CBSE [ Delhi ]_X_Mathematics_2009_Set III
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Q1
In figure, CP and CQ are tangents to a circle with centre O. ARB is another tangent touching the circle at R. If CP = 11 cm, and BC = 7 cm, then find the length of BR.
Marks:1Answer:
Given, CP and CQ are tangents from point C.
Therefore,
CP = CQ = 11 cm
Also,
BQ = BR
BQ = CQ – BC
= (117) cm
= 4 cm
BR = 4 cm. 
Q2
For what value of p, are 2p – 1, 7 and 3p three consecutive terms of an A.P. ?
Marks:1Answer:
Given, 2p – 1, 7 and 3p are in A.P, then
7  (2p  1) = 3p  7
7  2p + 1 = 3p  7
5p = 8 + 7
p = 3 
Q3
The decimal expansion of the rational number will terminate after how many places of decimals?
Marks:1Answer:

Q4
In the given figure, M = N = 46°. Express x in terms of a, b and c where a, b and c are lengths of LM, MN and NK respectively.
Marks:1Answer:

Q5Marks:1
Answer:

Q6
Find the value of a so that point (3, a) lies on the line represented by 2x  3y = 5.
Marks:1Answer:
Since Point (3, a) lies on the line 2x – 3y = 5, so it will satisfy the equation of line.
Hence, 2(3) – 3(a) = 5
Or, 6 – 3a = 5
Or, 3a = 1
a = 1/3 
Q7
A cylinder and a cone are of same base radius and of same height. Find the ratio of the volume of cylinder to that of the cone.
Marks:1Answer:
Given,
Radius of cylinder = Radius of cone = r (say)
Height of cylinder = Height of cone = h (say)
Volume of cylinder / Volume of cone = r²h/(1/3)r²h = 1/(1/3) = 3 : 1 
Q8
Find the distance between the points .
Marks:1Answer:

Q9
Write the median class of the following distribution:
Classes Frequency
0 – 10 4
10 – 20 4
20 – 30 8
30 – 40 10
40 – 50 12
50 – 60 8
60 – 70 4Marks:1Answer:
Classes
Frequency
Cumulative frequency
0 – 10
4
4
10 – 20
4
8
20 – 30
8
16
30 – 40
10
26
40 – 50
12
38
50 – 60
8
46
60 – 70
4
50
Total number of observations (n) = 50.
So, n/2 = 25.
The cumulative frequency 26 is just greater than n/2 = 25.
So, 30 – 40 is the median class. 
Q10
For what value of p, (4) is a zero of the polynomial x^{2} – 2x – (7p + 3) ?
Marks:1Answer: