Guess Paper – 2009
Class – X
Subject – Mathematics
Time: 3 hrs St. Luke’s Sr. Sec. School, Solan. Marks: 80
General Instructions:
Ø All questions are compulsory.
Ø The question paper is of 30 questions divided into four sections –A, B, C and D. Section A contains10 questions of 1 marks each. Section B is of 5 questions of 2 marks each , section C is of 10 questions of 3 marks each and Section D is of 5questions of 6 marks.
Ø There is no overall choice.
Ø In question on construction, the drawing should be neat and exactly as per the given measurements.
Ø Use of calculator is not permitted.
Ø No credit will be given for cutting, scribbling in section A
(SECTION A)
1. If 0.2316 is expressed in the form for smallest value of whole numbers n and m. write these values of n and m.
2. What is the product of three zeros of the cubic ?
3. The pair of linear equations 7x-3y = 4; 3x + =4 is consistent only when (a) k = 9 (b) k = -9 (c) (d)
4. If α = and β = be two roots of the quadratic equation , write the value of k.
5. If the last term of an A.P. is 119 and the 8th term from the end is 91 then common difference of the AP is
(a) 2 (b) 4 (c) 3 (d) -3
6.
A
4cm
B
D
C
P
x
Q
M
R In the fig. , D is the mid point of BC and M is the mid point of QR. If the area of DABC = 100 cm2 and the area of DPQR = 144cm2, write the value of x.
7. State the section formula for finding the coordinates of a point which divides the join of two points in a given ratio.
8. In a right angled triangle DABC, ÐA = 90o and = 2k, find the value of k.
9.
A
B
P
C
Q
RA circle touching the side of a DABC at P and touching AB and AC produced at Q and R respectively. If AB = 4.4cm, BC = 3cm and AC = 4cm, find the length of the tangent AQ.
10. Write the formula for finding the curved surface of the frustum of a cone having slant height l and the radii of its circular ends as R and r.
(SECTION B)
11. If where = (i =1, 2, 3 …) are the class marks of a grouped data and are the corresponding frequencies. If = 200 and =12, find .
12. A card is drawn at random from well shuffled deck of playing cards. Find the probability that the card drawn is (i) a card of spade or an ace. (ii) a red king (iii) neither a king nor a queen (iv) either a king or a queen.
13. A hemispherical bowl of internal diameter 36cm is full of some liquid. This liquid is to be filled in cylindrical bottles of radius 3cm and height 6cm. Find the number of bottles needed to empty the bowl.
14. Without using trigonometric tables evaluate;
15. Find the roots of the equation 2x2 – 6x + 3 = 0 by method of completing the squares.
(SECTION C)
16. Find the zeros of the polynomial ,and verify the relations between the zeros and the co-efficient of the polynomial.
17. Solve the system of equation: ; bx – ay + 2ab = 0.
18. A passenger train takes 2 hours less for a journey of 300km. If its speed is increased by 5km/hr from its original speed. Find the original speed of the train. OR
Solve for x: ; a≠0,b≠0,x≠0
19. A contract on construction job specifies a penalty for delay of completion beyond a certain date as follows: Rs. 200 for the first day, Rs.250 for the second day, Rs.300 for the third day, etc. the penalty for each succeeding day being Rs.50 more than for the preceding day. How much money the contractor has to pay as penalty, if he has delayed the work by 30 days?
20. DABC is a right triangle, right angled at B. AD and CE are the two medians from A and
C respectively. If AC = 5cm and AD = cm, find the length of CE.
OR
In an equilateral triangle ABC, the side BC is divided at D such that BD = BC. Prove that 25AD2 = 21 AB2
21. Prove that coordinates of the point dividing the line segment joining the points (x1,y1) and (x2,y2) internally in the ratio m1:m2 are given by { , }
22. If , prove that OR
Prove the identity =
23.
A
B
P
C
Q
RA circle is touching the side BC of DABC at P and is touching AB and AC when produced at Q and R respectively. Prove that AQ = ½(perimeter of DABC).
24. Construct DABC with ÐB= 90o, BC = 7cm and AB = 6cm .Then construct another triangle similar to DABC so that the corresponding sides of the second triangle be 5/7 times than those of the DABC.
25.
