 32 cm 25. Construct a quadrilateral ABCD in which AB = 6.1 cm, BC = 5.4 cm, CD = 4.9cm, AD = 5.1cm and BD = 5.9 cm. Also 12 cm 14 cm construct a triangle equal to the area of quadrilateral ABCD. O

18. In the given figure, the total surface area of the given square based pyramid is 384 sq cm. and D the side of a square base is 12 cm, find the slant height of pyramid.[Ans: 10 cm]

C

B

A

19. Ram takes 16 days and Shyam takes 24 days to finish a piece of work separately. Ram alone worked for 4 days and Shyam alone for 6 days. In how many days will the remaining work be finished if they worked together?[Ans: 4.8 days ] 20. A shopeeer sells an article at 8% discount and gains Rs. 40.

If he does not allow any discount, he will gain Rs. 60. At what price did the purchase the article?[Ans: MP = Rs. 250, CP = Rs. 190] 21. The compound amount of a sum of money in 3 years and 4 years are Rs. 3240 and Rs. 3888 respectively, find the rate of interest compounded yearly and the sum.[Ans: R = 20%, Rs. 1875] 22. Prove that the parallelograms standing on the same base and between same parallels are equal in area.

E

23. In the given figure, O is the centre of a circle. AB is a chord, C and D are two points on AB. If AC = BD and arc

A O

C

F

D B 41

42

BC = 12cm and area of parallelogram ABCD = 54 cm2. Find the measure of AB. [Ans: 9 cm] (b) Find the volume of the given prism.[Ans: 30 7 = 79.37cm3]

SET X Send-Up Test: 2009 SEDIPS Answer all the questions Group 'A' 7. 3 – 9.3a –2 (a) Simplify : 3a+2 – 3a + 1

[9 × (2 + 2) = 36]

A

a

1.

2.

3.

B

3 3 (b) Evaluate: 54a7b9 × 4a2b3 [Ans: 6a3b4] (a) Solve: x – 4 = x – 2 [Ans: 4] (b) The sum of two numbers is 10 and their product is 21.

Find the numbers.

[Ans: 7, 3] (a) Find the arithmetic mean from given data: [Ans: 5.06] x 2 4 6 8 f 3 4 5 3 (b) Find the class and frequency of median from the following graph [Ans: 40 – 60, f = 10]

O 20 40 60 80 100 Mark obtained

4.

5.

E

6.

7.

8.

X

(a) Find the probability of having a number which is prime 2 or odd when a dice is thrown.

[Ans: 3] (b) If three children are born in a family, calculate the probability that all children are girls by drawing a tree 1 diagram.

[Ans: ] 8 (a) ABCD is a parallelogram A D in which ∠ABC = 30°, 43

30° B

C

C 6 cm F

Y 60 50 40 30 20 10

4 cm

4 cm

[Ans: 1]

D

(a) If the surface area of a sphere is 1386 sq cm, find its radius.

[Ans: 10.5 cm] (b) A cone has radius of base 7cm and its slant height is 25cm. Find its volume.

[Ans: 1232 cm3] (a) Pravin bought a second hand bike for Rs. 45000. He spent Rs. 3260 on its repair. If he sold it for Rs. 44520, find his gain or loss percent.

[Ans: 7.74 %] (b) The price of a machine is depreciated from Rs. 50000 to Rs. 40500 in two years. Find the rate of depreciation.[Ans: 10%] (a) PQRS is a parallelogram in which the altitude SM on the side PQ is 6 cm, the altitude SN on the side QR is 5cm and its area is 45 sq cm. Find the sides of the parallelogram.

[Ans: QR = 9cm, PQ = 7.5 cm] D

(b) In the given figure, O is the centre of the circle. If ∠ACB = 30°, find the value of ∠ DBA. [Ans: 60°]

C O B

A

B 44

A

O

C D

9.

(a) In the given circle, O is the centre and ABCD is a cyclic quadrilateral. If ∠ADB = 30°, what will be the value of ∠BCD? [Ans: 120°]

(b) In the given figure, ABE is a tangent where B is the point D of contact. If AB = BC and A ∠DBC = 105°, find ∠DBA .[Ans: 25°]

16. A boy who is 1.5m tall is flying a kite. When the length of the string of kite is 200m, it makes an angle of 30° with horizontal. At what height is the kite from the ground [Ans: 101.5m] 17. Find the total surface area of given solid made of hemisphere and cone.

O

B

[Ans: 858 cm2]

C

C

E

24 cm

O

C

O 31 cm

10.

