CBSE [ Delhi ] - 2008 (Set - II )
Mathematics
CLASS X
Time Allotted: 03:00:00
Maximum Marks: 80
1. All questions are compulsory.
2. The question paper consists of thirty questions divided into four sections, Question (110) each question is of 1 mark Q(11-15) each question is of 2 marks, Q(16-25) each
question is of 3 marks and Q(26-30) each question is of 6 marks.
3. All the questions(1-10) 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 two marks, three questions of three marks and two questions of 6 marks each. You
have to attend only one of the alternatives in all such questions.
5. In question of construction drawing should be neat and exactly as per the given
measurments.
6. Use of calculators is not permitted.
7. To view the answer, click on the Answer link alongside the Question.
Q 1)Find the value of k, so that the following system of equations has no solution: 3x
– y –5 = 0; 6x – 2y – k = 0. ( 1 Marks )
Q 2)The nth term of an AP is 6n + 2. Find its common difference. ( 1 Marks )
Q 3)In Figure, AD = 4 cm, BD = 3 cm and CB = 12 cm, find cot
<!--[endif]-->
( 1 Marks )
Q 4)Write the zeroes of the polynomial x2 – x – 6. ( 1 Marks )
Q 5)if <!--[if !vml]--> <!--[endif]-->is a rational number ( <!--[if !vml]-->
<!-[endif]-->), what is the condition on q so that the decimal representation of <!--[if
!vml]-->
<!--[endif]-->is terminating?
( 1 Marks )
Q 6)From a well shuffled pack of cards, a card is drawn at random. Find the
probability of getting a black queen. ( 1 Marks )
Q 7)Which measure of central tendency is given by the x-coordinate of the point of
intersection of the “more than ogive” and “less than ogive”? ( 1 Marks )
Q 8)In figure, O is the centre of a circle. The area of sector OAPB is 5/18 of the area
of the circle. Find x.
<!--[endif]-->
( 1 Marks )
Q 9) <!--[if !vml]->
[endif]-->
<!--
<!--[endif]-->
( 1 Marks )
Q 10)In figure, P and Q are points on the sides AB and AC respectively of triangle ABC
such that AP = 3.5 cm, AQ=3cm, PB = 7 cm and QC = 6 cm. If PQ = 4.5 cm, find BC.
<!--[endif]-->
( 1 Marks )
Q 11)For what value of p, the points (2, 1), (p, – 1) and (– 1, 3) are collinear? ( 2
Marks )
Q 12)Without using trigonometrical tables, evaluate the
following:
<!--[endif]-->
<!--[if gte mso 9]-->
( 2 Marks )
Q 13)Find the zeroes of the quadratic polynomial 6x2 – 3 – 7x and verify the
relationship between the zeroes and the co-efficients of the polynomial. ( 2 Marks )
Q 14)A die is thrown once. Find the probability of getting
(i)an even prime number
(ii) a multiple of 3. ( 2 Marks
)
Q 15)ABC is an isosceles triangle, in which AB = AC, circumscribed about a circle.
Show that BC is bisect at the point of contact. ( 2 Marks )
OR
In figure, a circle is inscribed in a quadrilateral ABCD in which angle B = 90o. If AD =
23 cm, AB=29cm and DS = 5 cm, find the radius (r) of the circle.
<!--[endif]-->
( 1 Marks )
Q 16)Prove that:
<!--[endif]-->
( 3 Marks )
OR
Prove that:
<!--[endif]-->
( 3 Marks )
Q 17)Find the 10th term from the end of the A.P. 8, 10, 12, …….., 126. ( 3 Marks )
Q 18)Represent the following system of linear equations graphically.
From the graph, find the points where the lines intersect Y-axis:
3x + y – 5 = 0; 2x – y – 5 = 0. ( 3 Marks )
Q 19)Find the roots of the following equation:
<!--[endif]-->
( 3 Marks )
Q 20)Show that <!--[if !vml]-->
( 3 Marks )
<!--[endif]-->is an irrational number.
Q 21)In figure, find the perimeter of shaded region where ADC, AEB and BFC are
semi-circles on diameters AC, AB and BC respectively.
<!--[endif]-->
( 3 Marks )
OR
Find the area of the shaded region in figure, where ABCD is a square of 14
cm.
<!--[endif]-->
( 3 Marks )
Q 22)If the distance of P(x, y) from the points A(3, 6) and B(–3, 4) are equal, prove
that 3x + y = 5. ( 3 Marks )
Q 23)If the diagonals of a quadrilateral divide each other proportionally, prove that it
is a trapezium. ( 3 Marks )
OR
Two triangles ABC and DBC are on the same base BC and on the same side of BC in
which <!--[if !vml]-->
<!--[endif]-->. If CA and BD meet each other at E,
show that AE.EC = BE.ED. ( 3 Marks )
Q 24)Construct a
a
similar to
.
