2009 CBSE Sample Question Paper - I Mathematics - Class X Question paper
Sample Question Paper - I
Mathematics - Class X
Time : Three hours Max.Marks :80
1. All Questions are compulsory.
2. The question paper consists of thirty questions divided into 4 sections A, B, C and D.
Section A comprises of ten questions of 01 mark each, section B comprises of five
questions of 02 marks each, section C comprises of ten questions of 03 marks each and
section D comprises of five questions of 06 marks each.
3. All questions in Section A are to be answered in one word, one sentence or as per the
exact requirement of the question.
4. There is no overall choice. However, internal choice has been provided in one question of
02 marks each, three questions of 03 marks each and two questions of 06 marks each.
You have to attempt only one of the alternatives in all such questions.
5. In question on construction, drawings should be neat and exactly as per the given
6. Use of calculators is not permitted.However you may ask for mathematical tables.
1. Write the condition to be satisfied by q so that a rational number has a terminating
2. The sum and product of the zeroes of a quadratic polynomial are - ½ and -3 repectively.
What is the quadratic polynomial?
3. For what value of k the quadratic equation x2 - kx + 4 = 0 has equal roots?
4. Given that tan theta = 1/root5 , what is the value of -
5. Which term of the sequence 114, 109, 104 .... is the first negative term ?
6. A cylinder, a cone and a hemisphere are of equal base and have the same height. What is
the ratio in their volumes?
7. In the given figure, DE is parallel to BC
and AD = 1cm, BD = 2cm. What is the ratio of the
area of triangle ABC to the area of triangle ADE?
8. In the figure given below, PA and PB are tangents to the circle
drawn from an external point P. CD is a third tangent
touching the circle at Q. If PB = 10cm, and CQ = 2cm, what
is the length of PC?
9. Cards each marked with one of the numbers 4,5,6....20 are placed in a box and mixed
thoroughly. One card is drawn at random from the box. What is the probability of getting an
even prime number ?
10. A student draws a cumulative frequency curve for the marks obtained by 40 students of a
class, as shown below. Find the median marks obtained by the students of the class.
11 Without drawing the graphs, state whether the following pair of linear equations will
represent intersecting lines, coincident lines or parallel lines :
6x - 3y + 10 = 0
2x - y + 9 = 0
Justify your answer.
12. Without using trigonometric tables, find the value of
13 Find a point on the y-axis which is equidistant from the points A(6,5) and B (-4,3).
14 In the figure given below, AC is parallel to BD,
Is AE/CE=DE/BE ? Justify your answer.
15. A bag contains 5 red, 8 green and 7 white balls. One ball is drawn at random from the bag,
find the probability of getting
(i) a white ball or a green ball.
(ii) neither a green ball not a red ball.
One card is drawn from a well shuffled deck of 52 playing cards. Find the probability of getting
(i) a non-face card
(ii) A black king or a red queen.
16 Using Euclid’s division algorithm, find the HCF of 56, 96 and 404.
Prove that is an irrational number
17. If two zeroes of the polynomial x4+3x3-20x2-6x+36 are root (2) and -[root(2)] , find the other zeroes
of the polynomial.
18. Draw the graph of the following pair of linear equations
x + 3y = 6
2x - 3y = 12
Hence find the area of the region bounded by the
x = 0, y = 0 and 2x - 3y = 12
19. A contract on construction job specifies a penalty for delay of completion beyond a
certain date as follows: Rs 200 for Ist day, Rs. 250 for second day, Rs. 300 for third
day and so on. If the contractor pays Rs 27750 as penalty, find the number of days for
which the construction work is delayed.
20. Prove that :
21 Observe the graph given below and state whether triangle ABC is scalene, isosceles or
equilateral. Justify your answer. Also find its area.
22. Find the area of the quadrilateral whose vertices taken in order are A (-5,-3) B(-4, -6),
C(2,-1) and D (1,2).
23. Construct a triangle ABC in which CA = 6cm, AB = 5cm and angle BAC = 45°, then construct a
triangle similar to the given triangle whose sides are 6/5 of the corresponding sides of the
24 Prove that the intercept of a tangent between two parallel tangents to a circle subtends a
right angle at the centre of the circle.
25 A square field and an equilateral triangular park have equal perimeters.If the cost of
ploughing the field at rate of Rs 5/ m^2 is Rs 720, find the cost of maintaining the park at the
rate of Rs 10/m^2.
An iron solid sphere of radius 3cm is melted and recast into small sperical balls of
radius 1cm each. Assuming that there is no wastage in the process, find the number of
small spherical balls made from the given sphere.
26. Some students arranged a picnic. The budget for food was Rs 240. Because four students
of the group failed to go, the cost of food to each student got increased by Rs 5. How
many students went for the picnic?
A plane left 30 minutes late than its scheduled time and in order to reach the destination
1500km away in time, it had to increase the speed by 250 km/h from the usual speed.
Find its usual speed.
27. From the top of a building 100 m high, the angles of depression of the top and bottom of
a tower are observed to be 45° and 60° respectively. Find the height of the tower. Also
find the distance between the foot of the building and bottom of the tower.
The angle of elevation of the top a tower at a point on the level ground is 30°. After walking
a distance of 100m towards the foot of the tower along the horizontal line through the foot
of the tower on the same level ground , the angle of elevation of the top of the tower is 60°.
Find the height of the tower.
28 Prove that in a right triangle, the square of the hypotenuse is equal to the sum of the
squares of the other two sides.
Using the above, solve the following:
A ladder reaches a window which is 12m above the ground on one side of the street.
Keeping its foot at the same point, the ladder is turned to the other side of the street to
reach a window 9m high. Find the width of the street if the length of the ladder is 15m.
29. The interior of building is in the form of a right circular cylinder of radius 7m and height 6m,
surmounted by a right circular cone of same radius and of vertical angle 60°. Find the
cost of painting the building from inside at the rate of Rs 30/m2
30. The following table shows the marks obtained by 100 students of class X in a school
during a particular academic session. Find the mode of this distribution.
Marks No. of students
Less then 10 7
Less than 20 21
Less than 30 34
Less than 40 46
Less than 50 66
Less than 60 77
Less than 70 92
Less than 80 100
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