11.

12.

13.

14.

15.

Group 'B' [16 × 4 = 64] In the class IX, 58% students failed in Account, 39% in English and 25% in Statistics, 32% in Account and English, 19% in Account and Statistics, 17% in English and Statistics, 13% in all the three subjects. (a) Draw a Venn -diagram to show above information. (b) What percent passed in all three subjects. [Ans: 33%] Find HCF of : m6 – 1, m5 + m3 + m and m3 + 2m2 + 2m + 1[Ans: m2+ m + 1] Solve : 4. 3x + 1 – 9x = 27 [Ans: 2,1] 1 2 4 8 1   Simplify: + 2 + 4 + 8 Ans:  x+1 x +1 x +1 x –1 x – 1  A number of two digits is 36 less than the number with the digits reversed. If the unit digit exceeds twice the tens digit by 1, find the number [Ans: 37] Find the first quartile from the table given below:[Ans: 88.75] Wages (Rs.) 50 – 70 – 90 – 110– 130 – 70 90 110 130 150 No. of 5 8 15 12 10 workers

18. The figure is the square pyramid in which vertical height OP is 8 cm, and length of base side is 12 cm, find its total surface area.[Ans: 384 cm2]

P

19. A and B can do a piece of work in 24 days. A takes 40 days to complete the same work. After they work for 8 days, A leaves. If B completes the remaining work, in how many days was the whole work completed?

[Ans: 48 days] 20. A shopkeeper sells an article at 5% discount and makes a profit of Rs. 15. If he does not allow any discount, he will gain Rs. 25. At what price did he purchase the article?[Ans: MP = Rs. 200, 21. Find the difference between interest compounded yearly and half yearly on Rs. 16000 in 2 years at 10% p.a.[Ans: Rs. 88.1] 22. Prove that the triangles standing on the same base and between ame parallels are equal in area.

A 23. In the given figure, M and N are the mid points of arc AB and arc AC respectively. Prove that AE = M N E F AF. B

45

46

C

(ii) How many students have secured less than 25 marks?

[Ans:25]

24. Verify experimentally that inscribed angles standing on the same arc of a circle are equal. (Two circles of radii at least 3cm are necessary.)

25. Construct a quadrilateral ABCD in which AB = BC = 5cm, CD = DA = 6 cm and ∠BAD = 60°. Also construct a triangle whose area is equal to the area of quad ABCD.

100 90 80 70 60 50 40 30 20 10 O 10 20 30 40 50 60 70 80 90 100

SET XI

Marks

National PABSON Answer all the questions Group 'A' a2x . ax – 1 – ax 1. (a) Simplify : a3x – a x + 1 (b) Evaluate: 2.

3.

5

32a2b–1c ÷

5

4.

[9 × (2 + 2) = 36] 1 [Ans: a ] 2a [Ans: 3c ]

24a–3b–1c6

3 (a) Solve: x2 – 1 – 2 = 0 [Ans: ± 3] (b) When a number increases by 25% it becomes 10. Find the number.

[Ans: 80] (a) Find the class of the upper quartile of the data.[Ans: 50 – 60] Class No. workers

0-10 1020 of 3 4

2030 6

3040 5

5.

5cm

(b) Find the total surface area of the given triangular prism.

[Ans: 72cm2]

40-50 50-60 11

(a) From a well shuffled pack of cards, a card is drawn at random. Find the probability of getting the card red or 7  ace. . Ans:13   (b) In a bag there are 3 green and 4 red identical balls. If two balls are drawn at random one after another. Show all the probabilities in a tree diagram and find the probability of not getting both balls green without 1 replacement .

[Ans: 7 ] (a) In ∆ABC, AB = 6cm, ∠A = 100° and ∠C = 20°. Find the side BC, if the area of ∆ABC is 12 3 cm2 [Ans: 8 cm]

3cm

15cm

10

(b) Study the given ogive and answer the following questions. (i) How many students have secured distinction marks? [Ans: 10]

47

6.

(a) If the radius and height of a right circular cone are 3cm and 4cm respectively, find its total surface area.[Ans: 75.43 cm2 ] (b) The sum of the radius and height of a cylinder is 15cm.

If its base circumference is 44cm, find its volume[Ans: 1235 cm3]

7.

(a) An article was sold for Rs. 1560 at the profit of 30%.

Find the cost price.

[Ans: Rs. 1200]

48

(b) In how many years will the population of a town be 209475 from 190000 at the growth rate of 5% per annum?

[Ans: 2 yrs] A

8.