( 3 Marks )
in which AB = 6.5 cm,
and BC = 5.5 cm. Also construct
, whose each side is 3/2 times the corresponding side of the
Q 25)Determine the ratio in which the line 3x + 4y – 9 = 0 divides the line-segment
joining the points (1, 3) and (2, 7). ( 3 Marks )
Q 26)A statue 1.46 m tall stands on the top of a pedestal. From a point on the ground, the
angle of elevation of the top of the statue is 60o and from the same point, angle of
elevation of the pedestal is 45o. Find the height of the pedestal.
(Use <!--[if !vml]-->
<!--[endif]-->)
( 6 Marks )
Q 27)In a class test, the sum of the marks obtained by P in mathematics and science
is 28. Had he got 3 marks more in mathematics and 4 marks less in science, the
product of marks obtained in two subjects would have been 180. Find the marks
obtained in the two subjects separately. ( 6 Marks )
OR
The sum of the areas of two squares is 640 m 2. If the difference in their perimeters
be 64 m, find the sides of the two squares. ( 6 Marks )
Q 28)100 surnames were randomly picked up from a local telephone directory and
the distribution of number of letters of the English alphabet in the surnames was
obtained as follows:
No. of
1-4
4-7
7-10
10-13
13-16
16-19
letters
No. of
6
30
40
16
4
4
surnames
Determine the median and mean number of letters in the surnames. Also find the
modal size of surnames.
( 6 Marks )
Q 29)Prove that the ratio of the areas of two similar triangles is equal to the ratio of
squares of their corresponding sides. Using the above result, prove the following:
In a triangle ABC, XY is parallel to BC and it divides triangle into two parts of equal
area. Prove that: <!--[if !vml]-->
<!--[endif]-->
( 6 Marks )
Q 30)A bucket made up of a metal sheet is in the form of a frustum of a cone of height 16
cm with diameters of its lower and upper ends as 16 cm and 40 cm respectively. Find the
volume of the bucket. Also find the cost of the bucket if the cost of metal sheet used is
Rs. 20 per 100 cm2. ( <!--[if !vml]-->
<!--[endif]-->)
( 6 Marks )
OR
A farmer connects a pipe of internal diameter 20 cm from a canal into a cylindrical
tank in his field which is 10 m in diameter and 2 m deep. If water flows through the
pipe at the rate of 6 km/h., in how much time will the tank be filled? ( 6 Marks )
CBSE [ All India ] - 2008 (Set - II )
Mathematics
CLASS X
Time Allotted: 03:00:00
Maximum Marks: 80
1. All questions are compulsory.
2. The question paper consists of 30 questions divided in to four sections - Q(1-10) each
question is of 1 mark, Q(11-15) each question is of 2 marks, Q(16-25) each question is of
3 marks and Q(26-30) each question is of 6 marks.
3. All questions of 1 mark 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, an internal choice has been provided in one
question of two marks each, three questions of three marks each and two questions of 6
marks each. You have to attempt only one of the alternative in all such questions.
5. In question of construction the drawing should be neat and exactly as per the given
measurements.
6. The use of calculator is not permitted.
7. To view the answer, click on the Answer link alongside the Question.
Q 1)In figure 1, If
( 1 Marks )
Q 2)If
( 1 Marks )
Q 3)Find the perimeter of the given figure, where
( 1 Marks )
Q 4)A bag contain 4 red and 6 black balls. A ball is taken out of the bag at random. Find the probability of
getting a black ball. ( 1 Marks )
Q 5)Find the Median of the following data:
Marks
0-10
10-20
20-30
obtained
Frequency 8
10
12
( 1 Marks )
Q 6)Write a rational number between
30-40
40-50
50-60
22
30
18
. ( 1 Marks )
Q 7)Write the number of zeros of the polynomials Y = f(x), whose graph is given in the
figure.
( 1 Marks )
Q 8)Is
= -3 a solution of the equation
( 1 Marks )
Q 9)D, E and F are the mid-points of the sides AB,BC and CA respectively of triangle
ABC. Find
. ( 1 Marks )
Q 10)Write the next term of the A.P
( 1 Marks )
Q 11)Cards, Marked with number 5 to 50 are placed in a box and mixed thoroughly. A
card is drawn from the box at random. Find the probability that the number on the taken
out card is:
1. A prime number less tan 10.
2. A number which is a perfect square. ( 2 Marks )
Q 12)For what value of k are the points (1, 1), (3, k) and (-1, 4) collinear? ( 2 Marks )
OR
Find the area of the <!--[if !vml]-->
<!--[endif]-->
( 2 Marks )
Q 13)In figure 4, OP is equal to diameter of the circle. Prove thatABP is an equilateral
triangle.
