FRP - CBSE Sample Paper, Worksheets, Syllabus, Notes, Assi Class... · SAMPLE QUESTION PAPER . ... If the 7 times the 7th term of A.P. is equal to 11 times its 11th term, ... If one

DAV PUBLIC SCHOOL, CHANDRASEKHARPUR, BHUBANESWAR – 21

Question Bank SUMMATIVE ASSESSMENT - II

MATHEMETICS SAMPLE QUESTION PAPER

CLASS – X Multiple Choice Questions of one mark each:

1. The value of k for which equation (k – 1) x2 – 2kx + 2x + 1 = 0 has real and equal roots are:

a) 0, 3 b) 2, 1 c) 0, 34 d) 0, 1

2. If the 7 times the 7th term of A.P. is equal to 11 times its 11th term, then its 18th term is : a) 7 b) 18 c) 0 d) 11

3. Which of the following statements is true? a) The common point of a tangent and the circle is called the centre of the circle. b) A secant of a circle intersects the circle in two distinct points. c) We can draw only one tangent to a circle from a point in the exterior of the circle. d) The tangents drawn at the end points of a chord are parallel.

P R 4. In figure 1 if O is the centre of a circle, PQ is a chord,

And the tangent PR at P makes an angle of 500 with PQ Then ∠POQ is equal to: a) 900 b) 1000 c) 750 d) 800 Q

Fig. 1 5. The length of the tangent drawn from a point Q outside a circle is 16cm.

If the diameter of the circle is 24 cm, then the distance of Q from the Centre of the circle is: a) 10cm b) 12 cm c) 8 cm d) 20 cm

6. To divide a line segment AB in the ratio 5:7, first a ray AX is drawn so that ∠BAX is an acute angle of them at equal distances points are marked on the ray AX such that the minimum number of these points is : a) 8 b) 12 c) 10 d) 11

7. If the sum of the areas of two circle with radius R1 and R2 is equal to the area of a circle of radius R, then: a) R1

2 + R22 = R2 b) R1 + R2 = R c) R1 + R2 < R d) R1

2 + R22 < R2

8. If perimeter of a circle is equal to that of a square, then the ratio of their areas is: a) 22 : 7 b) 7 : 22 c) 14 : 11 d) 11 : 14

9. A pole 6m high casts a shadow 2√3m on the ground, then the elevation of the sun is: a) 900 b) 300 c) 450 d) 600

10. A card is drawn from a deck of 52 cards. The event E is that card is not an ace of heart. The number of outcomes favorable to E is: a)13 b) 51 c) 3 d) 49

11. The equation x + 2−x = 4 has a) two real roots b) only one real root c) no real root d) more than two roots 12. If 3, 4 + p, 7 – p are in A.P. then p must be equal to:

a) 0 b) 31

c) 31

− d) 32

13. From a point P which is at a distance of 5cm from the centre O of a circle of radius of 3cm, the pair of tangents PQ and PR are drawn to the circle. Area of Quadrilateral PQOR is: a) 12 cm2 b) 15cm2 c) 20cm2 d) 24cm2

O

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14. In the given figure 2, AP is tangent to the circle with Centre O such that OP = 4 cm ∠OPA = 300 then AP is Equal to:

a) 4cm 4 cm b) 2cm c) 2√3cm A P d) 4√3cm Fig. 2

15. If two tangents are inclined with each other at an angle of 600 and are drawn to a circle of radius 3 cm, then the length of each tangent is equal to:

a) 2

33 cm b) 6 cm c) 3 cm d) 3√3 cm

16. If the radii of two concentric circles 4 cm and 5 cm, then the length of each chord of one circle which is tangent to the other is: a) 3 cm b) 6 cm c) 9 cm d) 1 cm 17. Areas of the largest triangle that can be inscribed in a semicircle of radius r units is:

a) r2 sq. unit b) 21

r2 sq. unit c) 2r2 sq. unit d) √2r2 sq. unit

18. A solid sphere of radius is melted and cast into the shape of a solid cone of height r, the radius of the base of the cone is: a) 4r b) 3r c) 2r d) r 19. If the altitude of sun is 600, then the height of vertical tower will cast a shadow of length 30 m is: a) 30√3 m b) 15 m c) 10√3 m d) 15√2 m 20. If 3 coins are tossed simultaneously, then the probability of getting at least two heads is:

a) 41

b) 83

c) 21

d) 43

21. If -2 and 3 are roots of quadratic equation, x2 – (p + 3)x + q = 0, then the value of p and q are: a) p = - 2, q = - 6 b) p = 2, q = -6 c) p = 2, q = 6 d) p = -2, q = 6 22. If the common difference of an A.P is 5, a =4 then 11th term is: a) 15 b) 45 c) – 45 d) -75 23. A point p is at a distance of 13 cm. from the centre C of a circle and PT is tangent to the given circle. If the diameter of the circle is 10 cm, then the length of the tangent PT is: a) √69 cm b) 11.5 cm c) 12 cm d) √194 cm 24. In the adjoining figure 3, PA and PB are tangents

to a circle with O. If ∠OAB = 350, then ∠APB is A equal to:

a) 700 P b) 550 c) 900 B d) 650 Fig. 3

25. If the length of the shadow of a tower is √3 times that of its height, then the angle of the elevation of the sun is: a) 150 b) 300 c) 450 d) 600

O

30o

O 35o



26. A bag contains 5 red, 4 white and 3 black balls. If a ball is drawn from the bag at random then the probability of the ball being not black is:

a) 125

b) 31

c) 43

d) 41

27. The distance of the point (-5, -7) from the y-axis is a) – 5 units b) 5 units c) – 7 units d) 7 units 28. If the midpoint of the line segment joining (2a, 4) and (-2, 3b) is (1, 2a + 1), then the values of a and b are: a) a = 2, b = 2 b) a = 2, b = -2 c) a = 1, b = 1 d) a = -2, b = 2 29. If the diameter of a semicircle is d, then its area is:

a) 21

πd2 b) 41

πd2 c) 81

πd2 d) 161

πd2

30. If the volume of a sphere is 4851 cm3, then its surface area is: a) 1286 cm2 b) 1386 cm2 c) 1486 cm2 d)2460 cm2 31. The values of x obtained from the quadratic equation 4√5x2 + 7x - 3√5 = 0 are :

a) 53,

45 −

b) 5

3,4

5− c)

53,

45

d) 53,

45 −−

32. A secant of a circle intersects the circle in: a) one point only b) two points c) three points d) no point 33. If the sum of the first q terms of an A.P. is 2q + 3q2, the common difference is : a) 2 b) 6 c) 5 d) 7 34. In the given figure 4, find CD if AB = 5cm: C a) 5 cm b) 4 cm D c) 3 cm A d) 2 cm B Fig. 4 35. AB and AC are two non – parallel lines intersecting at the point A. The centre of the circle touching both these lines will be in: a) AB b) AC c) BC d) Bisector line of ∠BAC 36. In the following figure 5, find the perimeter of ∆ APQ

if AB = 6 cm. a) 10 cm b) 12 cm c) 15 cm P Q d) 6 cm

B C 37. The angles of elevation two points at distances a

and b in a horizontal line through the base of the tower of the top of the tower are complementary to each other. Then the height of the tower is: Fig. 5 a) a + b b) ab c) √ab d) 2ab

O.

A



38. The perimeter of the figure is: a) 82 m b) 52 m c) 70 m d) 72 m 12 cm 39. Eight solid spheres of the same size are made by melting a solid metallic cylinder of base diameter 6 cm 14 cm Fig. 6 and height 32 cm. The diameter of each sphere is: a) 3 cm b) 6 cm c) 12 cm d) 8 cm 40. A card is drawn from a deck of 52 cards. The event E is that card is not an ace of spades. The number of outcomes favourable to E is:

a)13 b) 4 c) 3 d) 51 41. If the equation 4x2 – 3x – p = 0 has real roots, then the values of p are given by:

a) p16

9−≤ b) p >

169−

c) p < 16

9− d) p

169−

≥

42. If the nth term of an A.P. is given by an = 3n – 2. Then the sum of first 12 terms is: a) 210 b) 220 c) 240 d) 280 43. In the adjoining figure 7, PA and PB are tangents A from P to a circle with centre O. If the radius of the circle is 5 cm and AP ⊥ BP then the length of OP is: a) 5 cm P b) 5√2 cm c) 8 cm B d) 10 cm Fig. 7 44. In the adjoining figure 8, PA and PB are tangents to a A