D

(a) In the adjoining figure, ABCD is a trapezium in which AD // 1 BC and AD = 2 BC. If the area B of ABCD is 120 cm2 and height (DM) = 5cm, find the area of ∆ADC. [Ans: 40 cm2]

M

(b) In the given circle, O is the centre and ∠ABC = 150°. Find the value of x.

[Ans: 60°]

O

(a) In the given circle O is the centre and MNQP is a cyclic quadrilateral. If ∠MPQ = 110°, find ∠QMN. [Ans: 20°]

(b) In the given figure O is the centre of the circle EBF is a tangent where B is the point of contact. If AB is a diameter and ∠DBF = 72°, find the value of ∠BCD. [Ans: 108°]

C

x 150° A

9.

C

B

P

Q

110°

M

N

O

A D O E

only, 40 are fond of playing basketball only. If 20 students are fond of playing football and basketball only, by drawing a Venn-diagram. Find (i) the number of students who play all games. (ii) how many students don't play any game? [Ans: 10, 40] 11. Find the HCF and LCM of : a2 + b2 – c2 + 2ab, b2 + c2 – a2 + 2bc and c2 + a2 –b2 + 2ca.

[Ans: HCF = a + b + c, LCM = (a + b + c) (a + b – c) (a + c – b) (b + c – a)] 5x – 4 5x – 3 12. Solve: =2+ [Ans: 5] 2 5x + 2 1 1 1 1 16a 13. Simplify: a –3 – a – 1 + a + 3 – a + 1[Ans: (a2 – 9) (a2 – 1) ] 14. A number of two digits exceeds seven times the sum of the digits by 6. If 45 subtracted from the number, the digits are interchanged. Find the number.

[Ans: 83] 15. Find the median from the given data.

[Ans: 16.875] Age 5 -10 10 – 15 – 20 – 25 – 30 – 15 20 25 30 35 No. of 6 7 8 4 5 2 students 16. A man of height 1.68 m observes a pillar of height 31.68m and finds the angle of elevation of the top of the pillar to be 60°. How far is the man from the base the pillar. [Ans: 17.32m] 17. Find the volume of the solid given alone side. [Ans 667.33 cm2] 7 cm

C B

15 cm

F

Group 'B' [16 × 4 = 64] 10. In a survey of 200 students, 70 are fond of playing cricket, 80 football and 100 basketball. Similarly 20 are fond of playing cricket and football only, 30 cricket and basketball 49

18. Find the total surface area of the 14 cm given solid figure which is the combination of prism and pyramid. [Ans: 672 cm2] 12cm

50

6cm 12cm

19. A tap can fill 25% of a tank in 3 hours and another tap can empty whole tank in 15 hours. If both the taps are opened at the same time and the capacity of a tank is 1000 liter in what time 100 liter water will be collected in the tank.[Ans: 6 hrs] 20. After allowing 7% discount on the marked price and levying 11% VAT, an article is sold. If the amount of VAT is Rs. 102.30, find the marked price of the article and the discount amount.

[Ans: MP = Rs. 1000, Discount = Rs. 70] 21. The simple interest on certain sum of money in 3 years at 30% per annum will be Rs. 1188 less than the compound interest. Find the sum.

[Ans: Rs. 4000] 22. Prove that a rectangle and the parallelogram standing on the same base and between the same parallel lines are equal in area.

A

{ = DC { , 23. In the given figure if BC prove that PQ // DB.

SET XII J.S.T. Examination, 2065 Attempt all the questions.

Group "A" [9 × (2 + 2) = 36] 6 7 35 × 24 × 5 [Ans: 1] 1. (a) Evaluate: 426 × 207 ×6 3 (b) Simplify:

128 + 4

2.

4

54 –

3

250

500 – 108

2 x (a) Solve: 3x –3 = 3 [Ans: 1,9] (b) A number is such that it is as much greater than 21 as it is less than 37. Find the number.

[Ans: 29] –––

3.

D P

(a) In a data X = 10.4, Σfx = 1040 and N = 25P what is the value of P? [Ans: 4] Y

C F

Q

(b) From the given ogive in the figure, find the first quartile.

[Ans: 8 .67]

B

24. Verify experimentally that the length of two tangents to a circle at the point of contact from an external point are equal. (Two circles of radii more than 3cm are necessary) 25. Construct a triangle PQR in which PQ = 7cm, QR = 5.5cm and PR = 6cm. Construct a parallelogram OMNQ equal in area to the triangle PQR such that OQ = 8cm.