( 2 Marks )
Q 14)If one zeros of polynomial <!--[if !vml]-->
reciprocal of the other, find the value of a. ( 2 Marks )
Q 15)Without using trigonometric tables, evaluate the following :
<!--[endif]-->is
( 2 Marks )
Q 16)Prove that
( 3 Marks )
OR
Prove that
( 3 Marks )
Q 17)Solve for x and y :
( 3 Marks )
OR
Solve for x and y :
37x+43y=123
43x+37y=117
( 3 Marks )
Q 18)Use Euclid’s Division Lemma to show that the square of any positive integer is
either of the form 3m or 3m+1 for some integer m. ( 3 Marks )
Q 19)The sum of 4th and 8th terms of an A.P is 24 and the sum of 6th and 10th terms
is 44. Find the first three terms of the A.P. ( 3 Marks )
Q 20)Prove that <!--[if !vml]-->
<!--[endif]-->is an irrational number. ( 3 Marks )
Q 21)D and E are the points on the sides CA and CB respectively of <!--[if !vml]-->
<!--[endif]-->ABC right-angled at C. Prove that <!--[if !vml]->
<!--[endif]--><!--[if gte mso 9]--> ( 3 Marks )
OR
In the given figure , <!--[if !vml]--
>
<!--[endif]-->
<!--[if !vml]-->
( 3 Marks )
Q 22)Draw a <!--[if !vml]--> <!--[endif]-->ABC with side BC= 6 cm and AB = 5 cm
and angle ABC = 60 degree. Construct a <!--[if !vml]--> <!--[endif]-->AB’C’ are <!-[if !vml]--> <!--[endif]-->of the corresponding sides of <!--[if !vml]-->
>ABC.
<!--[endif]--
<!--[endif]-->
( 3 Marks )
Q 23)In Figure 6. ABC is a right angled triangle right-angled at A. Semicircle
are drawn on AB,AC and BC as diameters. Find the area of the shaded
region.
( 3 Marks )
Q 24)The coordinates of A and B are (1,2) and (2,3) respectively. If P lies on AB, find
the coordinates of P such that <!--[if !vml]-->
9]--> ( 3 Marks )
<!--[endif]--><!--[if gte mso
Q 25)If the point P(x,y) is equidistant from the point A(3,6) and B(-3,4), prove that
3x+y-5=0 ( 3 Marks )
Q 26)A tent consists of a frustum of a cone, surmounted by a cone. If the diameters
of the upper and lower circular ends of the frustum be 14 m and 26 m respectively,
the height of the frustum be 8 m and the slant height of the surmounted conical
portion be 12 m, find the area of canvas required to make the tent. ( Assume that
the radii of the upper circular end of the frustum and the base of surmounted conical
portion are equal) ( 6 Marks )
Q 27)The angle of elevation of a jet fighter from a point A on the ground is 60
degree. After a flight of 10 sec. the angle of elevation changes to 30 degree. If the
jet is flying at a speed of 432 km./hr , find the constant height at which the jet is
flying. ( 6 Marks )
Q 28)Find the mean, mode and median of the following data :
Classes
Frequency
0-10
3
10-20
8
20-30
10
30-40
15
40-50
7
50-60
4
60-70
3
( 6 Marks )
Q 29)Prove that the area of the ratio of two similar triangle is equal to the ratio of
the square on their corresponding sides.
Using the above, do the following :
The diagonal of the Trapezium ABCD, with AB|| DC intersect each other at the point
O if AB = 2CD, find the ratio of the area of triangle AOB to the area of triangle
COD. ( 6 Marks )
OR
Prove that the length of the tangent drawn from an external point to a circle are
equal.
Using the above , do the following
In fig. TP and TQ are tangent from T to the circle with center O and R is any point on
the circle, if AB is a tangent to the circle at R prove that.
TA+AR=TB+BR
<!--[if !vml]-->
<!--[endif]-->
( 6 Marks )
Q 30)A motor boat whose speed is 18 km/hr in still water takes 1 hr more to go 24
km upstream than to return downstream to the same spot . Find the speed of the
stream. ( 6 Marks )
OR
Two water tapes together can fill a tank in <!--[if !vml]-->
<!--[endif]->hours. The tap of larger diameter takes 10 hours less
than the smaller one to fill the tank separately. Find the time in which each tap can
separately fill the tank. ( 6 Marks )