circle with centre C if ∠BPC is 350, then ∠ACP = a) 550 b) 350 P

c) 700 B d) 650 Fig. 8

45. A ladder 12 m long tests against a wall. If it reaches the wall at height of 6√3 m, then the angle of elevation is: a) 300 b) 450 c) 600 d) 750 46. If a card is drawn from a well shuffled pack of 52 cards, then the probability of getting a black face card is:

a) 134

b) 133

c) 523

d) 263

47. If the distance between the points (p, -5) and (2, 7) is 13 units, then the values of p are: a) (3, 7) b) (-3, 7) c) (3, -7) d) (-3, -7) 48. If one end of the diameter of circle is (2, 3) and the centre is (-2, 5) then the other is: a) (-6, 7) b) (6, -7) c) (0, 8) d) (0, 4)

O 35o

O 90o



49. In the adjoining figure 9, O is the centre of a circle.

If OA = 10 cm, OB = 15 cm and ∠BOD = 720, then the area of the shaded region is: O a) 5π cm2 b) 10π cm2

c) 25π cm2 d) 35π cm2 Fig. 9

50. If a sphere and a cube have equal surface areas, then the ratio of the diameter of the sphere of the edge of the cube is:

a) 1 : 2 b) 2 : 1 c) 6:π d) π:6

Questions of two mark each: 1. Solve for x: 6a2x2 – 7abx – 3b2 = 0, a ≠ 0. 2. Find the sum of 1 + 6 + 11 + 16 + …..+81. 3. A quadrilateral PQRS is drawn so as to circumscribe a circle as shown in the give figure 10. Prove that:

PS + QR = PQ + RS. P X S Q C B Y T Q Z R Fig. 10 O A P Fig. 11

4. In the given figure 11, a square OABC is inscribed in a quadrant OPBQ. IF OA = 20 cm, find the area of the shaded region (use π = 3.14)

5. The slant height of the frustum of a cone is 4 cm and the perimeters of the circular ends are 18 cm and 6 cm. Find the curved surface area of the frustum.

6. Find the ratio in which the line segment joining the points A(3, -6) and B(5, 3) is divided by x-axis. Also find the co-ordinate of the point of intersection. OR Find a relationship between x and y such that the points p(x, y) is equidistant from the points A(2, 5) and B(-3, 7).

7. Show that the points (7, 10), (3, -4) and (-2, 5) are vertices of an isosceles triangle. 8. A bag contains cards numbered 1, 2, 3, ……..19, 20. A card is drawn at random from the bag. Find the probability

that the card drawn has a prime number in it. 9. Find the roots of the quadratic equation 3√2x2 – 5x - √2 = 0. 10. If the numbers n – 2, 4n – 1 and 5n + 2 are in A.P., find the value of n. 11. A square park has each side of 100 m at each corner of the park, there is a flower bed in the form of a quadrant

of radius 14 m. Find the area of the remaining part of the park. A

12. In the given figure 12, if AB = AC, then prove that BE = EC. OR D E PA and PB are tangents from an external point P to a circle with centre O, such that PA = 15 cm and ∠APO = 300. Find the length of the chord AB. B F c Fig. 12

13. 2.2 cubic dm of metal is to be drawn into a cylindrical wire 0.50 cm in diameter. Find the length of the wire.

C D

A B

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14. Find the values of y for which the distance between the points P(2, -3) and Q(10, y) is 10 units. 15. Find the ratio in which y-axis divides the line segment joining the points A(5, -6) and B(-1, -4). 16. A coin is tossed 3 times. Find the probability of getting all heads. 17. Find the value of p for which the quadratic equation 2x2 – 6x + p = 0 has real and different roots. 18. Find the sum of the numbers between 50 and 100 which are divisible by 7.

OR 19. If the sum of first n terms of an A.P. is 4n2 + 5n, then find its nth term.

20. Prove that the angle between the two tangents

drawn from an external point to a circle is A supplementary to the angle subtended by the line B P C segments joining the points of contact at the centre.

21. In the adjoining figure 13, a circle touches the side Q R BC of a ∆ABC, at P and touches AB an AC at Q and R Respectively. If AQ = 5 cm, find the perimeter of ∆ABC

22. If the point (-4, 1)divides the line segment joining the points A(2, -2) and B in the ratio 3 : 5, then find the Fig. 13 co-ordinates of point B.