1 [Ans: 1 ] 23

20 16 12 8 4 O 4 8 12 16 20 Marks obtained

4.

X

(a) A dice is rolled once. Write the sample space and find the probability that the outcome is either a prime 5 number or an even numbers. [Ans: S = {1,2,3,4,5,6}; 6) (b) There are 5 black and 8 white balls of same shape and size in a basket. If two balls are drawn randomly in succession without replacement from the basket. Show the probability of all possible outcomes A in tree 26cmdiagram.

D 80° 43cm

51

52

40°

B

C

9.

5.

(a) Find the area of the adjoining parallelogram.[Ans: 968.18 cm2] A'

A

(a) In the figure, O is the centre of circle. If ∠OBC = 60° and BC //OE, then find the measure of ∠BAE. [Ans: 60°]

6cm

(b) What value of h in the prism shown in the figure makes its B total surface area 528 cm2?[Ans: 20cm] 8cm

B'

h

C

6.

(a) Find the curved surface area of the given cylinder.[Ans: 3520 cm2]

C'

(b) From the given information in 8 cm O C figure, find the measure of AB.[Ans: 15 cm]

8 cm

A

140cm

B

7.

8.

(b) A cone whose radius of base is 7cm has a volume of [Ans: 24cm] 1232 cm3, Find the height of the cone. (a) If a shopkeeper sold a watch for Rs. 640 at a loss of 20% . Find the cost price of the watch.

[Ans: 800] (b) A motorcycle which was purchased at Rs. 90000 was sold for Rs. 81000 after one year. At what percent was it depreciated?

[Ans: 10 %] E (a) In the given figure parm. BCDE and ∆AED stand on same base and between the same parallel lines. The area of ∆AED is B A 32cm2. Find the area of ∆BCD.[Ans: 32 cm2]

D

35°

A

13.

C

x

(b) In the adjoining figure O is the centre of circle. Find the value of x.

[Ans: 125°]

11.

12.

C D

10.

B

O

14.

15.

Group "B" [16 × 4 = 64] In a survey of a group of people, showed that: 60 liked tea, 45 liked coffee, 30 liked milk, 25 liked coffee as well as tea.

20 liked tea well as milk, 15 liked coffee as well as milk and 10 liked all the three. How many people were asked this question? Solve by drawing the Venn-diagram. [Ans: 85] Find the LCM of : 3x2 + 12x + 12, x2 – ax + 2x – 2a, x2 – 3x – 10 [Ans: 3(x + 2)2 (x – a) (x – 5)] If a + b + c = 0 prove that: 1 1 1 xb + x–c + 1 + xc + x–a + 1 + x–a+ x–b + 1 = 1 Simplify: 1 1 1 1 x2y2 + – [Ans: 2– 2 2 y x y y x y x4 – y4 ] 1 + x y – x 1 + x2 y2 – x2 The product of the present ages of two brothers is 160. 4 years ago. elder brother was twice as old as is younger brother. Find their present ages.

[Ans: 16 yrs, 10 yrs] The following table shows the age of the workers of a factory in a village. Find the third quartile.

[Ans: 51.5]

A

Age O

E

60°

B

C

53

54

20

- 30

- 40

– 50

– 60

–

30 of 5

40 9

50 10

60 6

70 4

No. worker 16. A man 1.6m tall, observes the top of a pillar of the height 26.6m situate d in front of him and the angle of elevation to be 30°. How far is the man from the pillar? Find it. [Ans: 43.3 m] A

17. The given figure is a solid made of cone and an hemisphere in which OA = OA' = 7cm. A'P = 25cm, find the volume of the given solid objects.

[Ans: 1950.67 cm3]

P

O

A'

18. Given figure is combined form of pyramid and cubical prism. If the area of the base of cubic prism is 144 cm2 and height of the obtained figure is 20cm. Find the total surface area of the given figure.[Ans: 960 cm2]

23. In the figure, AB // ED, BF //DC and BF = DC. Prove that ∆AFE = 1 2 quadrilateral BFDC. 24. Verify experimentally that the angle at the circumference is equal to half of the angle at the centre, both standing on the same arc of a circle. (Two circles of radii not less then 3cm are necessary.)

25. Construct a triangle ABC having AB = 7.1cm, ∠BAC = 60° and AC = 5.7cm. Also construct a parallelogram having one side 7.5cm and equal in area to the triangle ADC.

20 cm

19. A man undertakes to do a certain job in 32 days. He hires 12 men for the job. At the end of 8 days only one fifth of the work was completed. How many extra men must be employed in order to complete the work in time.