A
B
C
D
E
F In the figure a crescent is formed by two circles which touch at A. C is the centre of the larger circle. The width of the crescent at BD is 9cm and at EF it is 5cm. Find the area of the shaded region. OR
18cm
22cm
10cm
8cmAn oil funnel of tin sheet consists of a cylindrical portion 10cm long attached to a frustum of a cone. If the total height is 22cm, diameter of the cylindrical portion is 8cm and the diameter of the top of the funnel is 18cm, find the area of the tin required to make the funnel.
(SECTION D)
26. A bucket made of a metal sheet in the form of a frustum of a cone of height 16cm with radii of its lower and upper ends as 8cm and 20cm respectively. Find the cost of the bucket if the cost of the metal sheet is Rs. 15 per 100cm2. OR
A building is in the form of a cylinder surmounted by a hemispherical vaulted dome and contains 41 m3 of air. If the internal diameter of the building is equal to its total height above the floor, find the height of the building.
27. Two stations due South of a leaning tower which leans towards the North are at a distances of ‘a’ and ‘b’ from its foot. If ‘α’ and β’ be the elevations of the top of the tower from these stations, prove that its inclination ‘θ’ to the horizontal is given by cot θ = bcot α – a cot β/ b – a. OR
The angle of elevation of an aero plane from A on the ground is 45o.After 15 sec flight, the angle of elevation changes to 30o.If aero plane is flying at a height of 3000m, find the speed of the plane.
28. Prove that the ratio of the areas of two similar triangles is equal to the the ratio of the squares of their corresponding sides.
Using the above statement solve the following:
The areas of two similar triangles ABC and PQR are in the ratio 25:36. If BC = 6.5cm, find the length of QR.
29. The median of the following data is 525. Find the values of x and y, if the total frequency is 100.
CLASS INTERVAL
FREQUENCY
0-100
2
100-200
5
200-300
X
300-400
12
400-500
17
500-600
20
600-700
Y
700-800
9
800-900
7
900-1000
4
30. If a boy’s age & his father’s age amount together to 24 years & the fourth part of the product of their ages exceeds the boy’s age by 9 years. Find how old they are? OR
The sum of the ages of A and B is 49years. A says to B “Iam twice as old as you were when I was as old as you are”. Find their present ages.
Class – X
Subject – Mathematics
Time: 3 hrs St. Luke’s Sr. Sec. School, Solan. Marks: 80
General Instructions:
Ø All questions are compulsory.
Ø The question paper is of 30 questions divided into four sections –A, B, C and D. Section A contains10 questions of 1 marks each. Section B is of 5 questions of 2 marks each , section C is of 10 questions of 3 marks each and Section D is of 5questions of 6 marks.
Ø There is no overall choice.
Ø In question on construction, the drawing should be neat and exactly as per the given measurements.
Ø Use of calculator is not permitted.
Ø No credit will be given for cutting, scribbling in section A
(SECTION A)
1. If 0.2316 is expressed in the form for smallest value of whole numbers n and m. write these values of n and m.
2. What is the product of three zeros of the cubic ?
3. The pair of linear equations 7x-3y = 4; 3x + =4 is consistent only when (a) k = 9 (b) k = -9 (c) (d)
4. If α = and β = be two roots of the quadratic equation , write the value of k.
5. If the last term of an A.P. is 119 and the 8th term from the end is 91 then common difference of the AP is
(a) 2 (b) 4 (c) 3 (d) -3
6.
A
4cm
B
D
C
P
x
Q
M
R In the fig. , D is the mid point of BC and M is the mid point of QR. If the area of DABC = 100 cm2 and the area of DPQR = 144cm2, write the value of x.
7. State the section formula for finding the coordinates of a point which divides the join of two points in a given ratio.
8. In a right angled triangle DABC, ÐA = 90o and = 2k, find the value of k.
9.
A
B
P
C
Q
RA circle touching the side of a DABC at P and touching AB and AC produced at Q and R respectively. If AB = 4.4cm, BC = 3cm and AC = 4cm, find the length of the tangent AQ.
10. Write the formula for finding the curved surface of the frustum of a cone having slant height l and the radii of its circular ends as R and r.
(SECTION B)
11. If where = (i =1, 2, 3 …) are the class marks of a grouped data and are the corresponding frequencies. If = 200 and =12, find .
