Sample Paper – 2009
Class – X
Subject – Mathematics
Section-A
1. Without actually performing the long division, state whether the following no. will have a terminating decimal expansion.
2. If tan A = cot B prove A + B =900.
4. Find the circumference of circle whose area is 6.16 cm2.
5. Write the frequency distributor from following data :
Marks (more than) 0 10 20 30 40 50 60 70 upto 80
No. of students 100 97 87 73 50 25 6 2
6. If Cos and tan , find value of sin ( ), where are acute angles.
7. The sides of traingle are given below, Determine the given triangle is right angle or not
a = 9 cm, b = 12 cm, and c = 15 cm.
8. If Sin A = , Calculate tan A.
9. PErimeter of a sector = _________________________
10. Empirical relation between the three measures of tendency.
Section - B
11. For what value of k the following system of eq. will be inconsistent.
kx + 2y - 5 = 0
8x + ky - 10 = 0
12. Show that (-1, -1), (5, 7) & (8, 11) are collinear.
15. Five cards : tan, Jack, queen and once of heart are well shuffled with their face downwards. One card is then picked at random.
(i) What is probability the card is quen.,
(ii) If a king is drawn first and put a side, what is the probability that second
picked up is an ace.
Section - C
16. Prove is an irrational no.
or
Prove product of two consecutive positive integers is divisible by 2.
17. If are zeroes of f(x) = 3x2 - 4x + 1, find quad polynomial whose zeroes are .
18. Draw the graphs of eq. x-y+1 = 0 and 3x + 2y - 12 = 0 Determine the coordinate of vertices of triangle formed by these lines and x-axios and shade the triangular region.
19. If first term of AP is 2 and sum of first 5 terms is equal to one fourth of sum of next 5 terms; find sum of 30 terms. Also show 20th term is -112.
OR
Find k if given value of 'x' is kth term of given AP
20. Draw a ABC with side BC = 7 cm, B=450, A = 1050, Then construct a whose sides one times the corresponding sides of ABC.
21. Prove opposite sides of quadrilateral circumscribing a circle a circle subtend supplementary angles at centre of circle.
22. Points (2, 1) & (1, -2) are equidistent from (x, y) show x + 3y = 0
or
Determine the ratio in which P (a, -2) divides the join of A (-4, 3) & B (2, -4). Find the value of a, also.
23. If x = a sec + b tan and y = a tan + b sec , prove x2 - y2 = a2 - b2.
24. Find the value of k for which given eq. has real & equal roots
x2 - 2 (1 + 3k) x + 7 (3 + 2k) = 0
25. If (-2, 3), (4, -3) & (4, 5) are the mid pt. of sides of , find coordinates of centroid.
Section - D
26. The angle of elevation of a cliff from a fixed point is . After going up a distance of k metres towards the top of clieff at angle of , it is found that angle of elevation is . Show height of clieff is metres.
27. If two pipes function simultaneously, the reservoir will be filled in 12 hr. one pipe fills the reservoir 10 hr. faster than other. How many hours it takes the second pipe to fill reservoir.
or
A motor boat goes 30 km upstream & returns back to starting point in 55 minutes. If speed of boat is still water is 22 km/hr, find rate of current.
28. Prove that ratio of areas of 2 similar is equal to ratio of sq. of any two corresponding sides. By using same theorem find BC, If the areas of 2 similars s ABC & PQR are 64 cm2 and 121 cm2 respectively and QR = 15.4 cm.
29. A right triangle whose sides are 15 cm & 20 cm is made to revolve about its hypotenuse. find volume and surface area of cone so formed (use = 3.14)
OR
The height of cone is 30 cm. A small cone is cut-off at the top by plene parallel to base. If its volume be of vol. of given cone, at what height above the base is section made.
30. Find missing frequency in following distribution If N = 74 and median of distribution is 36
Marks 0-10 10-20 20-30 30-40 40-50 50-60 60-70 70-80
No. of students 2 8 ? 20 12 ? 4 3
Class – X
Subject – Mathematics
Section-A
1. Without actually performing the long division, state whether the following no. will have a terminating decimal expansion.