[Ans: 4] 20. When an article is sold at a discount of 10% of marked price, a profit of Rs. 8 is earned by the seller. If the same article was sold without allowing a discount a profit of Rs. 20 is earned. What should be the cost price of the article.[Ans: Rs. 100] 21. Find the compound amount and compound interest on Rs. 1 600 at 5% p.a. for 12 years interest is payable half yearly. [Ans: 646.13, Rs. 46.13] 22. Prove that the opposite angles of cyclic quadrilateral are supplementary.

B

A F E

C 55 D

56

SET XIII Joint S.L.C. Send-up Examination 2065 (KUHS/RBS/SXG/SXT] Answer all the questions Group 'A' + 9.3 2x – 1 3. 9 (a) Simplify : 12. 32x – 6.9x

[9 × (2 + 2) = 36]

x+1

1.

2.

3.

[Ans: 5]

4 4 [Ans: 4a3] (b) Evaluate : 128 a3 ÷ 2–1a–9 (a) Solve : x + x – 20 = 10 [Ans: 36] (b) 250 bananas were divided equally among a certain number of students. If there were 25 more students, each would receive half banana less. Find the total number of students.

[Ans: 25] (a) The arithmetic mean of 15 members is 12. When two numbers are eliminated the mean becomes 11. If the difference of the two eliminated numbers is 3, find the numbers.

[Ans: 20, 17]

5.

(b) Find the volume of the given triangular prism. [Ans: 346.4 cm3] 6.

(b) Find the median of the data related to the figure given alongside.

[Ans: 40]

Y 60 50 40

7.

30 20 10

0

10 20 30 40 50 60 70 80 X Markes obtained

8.

4.

(a) A boy can solve a problem accurately with a 4 probability of 5 . If he is given three problems, what is 57

the probability that he will solve at least two problems 48 accurately?

[Ans: 125 ] (b) A bag contains 15 red balls and 20 white balls. Two balls are taken randomly one after the other without replacement. Find the probability of getting the balls of P same color showing all the possible outcomes in the 59 S Q tree diagram.

[Ans: 119 ] O O (a) In the given figure along side, if 8 cm the area of the kite is 48 cm2, R find the measure of ∠PRQ. [Ans: 30°]

58

8 cm 20 cm

(a) The circumference of the base of the cylinder is 44cm and the sum of its radius and height is 17cm. Find the total surface area of the cylinder.

[Ans: 748 cm2] (b) If the total surface area of the hemisphere is 462 cm2, find its volume.

[Ans: 718.67 cm3] 1 (a) If the selling price of an article is less by 4 of the cost price, find the profit or loss percentage.

[Ans: 25%] (b) A computer, which is supposed to depreciate at the rate of 5% per annum, was sold at Rs. 36100 after two years. At what price was it bought? [Ans: Rs. 40,000] M 6 cm N (a) In the given figure, MNRP is a trapezium in which MN // PR, ∠MNR = ∠PRN = 90°, NR = P R 8cm, PM = 10cm and MN = 6cm. Calculate the area of the trapezium MNRP.

B

A 92°

(b) In the given figure, if AE // CD, ∠C = 108° and ∠B = 92°, find the measure of ∠EAR.[Ans: 20°]

C

R

108°

E D

E

9.

(a) In the given figure, AB is the diameter and AB //CD. If ∠BCD = 40°, find the value of ∠BEC. [Ans: 50°]

C

C

10.

11.

12.

13.

14.

O

A

B

40°

15 cm

D

D

(b) The length of external common O O 4 tangent to two circles of radii 12 12cm and 4cm is 15cm.

Calculate the distance between their enters.

[Ans: 17cm. ] Group 'B' [16 × 4 = 64] In a group of students, 20 study economics, 18 study history, 21 study science, 7 study economics only, 10 study science only 6 study economics and science only and 3 study science and history only. (a) Represent the above information in the Venn-diagram. (b) How many students study all three subjects? (c) How many students are there in the group? [Ans: 2, 41] Find the H.C.F. of : m(m + 1) – n(n + 1), m(m + n) – (1 + n) and (n + 1) – m (m + n) [Ans: m + n + 1] 1 [Ans: 2,3] Solve: 3x – 3 + 32 – x = 13 2a 4a3 8a7 1 1 [Ans: b – a] Simplify : a + b + a2 + b2 + a4 + b4 – a8 – b8 Surakshya said to Shirish, "I am twice as old as you were when I was a old as you are "If the sum of their present ages is 49, find their present ages.

