Sample Paper 8 – 2009
Class – X
Subject – Mathematics
Section - A
1. Define Euclid's division lemma.
2. The graph of y = f(x) are given so me polynomial f(x). Find the zeros of f(x).
3. Write AP when first term a and common difference d as; a = 10, d =
4. From a pt. Q, the length of tangents to circle is 24 cm and distence Q from centre is 25 cm. Find radius of circle.
5. The circumference of circle exceeds the diameter by 33.6 cm. Find radius.
6. Find mean of all the factors of 20.
7. Write the sample space when first die always show 6 If two dice are thrown simultaneously.
8. Find the value of (1-sin2) sec2
.
9. State whether true or false. Justify your answer tan A is not defined for A = 300.
10. Find the value of
Section - B
11. Solve the eq. 3x2 - 5x + 2 = 0, by completing the eq. method.
12. Prove (3, 3), (9, 0) and (12, 21) are vertices of right angled triangle.
13. A card is drawn at random from a pack of 52 cards, find the probability that card drawn is (i) neither heart nor a king (ii) a black king.
14. By completing the sq. method solve 3x2 + 7x + 4 = 0
15. Verify 1, 4, 7 are zeroes of x3 - 12x2 + 39x - 28. Also verify the relationship between zeroes and coefficients.
OR
Find all other zeroes of 3x4 + 6x3 - 2x2 - 10x - 5, If two of its zeroes are and
16. Prove is irrational.
OR
Find HCF of 117 and 65 & express it as a linear combination of 117 and 65.
17. Determine the ratio in which line 2x - 3y + 7 = 0 divide the jaoin of (3, 4)& (7, 8)
18. Solve graphically the system of linear eq. 2x + y = 8, x +1 = 2y. Also find the point, where the lines meet y-axis.
19. Prove that
20. Find the value of k, if (8,1), (l, -4) & (2, -5) are collinear.
21. If sum of n terms of AP is 5n = 5n2 + 3n, find the nth term.
OR
Find the sum of three digit numbers which leave remainder 2 when divided by 5.
22. Draw a line segment AB of length 8 cm. Taking A as centre draw a circle of radius 4 cm and taking B as centre, draw another circle of radius 3 cm. Construct tengents to each circle from the centre of other circle.
23. A circle touching BC of ABC at P and touching AB and AC produced at Q and R respectively. Prove AQ =
(perimeter of
ABC)
24. In fig, o is centre of circle with radius 14 cm. find area of shaded region.
or
A well of diameter 3 m is dug 14 m deep. Earth taken out of it has been spread evenly all around it in the slope of circularing of width 4m to form an embankment find height of embankment.
25. XY || AC and XY divides triangular region ABC into two parts equal in area. Determine AX / AB.
26. A metallic right circular cone 20 cm high and whose vertical angle is 600 is cut into two parts at the middle of its height by a plane parallel to its base. If the frustum so obtained he drawn into a wine of diameter cm. Find length of wire.
or
Water in a canal 30 dm wide and 12 dm deep is flowing with velocity of 10 km/hr. How much area will it irrigate in 30 minutes, If 8 cm of standing water is required for irrigation.
27. Prove that in a right-angled triangle, the square of hypotenuse is equal to sum of sq. of other sides. By using the theorem, Determine the length of ladder If it is placed in such a way that its foot is at distance of 5 m from wall and its top touches a window 12 m above the ground.
28. The following is the distributor of height of students
height in cm. 160-162 163-165 166-168 169-171 171-174
No. of student 15 118 142 127 18
find the mode of height of students.
29. The angle of elevator of top of tower from a point on same level as foot of tower is . On advancing 'p' meters towards the foot of tower, the angle of elevation becomes
.Show height 'h' of tower is given by
Also determine height of tower if p = 150 m, =300 and
= 600.
30. Rs. 6500 were divided equally among a certoun no. of persons. Had there been 15 more persons, each would have got Rs. 30 less. find original no. of persons.
or
The hypotenuse of a right angled traingle is one more than twice the shortest side. If the base of the triangle is one more then shortest side, Determine the length of three sides of triangle.
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