Time Allowed : 3 Hours Maximum Marks: 90
General Instructions:
(i) All questions are compulsory.
(ii) The question paper consists of 34 questions divided into four sections A, B, C and D, Section A comprises of 8 questions of 1 mark each. Section B comprises of 6 questions of 2 marks each. Section C comprises of 10 questions of 3 marks each and Section D comprises of 10 questions of 4 marks each.
(iii) Questions 1 to 8 in section A are multiple choice questions where you are to select one correct option out of the given four.
(iv) Use of calculators is not permitted.
SECTION A
Questions numbers 1 to 8 are of one mark each.
1. The common difference of the A.P., 1/2q, (1-2q)/2q, (1-4q)/2q,,.... is :
(i) -1 (ii) 1
(iii) q (iv) 2q
2. In figure, DE and DF are tangents from the external point D to a circle with center A.If DE = 5 cm and if DE is perpendicular to DF, then the radius of the circle is:
(i) 3 cm (ii) 5 cm
(iii) 4 cm (iv) 6 cm
3. In figure, a circle is inscribed in a quadrilateral ABCD touching its sides AB, BC, CD and AD at P, Q, R and S respectively. If the radius of the circle is 10cm, BC = 38 cm, PB = 27 cm and AD is perpendicular to CD,then the length of CD is
(i) 11 cm (ii) 20 cm
(iii) 21 cm (iv) 15 cm
4. A dice is thrown once. The probability of getting a prime number is
(i) 2/3 (ii) 1/3
(iii) 1/2 (iv) 1/6
5.A ladder 15 m long just reaches the top of a vertical wall. If the ladder make an angle of 60° with the wall, then the height of the wall is
(i) 15√3 m (ii) 15√3/2 m
(iii) 15/2 m (iv)15 m
6. A box contains cards numbered 6 to 50. A card is drawn at random from the box. The probability that the drawn card has a number which is a perfect square, is
(i) 1/45 (ii) 2/45
(iii) 1/9 (iv) 4/45
7.The point on the x-axis which is equidistant from the points(-1,0) and (5,0) is
(a) (0,2) (b) (2,0)
(c) (3,0) (d) (0,3)
8. If π is taken as 22/7, the distance (in metres) covered by a wheel of diameter 35 cm, in one revolution, is
(a) 2.2 (b) 1.1
(c) 9.625 (d) 96.25
SECTION B
Question numbers 9 to 14 carry 2 marks each.
9. Solve the following quadratic equation for x:
√2x² + 7x + 5√2 = 0
10. Find the number of all three-digit natural numbers which are divisible by 9.
11. In figure, two circles touch each other at the point C. Prove that the common tangent to the circles at C, bisects the common tangent at P and Q.
12. In figure, a quadrilateral ABCD is drawn to circumscribe a circle. Prove that
AB + CD = AD + BC
13. Two coins are tossed simultaneously. Find the probability of getting at least one head.
14.The length of the minute hand of a clock is 14 cm. Find the area swept by the minute hand in 5 minutes.
SECTION C
Question numbers 15 to 24 carry 3 marks each.
15. For what value of k, are the roots of the quadratic equation (k +4)x² + (k + 1 ) + 1 = 0 equal ?
16.The 19th term of an A.P. is equal to three times its sixth term. If its 9th term is 19, find the A.P.
17. Draw a pair of tangent to a circle of radius 4 cm, which are inclined to each other at an angle of 60°.
18. As observed from the top of a 60 m high lighthouse from the sea-level, the angles of a depression of two ships are 30 and 45. If one ship is exactly behind the other on the same side of the lighthouse, find the distance between the two ships.
19. Prove that the points A(2,3),B (-2,2) C (-1,-2) and D(3,-1) are the vertices of a square ABCD.
20. Find the ratio in which point P(-1,y) lying on the line segment joining points A(-3,10) and B(6,-8) divides it. Also find the value of y.
21. In figure, a square OABC is inscribed in a quadrant OPBQ of a circle. If OA = 21 cm, find the area of the shaded region.
22. A toy is in the form of a cone mounted on a hemisphere of same radius 7 cm.If the total height of the toy is 31 cm, find its total surface area.
23. A solid cone of base radius 10 cm is cut into two parts through the mid-point of its height, by a plane parallel to its base. Find the ratio in the volumes of the two parts of the cone.
24. A solid metallic sphere of diameter 8 cm is melted and drawn into a cylindrical wire of uniform width. If the length of the wire is 12 cm, find its width.
SECTION D
Question numbers 25 to 34 carry 4 marks each.
25. Solve for x:
1/(x-3) + 2/(x- 2) =8/x; x ≠0,2,3
26. A box contains cards numbered from 3,5,7,9,...35,37. A card is drawn at random from the box. Find the probability that the number on the drawn card is a prime number.
27.The sum of first n terms of an A.P. is 5n² + 3n. If its mth term is 168, find the value of m. Also find the 20th term if this A.P.
28. Prove that the lengths of tangents drawn from an external point to a circle are equal.
29. In figure, the sides AB, BC, CA of triangle ABC touch a circle with centre O and radius r at P, Q and R respectively.
30.
The angle of elevation of the top of the building from the foot of the
tower is 30° .The angle of elevation of the top of the tower from the
foot of the building is 60°. If the tower is 60 m high, find the height
of the building.
31.If the points A(1,-2), B(2,3),C(-3,2) and D(-4,-3) are the vertices of parallelogram ABCD , then taking AB as the base, find the height of this parallelogram.
32. Water running in a cylindrical pipe of inner diameter 7 cm, is collected in a container at the rate of 192.5 litres per minutes. Find the rate of flow of water in the pipe in km/hr.
33.While boarding an aeroplane, a passenger got hurt. The pilot, showing promptness and concern, made arrangements to hospitalize the injured and so the plane started by 30 minutes. To teach the destination, 1500 km away, in time the pilot increases the speed by 100 km/hr. Find the original speed/hour of the plane. Do you appreciate the values shown by the pilot, namely promptness in providing help to the injured and his efforts to reach in time?
34. A container open at the top and made up of metal sheet is in the form of a frustum of a cone of height 16 cm with the diameters of its lower and upper ends as 16 cm and 40 cm respectively. Find the cost of metal sheet used to make the container, if it costs Rs. 10 per 100 cm. (take π= 3.14 )
General Instructions:
(i) All questions are compulsory.
(ii) The question paper consists of 34 questions divided into four sections A, B, C and D, Section A comprises of 8 questions of 1 mark each. Section B comprises of 6 questions of 2 marks each. Section C comprises of 10 questions of 3 marks each and Section D comprises of 10 questions of 4 marks each.
(iii) Questions 1 to 8 in section A are multiple choice questions where you are to select one correct option out of the given four.
(iv) Use of calculators is not permitted.
SECTION A
Questions numbers 1 to 8 are of one mark each.
1. The common difference of the A.P., 1/2q, (1-2q)/2q, (1-4q)/2q,,.... is :
(i) -1 (ii) 1
(iii) q (iv) 2q
2. In figure, DE and DF are tangents from the external point D to a circle with center A.If DE = 5 cm and if DE is perpendicular to DF, then the radius of the circle is:
(iii) 4 cm (iv) 6 cm
3. In figure, a circle is inscribed in a quadrilateral ABCD touching its sides AB, BC, CD and AD at P, Q, R and S respectively. If the radius of the circle is 10cm, BC = 38 cm, PB = 27 cm and AD is perpendicular to CD,then the length of CD is
(i) 11 cm (ii) 20 cm
(iii) 21 cm (iv) 15 cm
4. A dice is thrown once. The probability of getting a prime number is
(i) 2/3 (ii) 1/3
(iii) 1/2 (iv) 1/6
5.A ladder 15 m long just reaches the top of a vertical wall. If the ladder make an angle of 60° with the wall, then the height of the wall is
(i) 15√3 m (ii) 15√3/2 m
(iii) 15/2 m (iv)15 m
6. A box contains cards numbered 6 to 50. A card is drawn at random from the box. The probability that the drawn card has a number which is a perfect square, is
(i) 1/45 (ii) 2/45
(iii) 1/9 (iv) 4/45
7.The point on the x-axis which is equidistant from the points(-1,0) and (5,0) is
(a) (0,2) (b) (2,0)
(c) (3,0) (d) (0,3)
8. If π is taken as 22/7, the distance (in metres) covered by a wheel of diameter 35 cm, in one revolution, is
(a) 2.2 (b) 1.1
(c) 9.625 (d) 96.25
SECTION B
Question numbers 9 to 14 carry 2 marks each.