[Ans: 28 yrs, 21 yrs] 59

15. Find out the third quartile of the data given below in the table.

[Ans: 75] Marks 0-20 20 - 40 - 60 60 - 80 80 obtained 40 100 No. of 5 10 15 5 10 students.

16. On a windy day, A boy of height 1.1m was flying his kite.

When the length of string of the kite was 33m, it makes an angle of 30° with the horizon. At what height was the kite above the ground, supposing that there is no slack in the string.

[Ans: 17.6 m] 17. What is the total volume of the cones formed when a right angled triangle of two perpendicular sides of 3 cm and 4cm length is rotated around its hypotenuse [Ans 37.31 cm3, 50.29cm3] 18. The ratio of the heights of the pyramid and the prism is 4:5, in solid figure given along side. If the volume of the square based prism is 1440 cm3 and the total height of the solid is 18cm, find the lateral surface area of the pyramid.[Ans: 240 cm2] 19. A can do a piece of work in 20 days, B can do it in 30 days and C in 40 days. Three of them started the work together but A left the work after 5 days and C left it 10 days before its completion. Calculate the number of days required to 1 finish the whole work.

[Ans: 17 ] 7 20. After allowing 20% discount on the marked price and then levying 10% VAT, a the radio was sold. If buyer had paid Rs. 320 for VAT, how much had he got in the discount?[Ans: 800] 21. According to the yearly compound interest, a sum of money amounts to Rs. 6050 in 2 years and Rs. 6655 in three years.

What was the sum?

[Ans: Rs. 5000]

60

22. Prove that the areas of the parallelogram on the same bas e and between the same parallel lines are equal.

A H B 23. ABCD is a cyclic quadrilateral. AB E and DC produced to meet at E, the C D circle with center E and radius EC L K cuts AB at H and HC, BC meet AD at K, L, respectively. Prove that CL = KL. 24. Verify experimentally that the sum of the opposite angles of a cyclic quadrilateral is 180°. (Two circles of radii not less than 3 cm are necessary) 25. Construct a triangle equal on area with the given quadrilateral ABCD in which AB = 4cm, BC = 5cm, CD = 4.5cm, DA= 6cm, and diagonal AC = 7cm.

SET XIV JOINT S.L.C. SEND-UP EXAMINATION-2065 Attempt all the questions.

Group A [ 10×(2+2)=40] x+3 x+2 3.4 – 2.4 40 1. a Simplify: [Ans: ] 5.42 + x – 3.4 x + 1 17

2.

b. a. b.

3.

a.

b.

3 5 Evaluate: 16x5 y7 ÷ 2x2 y4 [Ans: 2xy] 2 [Ans: 2] Solve : x + x - 3 = 3 Rs.60 was divided equally among a certain number of boys. If there were 2 more boys, each would receive Rs.1 less. Find the total number of boys and the total amount of money.

[Ans:Rs. 60, Rs.10] The arithmetic mean of 25 numbers is 8. If the three numbers, which are in the ratio of 2:3:4 are added, the mean becomes 8.75, find those three number [Ans: 10,15,20] Find the median of the data related to the figure given alongside.

[Ans: 15] Y 60 50 40 30 20 10

0

5 10 15 20 25 30 35

X

Age of people

4. a.

The probability of a day to be fine is 2/5. What is the probability of having only one day to be fine out of three days ?

[Ans: 54/125] b. A bag contains 5 red balls and 4 white balls of same size. Two balls are taken randomly one after other without replacement . Find the probability of getting

61

62

the balls of different colors showing all the possible outcomes in the tree diagram .

[Ans: 5/9] 5.

a.

b.

6.

a.

b.

7.

a. b.

8.

a.

In the given figure along side, if QR=8cm,PR=12cm and ∠PRQ=30°, find the area of kite.

[Ans: 48cm2]

E

9.

P Q

S

O

O

8 cm

In the given figure, AB is the diameter and AB//CD. If ∠BEC= 400, find the value of ∠BCD. [Ans: 500]

40°

O

A

B D

C

R

Find the surface area of the given triangular prism.[Ans: 155cm2]

b.

6 cm 10 cm

The circumference of the base of a cylinder is 88cm and the sum of its radius and height is 40 cm. Find the volume of the cylinder [Ans: 3520cm3] If the total surface area of a hemisphere is 462 cm2, find its curved surface area.

[Ans: 308cm2] If the cost price of an article is less by 1/4 of its selling price, find the profit of loss percentage.