23. A letter is chosen at random from the word O C “MATHEMATICS”. What is the probability that it is a vowel?

24. In the adjoining figure 14, OABC is a square of side 7 cm. If OAC is a quadrant of a circle with O as centre, then find the area of the shaded region. A B Fig. 14

25. If a sector of a circle of radius 6 cm and of central angle 1200 is rolled up so that the two bounding radii are joined together to form a cone, then find the radius of the resulting cone.

26. Prove that the points P(a, b + c), a(b, c + a) and R(c, a + b) are collinear. 27. Solve the quadratic equation 6x2 – 7x + 2 = 0 by t he method of completing the squares. 28. If the points P(a, -11), Q(5, b), R(2, 15) and S(1, 1) are the vertices of a ||gm PQRS, find the values of a and b. 29. In an A.P. , if Sn = 3n2 + 2n, find the A.P.

OR How many terms lie between 10 and 200, which when divided by 4 leave a reminder 3?

30. PA and PB are two tangents to a circle from a point P lying outside the circle. If PA is 5 cm, find the length of PB. 31. A bucket in the form of a frustum of a cone and holds 28.49 litre of water. The radius of the top is 28 cm and the

height is 15 cm. Find the radius of the bottom. 32. Find the difference of the areas of a sector of angle 1200 and its corresponding major sector of a circle of radius

4.2 cm. 33. A letter of English alphabets is chosen at random. What is the probability that it is a letter of the word “MEENU”.

34. One root of the equation 2x2 – 8x – m = 0 is 25

. Find the value of m and the other root.

OR If one root of the equation x2 + 12x – k = 0 is thrice the other, then find the value of k.

35. Find the sum of all two digit natural numbers.

. O



36. In the adjoining figure 15, XP and XQ are two tangents to a circle with centre O from a point at X outside the

circle. ARB is a tangent to the circle at R. Prove that XA + AR = XB + BR.

P A

X B Q Fig. 15

37. From the top of 7 m high building, the angle of elevation of the top of the tower is 600 and the angle of depression of its foot is 450. Determine the height of tower.

38. Find the value of k if the point A(k + 1, 2k), B(3k, 2k + 3)and C(5k – 1, 5k) are collinear. 39. If A(-5, 7), B(-4, -5) C(-1, -6) and D(4, 5) are the vertices of a quadrilateral, find the area of quadrilateral ABCD. 40. A pair of dice is rolled once. Find the probability of getting the same number in both dice.

OR A card is drawn at random from a well shuffled deck of 52 cards. Find the probability of getting a red queen.

41. Solve for x: ba

xbabx

bax

a 1,1,11

≠+=−

+−

, a + b ≠ 0, ab ≠ 0.

42. The first term of an A.P. is 5 and the last term is 45 and the sum is 400. Find the number of terms and the common difference. Also find the 7th term from the end. C

OR The sum of three Nos. in A.P. is 3 and their product is -35. Find the numbers.

43. Prove that a ||gm circumscribing a circle is a rhombus. OR

In the adjoining figure 19, ABC is right angled triangle With AB = 6 cm and AC = 8 cm. A circle with centre O has been inscribed inside the triangle. Calculate the radius of the inscribed circle. A Fig. 19 B

44. Draw a right triangle in which the sides (other than hypotenuse) are the length 4.5 cm and 6 cm. Then

construct another similar triangle whose sides are 53

th of the corresponding sides of given triangle.

45. The two opposite vertices of a square are (-1, 2) and (3, 2). Find the co-ordinates of the other two vertices. 46. Determine the ratio in which the point (-6, a) divides the join of A(-3, -1) and B(-8, 9). Also find the value of a. 47. All the three face cards of spades are removed from a well shuffled pack of 52 cards. A card is then drawn at

random from the remaining pack. Find the probability of getting (i) a black face card (ii) a queen (iii) a black card. 48. From a point on the ground, the angles of elevation of the bottom and the top of a transmission tower fixed at

the top of a 20 m high building are 450 and 600 respectively. Find the height of the tower. (Take √3 = 1.732)

O. R

O



49. In the adjoining figure 20, AB an CD are diameter of a circle with centre O. if OA = 7cm. Find the area of the shaded region.

