Sample Paper – 2008
Class – X
Subject – Mathematics
1. Find the LCM and HCF of 150 and 420.
2. If p(x) = 3x^{2} – 6x + 3 , find the sum and product of the zeroes. Form a polynomial having sum and product as 3α + 2β and 2α + 3β.
3. Find the sum of 15 terms of an AP having the nth term as 4n – 3.
4. Find the value of k for which the equations:
kx – 4y = 3
12x – (k+3)y = 6 have unique solutions.
5. DE is parallel to BC . If AD = 12.4cm , DB = 6.2cm, AE = 2x and EC = 6x – 2. Find the value of x.
6. What is the value of 1/tan45^{0 }.
7. Find the length of the arc if the area of sector is 450cm^{2} and radius is 7cm.
8. Find the mode of the following numbers. 19,11,14,19,12,19,14,12,11,19
9. When does a quadratic equation has equal roots ?
10. Find the probability that in a single throw of a pair of dice a sum greater than 8 comes.
SECTION-B
11. Find the mode of the following distribution :
CL | F |
100-120 | 8 |
120-140 | 12 |
140-160 | 16 |
160-180 | 13 |
180-200 | 5 |
13. Find the coordinates of the point which divides the line segment joining the points (-3,6) and (1,2) in the ratio 3:5 .
OR
In what ratio are the points (-1,4) and (5,-2) are divided by the coordinates of X axis.
14. If the distances of (x, y) from (5 ,1) and ( - 1, 5) are equal , prove that 3x = 2y
15. Find the sum of all numbers between 700 and 950 which are multiple of 8.
SECTION-C
16. Prove the following :
1+sinA + cosA = 2secA
cosA 1+sinA
17. A budget for a journey was decided as Rs 300. If there were 5 more students for the journey the budget would become Rs 2 less. Find the cost for the jouney.
OR
Raju attended 40 questions in his class test. One mark was awarded for every right answer and 1 mark was deducted for every wrong answer. He got 4 questions correct and 3 questions wrong during his first session. Find the number of questions he attended.
18. Show that the points (a,b+c) , (b,c+a) and (c,a+b) are collinear.
19. If tanA + sinA = m and tanA – sinA = n , show that m^{2} – n^{2} = 4√mn.
20. Construct a pair of tangents to a circle of radius 4cm and measure their lengths.
21. Solve the following equations graphically:
2x – 4y = 5
3x + 8y = 10
22. Which term of the A.P 1, 10, 19, 28, 37, ……is 153 more than its 25^{th} term?
23. Solve by using Quadratic formula: 4x^{2} + 2(b – 3a)x – 3ab = 0
24. Use section formula to show that A (4, 6), B (7, 7), C (10, 10) and D (7, 9) are the vertices of
a parallelogram.
OR
A rectangular park is 100m by 50m. It is surrounded by semi-circular flower beds all around. Find the cost of levelling the semi-circular flower beds at Rs 1.20 per square meter.
25.It is given that a box contains 600 iron nails out of which 20% have become rusted. Find the probability that the drawn nail is unrusted.
SECTION-D
26. A vessel is in the form of a hollow hemisphere mounted by a hollow cylinder. The diameter of the hemisphere is 14cm and the total height of the vessel is 13cm. Find the inner surface area , total surface area and the volume of the vessel.
27. Prove that the square of the hypotenuse is equal to the sum of the squares of the other two sides.
Using the above result show that sum of the squares of the sides of a rhombus is equal to the sum of the squares of its diagonals.
OR
Prove that the ratio of areas of 2 similar triangles is equal to the ratio of squares of their corresponding sides.
Using the above result prove that area of an equilateral triangle described on one side of a square is half the area of triangle described on one of its diagonals.
28. Find the median of the following distribution and deduce the 2 ogives from the given distribution:
CL | F |
25-29 | 1 |
30-34 | 1 |
35-39 | 3 |
40-44 | 4 |
45-49 | 7 |
50-54 | 9 |
55-59 | 3 |
60-64 | 8 |
65-69 | 4 |
29. From an aeroplane vertically above a straight horizontal plane the angles of depression of two consecutive kilometer stones on the opposite sides of the aeroplane are found to be α and β. Show that the height of the aeroplane is tanα.tanβ .
tanα + tanβ
30. A train travels a distance of 480km at a uniform speed. If the speed had been 8km/hr less , then it would have taken 3hrs more to cover the same distance. Find the speed of the train.