2. If tan A = cot B prove A + B =900.
4. Find the circumference of circle whose area is 6.16 cm2.
5. Write the frequency distributor from following data :
Marks (more than) 0 10 20 30 40 50 60 70 upto 80
No. of students 100 97 87 73 50 25 6 2
6. If Cos and tan , find value of sin ( ), where are acute angles.
7. The sides of traingle are given below, Determine the given triangle is right angle or not
a = 9 cm, b = 12 cm, and c = 15 cm.
8. If Sin A = , Calculate tan A.
9. PErimeter of a sector = _________________________
10. Empirical relation between the three measures of tendency.
Section - B
11. For what value of k the following system of eq. will be inconsistent.
kx + 2y - 5 = 0
8x + ky - 10 = 0
12. Show that (-1, -1), (5, 7) & (8, 11) are collinear.
15. Five cards : tan, Jack, queen and once of heart are well shuffled with their face downwards. One card is then picked at random.
(i) What is probability the card is quen.,
(ii) If a king is drawn first and put a side, what is the probability that second
picked up is an ace.
Section - C
16. Prove is an irrational no.
or
Prove product of two consecutive positive integers is divisible by 2.
17. If are zeroes of f(x) = 3x2 - 4x + 1, find quad polynomial whose zeroes are .
18. Draw the graphs of eq. x-y+1 = 0 and 3x + 2y - 12 = 0 Determine the coordinate of vertices of triangle formed by these lines and x-axios and shade the triangular region.
19. If first term of AP is 2 and sum of first 5 terms is equal to one fourth of sum of next 5 terms; find sum of 30 terms. Also show 20th term is -112.
OR
Find k if given value of 'x' is kth term of given AP
20. Draw a ABC with side BC = 7 cm, B=450, A = 1050, Then construct a whose sides one times the corresponding sides of ABC.
21. Prove opposite sides of quadrilateral circumscribing a circle a circle subtend supplementary angles at centre of circle.
22. Points (2, 1) & (1, -2) are equidistent from (x, y) show x + 3y = 0
or
Determine the ratio in which P (a, -2) divides the join of A (-4, 3) & B (2, -4). Find the value of a, also.
23. If x = a sec + b tan and y = a tan + b sec , prove x2 - y2 = a2 - b2.
24. Find the value of k for which given eq. has real & equal roots
x2 - 2 (1 + 3k) x + 7 (3 + 2k) = 0
25. If (-2, 3), (4, -3) & (4, 5) are the mid pt. of sides of , find coordinates of centroid.
Section - D
26. The angle of elevation of a cliff from a fixed point is . After going up a distance of k metres towards the top of clieff at angle of , it is found that angle of elevation is . Show height of clieff is metres.
27. If two pipes function simultaneously, the reservoir will be filled in 12 hr. one pipe fills the reservoir 10 hr. faster than other. How many hours it takes the second pipe to fill reservoir.
or
A motor boat goes 30 km upstream & returns back to starting point in 55 minutes. If speed of boat is still water is 22 km/hr, find rate of current.
28. Prove that ratio of areas of 2 similar is equal to ratio of sq. of any two corresponding sides. By using same theorem find BC, If the areas of 2 similars s ABC & PQR are 64 cm2 and 121 cm2 respectively and QR = 15.4 cm.
29. A right triangle whose sides are 15 cm & 20 cm is made to revolve about its hypotenuse. find volume and surface area of cone so formed (use = 3.14)
OR
The height of cone is 30 cm. A small cone is cut-off at the top by plene parallel to base. If its volume be of vol. of given cone, at what height above the base is section made.
30. Find missing frequency in following distribution If N = 74 and median of distribution is 36
Marks 0-10 10-20 20-30 30-40 40-50 50-60 60-70 70-80
No. of students 2 8 ? 20 12 ? 4 3
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