9. Solve the following quadratic equation for x:
√2x² + 7x + 5√2 = 0
10. Find the number of all three-digit natural numbers which are divisible by 9.
11. In figure, two circles touch each other at the point C. Prove that the common tangent to the circles at C, bisects the common tangent at P and Q.
12. In figure, a quadrilateral ABCD is drawn to circumscribe a circle. Prove that
AB + CD = AD + BC
14.The length of the minute hand of a clock is 14 cm. Find the area swept by the minute hand in 5 minutes.
SECTION C
Question numbers 15 to 24 carry 3 marks each.
15. For what value of k, are the roots of the quadratic equation (k +4)x² + (k + 1 ) + 1 = 0 equal ?
16.The 19th term of an A.P. is equal to three times its sixth term. If its 9th term is 19, find the A.P.
17. Draw a pair of tangent to a circle of radius 4 cm, which are inclined to each other at an angle of 60°.
18. As observed from the top of a 60 m high lighthouse from the sea-level, the angles of a depression of two ships are 30 and 45. If one ship is exactly behind the other on the same side of the lighthouse, find the distance between the two ships.
19. Prove that the points A(2,3),B (-2,2) C (-1,-2) and D(3,-1) are the vertices of a square ABCD.
20. Find the ratio in which point P(-1,y) lying on the line segment joining points A(-3,10) and B(6,-8) divides it. Also find the value of y.
21. In figure, a square OABC is inscribed in a quadrant OPBQ of a circle. If OA = 21 cm, find the area of the shaded region.
22. A toy is in the form of a cone mounted on a hemisphere of same radius 7 cm.If the total height of the toy is 31 cm, find its total surface area.
23. A solid cone of base radius 10 cm is cut into two parts through the mid-point of its height, by a plane parallel to its base. Find the ratio in the volumes of the two parts of the cone.
24. A solid metallic sphere of diameter 8 cm is melted and drawn into a cylindrical wire of uniform width. If the length of the wire is 12 cm, find its width.
SECTION D
Question numbers 25 to 34 carry 4 marks each.
25. Solve for x:
1/(x-3) + 2/(x- 2) =8/x; x ≠0,2,3
26. A box contains cards numbered from 3,5,7,9,...35,37. A card is drawn at random from the box. Find the probability that the number on the drawn card is a prime number.
27.The sum of first n terms of an A.P. is 5n² + 3n. If its mth term is 168, find the value of m. Also find the 20th term if this A.P.
28. Prove that the lengths of tangents drawn from an external point to a circle are equal.
29. In figure, the sides AB, BC, CA of triangle ABC touch a circle with centre O and radius r at P, Q and R respectively.
31.If the points A(1,-2), B(2,3),C(-3,2) and D(-4,-3) are the vertices of parallelogram ABCD , then taking AB as the base, find the height of this parallelogram.
32. Water running in a cylindrical pipe of inner diameter 7 cm, is collected in a container at the rate of 192.5 litres per minutes. Find the rate of flow of water in the pipe in km/hr.
33.While boarding an aeroplane, a passenger got hurt. The pilot, showing promptness and concern, made arrangements to hospitalize the injured and so the plane started by 30 minutes. To teach the destination, 1500 km away, in time the pilot increases the speed by 100 km/hr. Find the original speed/hour of the plane. Do you appreciate the values shown by the pilot, namely promptness in providing help to the injured and his efforts to reach in time?
34. A container open at the top and made up of metal sheet is in the form of a frustum of a cone of height 16 cm with the diameters of its lower and upper ends as 16 cm and 40 cm respectively. Find the cost of metal sheet used to make the container, if it costs Rs. 10 per 100 cm. (take π= 3.14 )
No comments:
Post a Comment