12. A card is drawn at random from well shuffled deck of playing cards. Find the probability that the card drawn is (i) a card of spade or an ace. (ii) a red king (iii) neither a king nor a queen (iv) either a king or a queen.
13. A hemispherical bowl of internal diameter 36cm is full of some liquid. This liquid is to be filled in cylindrical bottles of radius 3cm and height 6cm. Find the number of bottles needed to empty the bowl.
14. Without using trigonometric tables evaluate;
15. Find the roots of the equation 2x2 – 6x + 3 = 0 by method of completing the squares.
(SECTION C)
16. Find the zeros of the polynomial ,and verify the relations between the zeros and the co-efficient of the polynomial.
17. Solve the system of equation: ; bx – ay + 2ab = 0.
18. A passenger train takes 2 hours less for a journey of 300km. If its speed is increased by 5km/hr from its original speed. Find the original speed of the train. OR
Solve for x: ; a≠0,b≠0,x≠0
19. A contract on construction job specifies a penalty for delay of completion beyond a certain date as follows: Rs. 200 for the first day, Rs.250 for the second day, Rs.300 for the third day, etc. the penalty for each succeeding day being Rs.50 more than for the preceding day. How much money the contractor has to pay as penalty, if he has delayed the work by 30 days?
20. DABC is a right triangle, right angled at B. AD and CE are the two medians from A and
C respectively. If AC = 5cm and AD = cm, find the length of CE.
OR
In an equilateral triangle ABC, the side BC is divided at D such that BD = BC. Prove that 25AD2 = 21 AB2
21. Prove that coordinates of the point dividing the line segment joining the points (x1,y1) and (x2,y2) internally in the ratio m1:m2 are given by { , }
22. If , prove that OR
Prove the identity =
23.
A
B
P
C
Q
RA circle is touching the side BC of DABC at P and is touching AB and AC when produced at Q and R respectively. Prove that AQ = ½(perimeter of DABC).
24. Construct DABC with ÐB= 90o, BC = 7cm and AB = 6cm .Then construct another triangle similar to DABC so that the corresponding sides of the second triangle be 5/7 times than those of the DABC.
25.
A
B
C
D
E
F In the figure a crescent is formed by two circles which touch at A. C is the centre of the larger circle. The width of the crescent at BD is 9cm and at EF it is 5cm. Find the area of the shaded region. OR
18cm
22cm
10cm
8cmAn oil funnel of tin sheet consists of a cylindrical portion 10cm long attached to a frustum of a cone. If the total height is 22cm, diameter of the cylindrical portion is 8cm and the diameter of the top of the funnel is 18cm, find the area of the tin required to make the funnel.
(SECTION D)
26. A bucket made of a metal sheet in the form of a frustum of a cone of height 16cm with radii of its lower and upper ends as 8cm and 20cm respectively. Find the cost of the bucket if the cost of the metal sheet is Rs. 15 per 100cm2. OR
A building is in the form of a cylinder surmounted by a hemispherical vaulted dome and contains 41 m3 of air. If the internal diameter of the building is equal to its total height above the floor, find the height of the building.
27. Two stations due South of a leaning tower which leans towards the North are at a distances of ‘a’ and ‘b’ from its foot. If ‘α’ and β’ be the elevations of the top of the tower from these stations, prove that its inclination ‘θ’ to the horizontal is given by cot θ = bcot α – a cot β/ b – a. OR
The angle of elevation of an aero plane from A on the ground is 45o.After 15 sec flight, the angle of elevation changes to 30o.If aero plane is flying at a height of 3000m, find the speed of the plane.
28. Prove that the ratio of the areas of two similar triangles is equal to the the ratio of the squares of their corresponding sides.
Using the above statement solve the following:
The areas of two similar triangles ABC and PQR are in the ratio 25:36. If BC = 6.5cm, find the length of QR.
29. The median of the following data is 525. Find the values of x and y, if the total frequency is 100.
CLASS INTERVAL
FREQUENCY
0-100
2
100-200
5
200-300
X
300-400
12
400-500
17
500-600
20
600-700
Y
700-800
9
800-900
7
900-1000
4
30. If a boy’s age & his father’s age amount together to 24 years & the fourth part of the product of their ages exceeds the boy’s age by 9 years. Find how old they are? OR
The sum of the ages of A and B is 49years. A says to B “Iam twice as old as you were when I was as old as you are”. Find their present ages.
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