[Ans: 33%] The population of a town at the beginning of the previous year was 10,000. If it is believed that the population is growing at the rate of 4%,6% and 8% in the respective years, what will be the population at the end of the next year ?

[Ans: 11906] A B In the given figure, ABCD is a trapezium in which AB//DC, ∠ABC = ∠BCD = 900 , BC = D C 8cm and AD = 10cm . If the 2 area of the trapezium is 72 cm , calculate the length of the AB.[Ans: 6cm]

10.

11.

12.

13.

14.

b.

a.

In the given figure , If AE//CD, B 92° ∠CBA = 920 and ∠EAR=200 .

0 find the value of ∠BCD.[Ans: 108C ]

A 20°

R

E D

63

64

P and Q are centers of circles which touch at A. BC is a direct common tangent. Find the measure of ∠BAC. [Ans: 90°]

B C P

A

Q

D

Group - B [16×4=64] In a group of students, 20 study accountancy, 21 study mathematics,18 study history, 7 study accountancy only, 10 study mathematics only, 6 study accountancy and mathematics only, 3 study mathematics and history only . (i) Represent the above information in the Venn diagram. (ii) How many students study all the subjects ? (iii) How many students are there altogether ? [Ans: 2, 41] Find the H.C.F. of : ( a + c)( a - c ) + b ( 2a + b )( b + a ) ( b - a ) + c ( 2b + c ) and ( c + b ) ( c - b ) + a ( 2c + a ) [Ans: a + b +c] 1 [Ans: 4 and 5 ] Solve : 5x-5 + 5 4-x = 15 1 2 4 8 1 Simplify : x + 1 + x2 + 1 + x4 + 1 + x8 – 1 [Ans: x – 1 ] Tara said to Sabittre, '' I am half as old as you will be when I will be as old as you are.'' If the sum of therir present ages is 50, find their present ages.

[Ans: 20 years,30 years]

15. Find out the first quartile of the data given below in the table .

[Ans:12.92] Marks 5-10 10-15 15-20 20-25 25-30 obtained No. Of 4 6 8 8 4 Student 16. A man who is 1.5 m tall is flying a kite. when the length of the string of the kite is 120m, it makes an angle of 300 with horizon. What is the height of the kite from the ground, if there is no slack in the string ?

[Ans: 61.5] 17. What is the total surface of the cones formed when a right angled triangle having two perpendicular sides of 3 cm and 4 cm is rotated around its hypotenuse ? [Ans: 113.14cm2, 75.43cm2] 18. The solid shown in the adjoining figure has the square based prism of side 10 cm. If the ratio of the height of pyramid and prism is 3:2 and volume of the whole solid is 1200cm3, find the total surface area 10 cm of the solid .

[Ans: 680cm2 ]

22. Prove that the area of the parallelogram is double the area of the triangle on the same base and between the same parallel lines.

23. ABCD is a cyclic quadrilateral. AB A H B and DC produced to meet at E, the E circle with center E and radius EC C D cuts AB at H and HC, BC meet AD L K at K,L, respectively. Prove that CL =KL. 24. Verify experimentally that the central angle is double the inscribed angle standing on the same arc , in the same segment of the same circle. (Two circles of radii not less than 3 cm are necessary) 25. Construct a triangle equal in area with the given quadrilateral ABCD in which AB=5cm, BC=4cm, CD=DA=4.5 cm and ∠B=900 SET XV S.L.C. Send -Up Examination Attempt all the questions.

Group A [ 9×(2+2)=40] n+1 n+1 5 25 1. a. Evaluate : (5n)n–1 ÷ (5n–1)n+1 [Ans: 1/25]

19. A can do a piece of work in 45 days, B can do it in 60 days and C can do in 90 days. Three of them started the work together but A left the work after 15 days and B left it 5 b. days before its completion. Calculate the number of days required to finish the whole work.

[Ans: 27 days] 2. a.

20. After allowing 25% discount on the marked price and then b. levying 10 % VAT, a cycle was sold. If the discounted amount was Rs. 750, how much VAT was levied on the 3. a. price of the cycle ?

[Ans: Rs.225 ] 21. A sum of money amounts to Rs. 1331 in 3 years and to Rs. b.

1464.10 in 4 years, at the certain rate of interest compounded annually. Find the sum and the rate of interest.[Ans: Rs.1000, 10%] 65

66

z7/3 [Ans: y8/3] Solve : 5n–1 × 2n + 2 = 80 [Ans: n = 2] The product of two consecutive odd numbers is 255, find the odd numbers ?