OR

In the adjoining figure 21, the inside perimeter of a practice running track with semicircular ends and straight parallel sides is 312 m. The length of straight portion of the track is 90 m. If the track has a uniform width of 2 m throughout, find its area.

50. In the adjoining figure 22, A wooden article was made by scooping

out a hemisphere from each end of solid cylinder. If the height of the cylinder 10 cm and its base is of radius 3.5 cm, find the total surface area of the article.

Fig. 22

51. The sum of n terms of an A.P. 3n2 – n. Find out the first term and the

common difference. 52. A bag contains 60 balls out of which some are red, some are blue and

the remaining are black. If the probability of drawing a red ball is 207

and

that of blue ball is 52

, then find the number of black balls.

OR A coin is tossed 3 times. List the possible outcomes. Find the probability of getting at least 2 tails.

53. The diameter of front and rear wheels of a tractor are 80 cm. and 2 cm. respectively. Find the number of revolutions that the rear wheel will make in covering a distance in which the front wheel make 700 revolutions.

54. Find the area of the segment of a circle of radius 14 cm whose corresponding sector has a central angle of 1200.

(Use π = 722

)



OR

In the figure 23, arcs are drawn by taking vertices A,B and C on equilateral triangle of side 14 cm, to intersect the

sides BC, CA, and AB at their respective mid points D, E & F. Find the area of the shaded region. (Use π = 722

)

55. A vertically straight tree, 15 m high is broken by the wind in such a way that its top just touches the ground and

makes an angle of 600 with the ground. At what height from the ground did the tree break? 56. How many terms of the series 24 + 20 + 16 + ….. give the sum 72 ? Give reason for the two answer. 57. Draw a circle of radius 4 cm from a point 8 cm away from its centre, construct the pair of tangents to the circle

and measure their length. 58. Draw a pair of tangents to a circle of radius 4 cm which are inclined to each other at an angle of 600.

59. Find the ratio in which the point P

−

1116,

1113

divides the line segment joining the points A

23,

21

and B(2, -5).

60. In what ratio does the x-axis divide the line segment joining the points (-4, -6) and (-1, 7)? Find the co-ordinates of the point of division.

OR The line segment joining the points A(3, 2) and B(5, 1) is divided at the point P in the ratio 2 : 3 and its lies on the line 3x – 4y + k = 0. Find the value of k.

61. Solve for x: xbaxba1111

++=++

, a ≠ 0, b ≠ 0, x ≠ 0.

62. Which term of the A.P. 121, 117, 113 ………… is the first negative term. OR

In a flower bed, there are 23 rose plants in the first row, 21 in the second row, 19 in the third row and so on. There are 5 rose plants in the last row. How many rose plants are there in the flower bed.

63. Prove that the tangents drawn from an external point to a circle subtend equal angles at the centre of the circle. OR D R C In the adjoining figure 24, a quadrilateral ABCD circumscribe a Q circle. Prove that AB + CD = AD + BC.

64. Construct an isosceles ∆ whose base is 6 cm. S and altitude is 4 cm. and then construct another

similar ∆ whose sides are 211 times the corresponding A P B

sides of the isosceles ∆. Fig. 24 65. If the two vertices of an equilateral triangle are (0, 0) and (3, 0), find the third vertex. 66. Determine the ratio in which the line 2x + y – 4 = 0 divides the line segment joining the points A(2, -2) and B(3, 7).

Also find the co-ordinates of the points of division. 67. Find the probability of having 53 Sundays in (i) a leap year, (ii) a non leap year.



68. The angle of elevation of the top of a building from the foot of a tower is 300 and the angle of elevation of the top of the tower from the foot by the building is 600. If the tower is 50 m high, find the height of the building.

69. In the adjoining figure 25, the diameter of the circle with centre O is 28 cm. Semicircles are drawn on AQ and as

diameters. If AQ = 41

AB, find the area of shaded region.

(Fig 25)

(Fig. 26)

OR In the adjoining figure 26, a square OABC is inscribed in a quadrant OPBQ of a circle. If OA = 12 cm, find the area of the shaded region. (Use π = 3.14)

70. Find what length of canvas 2m in width is required to make a conical tent 20 m in diameter and 42 m in slant height allowing 10% for folds and stitching. Also find the cost of the canvas at the rate of Rs.60 per metre.

