Sample Paper – 2009
Class – X
Subject – Mathematics
Time : 3 hrs Marks :80
General Instructions
1. All questions are compulsory
2. The question paper consists of 25 questions divided in to three sections A, B and C .Section A
contains 7 questions of 2 marks each .Section B is of 12 Questions of 3 marks each and section
C of 6 Questions of 5 marks each
3. There is no overall choice .However ,internal choice has been provided in two questions of two
marks each, two questions of three marks each, two questions of five marks each
4. In question on construction ,drawing should be neat exactly as per the given measurements.
5. Use of calculators is not permitted.
SECTION - A
Q1. If x+3 is a factor of and
find a and b
Q2. Reduce the following rational expression into lowest terms
Q3. Solve for x
OR
Solve for x :
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Q4. What is the difference between the 20th terms of two AP with same common difference and first terms 3 and 8 ?, justify your answer .
OR
Find the number of terms of the AP 54, 51,48,.... so that their sum is 513.
Q5. If the diagonal BD of a quadrilateral ABCD bisects both and
,show that
Q6. A mixi is available for Rs 5,400 cash or Rs 1,400 cash down payment followed by Rs 4,240 after 6 months .Find the rate of interest charged under this instalment scheme
Q7. Two coins are tossed simultaneously. find the probability of getting
1. Two heads 2. at least one head
SECTION - B
Q8. Find the common root(s) of the equations
and
Q9. The hypotenuse of a right angles triangle is 4 more than three times the shortest side .If the third side is 4 less than four times the shortest side ,find the sides of the triangle
Q10. If a, b , c are pth ,qth , rth terms of an AP then prove that
Q11. A loan of Rs 48,800 is to be paid back in 3 equal annual instalment .If the rate of interest is 25%
per annum compounded annually .Find the instalment
Q12. The areas of two similar triangles are 81 Cm2 and 49Cm2 respectively .If the altitude of the bigger
triangle is 4.5Cm find the corresponding altitude of the smaller triangle
OR
In the trapezium ABCD AB parallel to CD and
If ar(DAOB) = 84Cm2 , ,find ar(DCOD)
Q13. In the given figure ABC is a triangle in which
A circle through B touches AC at D and intersect AB
at P .If D is the mid point of AC , show that
Q14. Construct D ABC having perimeter 14 Cm and Then construct the circum circle of the triangle
Q15. The radius and height of a solid right circular Cylinder are 10 Cm and 30 Cm respectively . It is melted and solid cones are prepared with diameter of the base 2 Cm and height 10 Cm . Find
how many such cones are prepared from the Cylinder
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Q16. Prove that
OR
Without using trigonometric table evaluate
Q17. Marks of 40 students in examination is represented by a frequency distribution .And their
mean marks is 40.5 find the missing frequencies.
Class | 0-10 | 10-20 | 20-30 | 30-40 | 40-50 | 50-60 | 60-70 | 70-80 |
Frequency | 5 | 3 | 4 | F1 | 7 | F2 | 6 | 3 |
Q18. The co-ordinates of one end of the diameter of a circle are (3,5) and the co-ordinates of its centre
are (7,4). Find out the co-ordinates of the other end of the diameter
Q19. Find the third vertex of a triangle , if two of its vertices are at (-3,1) and (0,-2) and the centroid is
at the origin
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Q20. Anuradha’s salary is Rs 15,000 per month and she contributes Rs 2,000 per month towards PF
and pays Rs 8,000 as annual LIC premium .She invests Rs4,000 in NSC and she donates
Rs 2,000 towards PM’s National Relief Fund .Find the income tax to be played by her for
the financial year
Q21. a) “In a triangle a line drawn parallel to one side to intersect the other sides in distinct points ,divides the two sides in the same ratio”. Prove
b) In the figure If PQ parallel to BC and PR parallel to
CD , Prove that
Q22. In the given figure O is the centre of the circle and OP
bisects angle APD prove that
Q23. A cone of height 15 Cm and diameter 7 Cm is mounted on a hemisphere of the same diameter .Determine the volume of the solid thus formed .(use )
OR
Find the number of bricks each measuring required to construct a wall 24m long ,6m high and 0.4m thick The mortar occupies
of the volume of the wall
Q24. A person standing on the bank of a river observes that the angle of elevation of the top a tree
standing on the opposite bank is . When he moves 40m away from the bank ,he finds the
angle of elevation to be . Find the height of the tree and the width of the river
OR
From the top of a building AB, 60 m high, the angles of depression of the top and bottom of
a vertical lamp post CD are observed to be 300 and 600 respectively Find
(i) the horizontal distance between AD and CD.
(ii) the difference between the heights of the building and the lamp post.
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Q25. The pie chart (as shown in the figure) represents the
amount spent on different sports by a sports club in
a year .If the amount spent by the club for hockey
is 30,000 .Find the total amount spent and amount spent
on each sports
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