[Ans: 15,17] 10, x + 4, 20, 25, 30, 35, 40 are in ascending order . If Q1 =15 find the mean.

[Ans: 11, 25] From the given figure curve, find the first quartile class.

[Ans: 8–12]

Simplify :

3

x6y–2z4 .

4

x–8y–8z4

Y 24 20 16 12 8 4 O 4 8 12 16 20 24 Marks

4.

a.

b.

5.

a.

P

b.

25°

O

35°

R

Q X

A Card is drawn from a well shuffeled pack of 52 cards. Find the probability of not getting a black face card .

[Ans: 23/26] A ball is drawn from a bag containing 4 black and 7 white balls randomly and not replaced, then another ball is drawn, Draw the tree diagram to show the probabilities.

D C Find the area of Quadrilateral 75° 2 35° ABCD. [Ans: 45 cm ]

E 70°

9.

8 cm

A

a.

In adjoining figure, 0 0 ∠BDC=32 , ∠ABE= 70 find the measure of ∠ACB.[Ans: 380]

A

B

32°

D

C

R P

b.

115°

b.

Find ∠QPR From figure.

[Ans: 60°]

B

Find the volume of given triangular prism. [Ans: 480 cm3]

In figure ∠PTQ=360 and PT=TQ then find the value of ∠STQ. [Ans: 72°]

T

S

36°

Q

20 cm

6.

7.

a.

What is the total surface area of given hemisphere .[Ans: 115.5cm2]

b.

Find the area of the curved surface of a cone whose slant height is 25 cm and height is 24 cm. [Ans: 550cm2] Find the profit percent when 6 pens are sold for the cost price of 9 pens.

[Ans: 50%] A motorcycle of Rs. 1,00,000 is depreciated at 10% p.a. find its value after one year .

[Ans: 90000]

a. b.

3.5 cm

Z

W

8.

a.

In given figure WZ// XY Prove that ∆WOX=∆YOZ .

O X

Group 'B' Group - B ( 16×4=64) 10. Among 100 students of a school, 85 students like Arithmetics, 65 like Geometry and 10 students did not like both. Then, find . (i) How many like both ( Geometry and Arithmetic) (ii) How many like Geometry only . (iii) Show these information in Venn-diagram [Ans: 60, 5] 11. Find the LCM of : 2a3 + a2 + a +2 and a3 - a2 + a - 1 [Ans: a + 1] a–4 = a + 16 [Ans: 9] 12. Solve : a –2

Y

67

68

1 2a 4a3 8a7 1 13. Simplify: a + x + a2 + x2 + a4 + x4 – a8 - x8 [Ans: x – a ] 14. The difference between the length and breadth of a rectangular field is 4 m. If the area of the field is 96 m2, find its perimeter.

[Ans: 40 m] Ans: 16.43] 15. Calculate third quartile(Q3) from data : Marks obtained 25 35 45 55 65 75 No. Of Student

5

6

8

10

7

4

16. The angle of elevation of a tower was observed to 450.

From a point on walking 100m away from the tower. it was found to be 300. Find the height of the tower . [Ans: 136.6m]

23. In figure, O Is the center of circle, AC is the chord. If BT=TC. Prove that ∠OAT=∠OBT.

24. Experimentally verify that sum of opposite angle of a cyclic quadrilateral are supplementary. (Two circles of radii not less than 3 cm are necessary) 25. Construct a triangle ABC in which AB = 4.2 cm, BC = 5.4 cm and AC =5.8 cm Construct a parallelogram with an angle 600 and its area equal to triangle ABC.

20 cm

17. Find the volume and total surface 5.6 cm area of given cylinder with 3 hemispherical ends.

[Ans: 2707.11cm , 1098.24cm2] 18. Find the total surface area of square based pyramid whose base is 6 cm and height is 4 cm .

[Ans: 96cm2] 19. Madan Bahadur and Hari Bahadur can do a piece of work in 20 days and 50 days respectively. They both started the work together and Hari Bahadur left after 5 days. In how many days will Madan Bahadur finish the remaining work? [Ans: 13 days] 20. The price of an article is marked at 25% above the cost price. If it is sold at a profit of Rs. 125 after allowing 15% discount, what will be the selling price.

[Ans: 132.80] 21. A certain sum of money amounts to Rs. 1323 in 2 years and Rs. 1389.15 in 3 years. Find the compound rate of interest and sum.

[Ans: R=5%, Rs.145.86] 22. Prove that the parallelograms standing on same base and between the same parallels are equals in area.

A E O

T C

69

70