Questions of four marks each: 1. A train travels at a certain average speed for a distance of 63 km. and then travels a distance of 72 km at an

average speed of 6km/hour more than its original speed. If it takes 3 hours to complete the journey, what is its original average speed?

OR

Two water taps together can fill a tank in 839 hours. The larger tap takes 10 hours, less than the smaller one to

fill the tank separately. Find the time in which each tap can separately fill the tank. 2. If (-5) is a root of the quadratic equation 2x2 + px – 15 = 0 and the quadratic equation p(x2 + x) + k = 0 has equal

roots, then find the value of p and k. 3. A circle touches the side BC of ∆ABC at p and touches AB and AC produced at Q and R respectively. Prove that AQ

= ½ (Perimeter of ∆ABC). 4. If the radii of the circular ends of a bucket 45 cm high are 28 cm and 7 cm, find the capacity of the bucket. Also

find the curved surface area of the bucket.



5. The angles of elevation of the top of a tower from two points on the level ground, at distances a and b units (a > b) from the base of the tower and in the same straight line with it, all complementary. Prove that the height of

the tower is ab units. OR

A boy is standing on the ground and flying a kite with a string of 150m at an angle of elevation of 300. Another boy is standing on the roof of a 25m high building and is flying his kite at an elevation of 450. Both the boys are on opposite sides of both the kites. Find the length of the string in meter correct to two decimal places, that the second boy must have so that the two kites meet.

6. A toy is in the form of a right circular cylinder with a hemisphere in one end and a cone on the other. The height and radius of base of the cylindrical part are 13 cm and 5 cm respectively. The radius of hemisphere and base of the conical part are same as that of the cylinder. Calculate the surface area of the toy, if the height of the cone is 12 cm.

7. Two pipes running together can fill a cistern in 1313 minutes. If one pipe takes 3 minutes more than the other to

fill the cistern, find the time in which each pipe would fill the cistern. OR

A 2-digit number is 4 times the sum of its digits and twice the product of its digits. Find the numbers. 8. Determine the A.P. whose third term is 16 and the 7th term exceeds the 5th term by 12. 9. Prove that the lengths of tangents drawn from an external point to a circle are equal. 10. In the given figure 27, ABCD is a trapezium

with AB||DC and ∠BCD = 900. BDEFB is quadrant. A B If AB = BC = 3.5 cm and DE = 2 cm, calculate the area of the shaded region.

11. The perimeters of the ends of a frustum of a cone are 36 cm and 48 cm. If the height of the frustum is 11 cm. Find its volume. D C Fig. 27

OR A cone of height 24 cm and radius of base 6 cm is made up of modeling clay. It is reshaped in the form of sphere. Fin d the radius of the sphere.

12. A pole 5 m high is fixed on the top of the tower. The angle of elevation of the pole observed from a point A on the ground is 600 and the angle of depression of point A from the top of the tower is 450. Find the height of the tower.

13. In an auditorium, seats are arranged in rows and column the number of rows was equal to the number of seats in each row. When the number of rows was doubled and the number of seats in each row is reduced by 10 the total number of seats increased by 300. Find (i) the number of rows in original arrangement, (ii) the number of seats in t he auditorium after arrangement.

OR A plane left 30 minutes late than the scheduled time and in order to reach the destination 1500 km away in time, it has to increase the speed by 250 km/hour from the usual speed. Find its usual speed.

14. The sum of first 15 terms of an A.P. is 105. And the sum of next 15 terms is 780. Find the first 3 terms o f the A.P. A

15. In the adjoining figure 28, a ∆ABC is drawn to circumscribe a circle with center O o o of radius 4 cm such that the segments BD and DC into which BC is divided by the point of contact D are the lengths 8 cm and 6 cm respectively. Find C B the sides AB and AC. 6 cm 8 cm Fig. 28



16. A straight highway leads to the foot of a tower. A man standing at the top of the tower observes a car at an angle of depression of 300, which is approaching at the foot of the tower with a uniform speed. Six second later, the angle of depression of the car is found to be 600 find the time taken by the car to reach the foot of the tower from this point.

17. In the adjoining figure 29, ABC is a right angled triangle, ∠B = 900, AB = 28 cm and BC = 21 cm. With AC as diameter A a semicircle is drawn and with BC as radius a quarter circle is drawn. Find the area of the shaded region.

18. A container shaped like a right circular cylinder having diameter 12 cm and height 15 cm is full of ice cream. The ice cream is to be filled into cones of height 12 cm and diameter 6 cm, having a hemispherical shape on the top. Find the number of such cones which can be filled with ice cream. OR B C A right angled triangle, with sides 15 cm and 20 cm is made to revolve 21 cm about its hypotenuse find the volume and the surface area of the double Fig. 29 cone so formed. Take π = 3.14.

19. A well of diameter 4m and 21m deep is dug. The earth, taken out of it, has been evenly spread all around it in the shape of a circular ring of width 3 m to form an embankment. Find the height of the embankment.

20. A triangle ABC is drawn to circumscribe a circle of radius 2 cm such that the segments BD and DC into which BC is divided by the point of contact D are of lengths 2 cm of 3 cm respectively. Find the sides AB and AC.

21. In the price of a book is reduced by Rs. 5 a person can buy 4 more books for Rs. 400. Find the original list price of the book.

OR

The sum of reciprocals of a child’s age (in years)2 years ago and 4 years ago from now is 125

. Find his present age.

22. Construct a triangle ABC in which BC = 8 cm and ∠B = 600 and ∠C = 450. Then construct another triangle whose

sides are 43

of the corresponding sides of ∆ ABC.

23. A solid toy is in the form of a hemisphere surmounted by a right circular cone. The height of the cone is 3 cm and the diameter of the base of the cone is 6 cm. Determine the volume of the toy. If a cube circumscribes the toy, then find the difference of the volumes of the cube and the toy. Also find the total surface area of the toy.

OR A cylindrical bucket of height 24 cm and base radius 24 cm are filled with sand. The bucket is emptied on the ground and a conical heat of sand is formed. If the height of the conical heap is 30 cm. Find the radius slant height of the heap.

24. A pole 10 cm high is fixed on the top of a tower. The angle of elevation of the top of the pole as observed from point A on the ground is 600 and the angle of depression of point A from the top of the tower is 450. Find the

height of the tower. (Use 3 = 1.73) 25. A trader bought a number of articles for Rs. 900, five were damaged and he sold each of the rest at Rs. 2 more

than what he paid for it, thus getting a profit of Rs. 80 on the whole transaction. Find the number of articles he bought. OR A wire 112 cm long, is bent to form a right angled triangle. If the hypotenuse is 50 cm long, find the area of the triangle.

26. The sum of 4 numbers in an A.P. is 32 and the ratio of the product of extremes to the product of means is 7 : 15. Find the numbers.



27. In the adjoining figure 30, PQ is a chord of length 8 cm of a circle with centre ). The tangents at P and Q intersect at T. If the radius of the circle is 5 cm, find the length.

P T Q Fig. 30

28. A 1.2 m tall girl spots a balloon moving with the wind in a horizontal line at a height of 88.2 m from the ground. The angle of elevation of the balloon from the eyes of the girl at that instant is 600. After sometime, the angle of elevation reduced to 300. Find the distance travelled by the balloon during the internal.

29. In the adjoining figure 31, two circular flower beds have been shown on the two sides of a square lawn ABCD of side 56m. If the centre of each circular flower bed is the point of intersection O of the diagonals of the square lawn, find the sum of the area of the lawn and the flower beds.

D C A B (FIG. 31)

30. A Gulabjamun, contains sugar syrup approximately 30% of its volume. Find how much syrup would be found in 45 gulabjamun, each shaped like a cylinder with two hemispherical ends with lengths 5 cm and diameter 2.8 cm.

OR From a solid cylinder whose height is 8 cm radius 6 cm, a conical cavity of height 8 cm and of base radius 6 cm is hollowed out. Find the volume of the remaining solid. Also find the total surface area of the remaining solid. (Take 𝜋 = 3.1416).



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FRP - CBSE Sample Paper, Worksheets, Syllabus, Notes, Assi Class... · SAMPLE QUESTION PAPER . ... If the 7 times the 7th term of A.P. is equal to 11 times its 11th term, ... If one