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MATHEMATICS PAPER 2005.
Time allowed: 3 hours; Maximum Marks: 100
| General Instructions: | |
| 1) | All questions are compulsory. |
| 2) | The question paper consists of 25 questions divided into three sections A, B and C Section A contain 10 (1- 10) questions of 3 marks each. Section B contains 10 questions 10 (11-20) questions of 4 marks each. Section C contains 5 (21-25) questions of 6 marks each. |
| 3) | There is no overall choice. However, an internal choice has been provided in each section. |
| 4) | In question on construction, the drawing should be neat and exactly as per the given measurements. |
| 5) | Use of calculator is not permitted. However, you may ask for Mathematical tables. |
| 6) | Please give the explanation for the answer where applicable. |
11.Solve the following system of equations graphically:
; 
.
Find the points where the lines meet the Y-axis.
12.A two digit number is such that the product
of its digits is 
If 
is
added to the number, the digits interchange their places, find the number.
13.The base radius and height of a right
circular solid cone are 
and 
respectively.
It is melted and recast into spheres of diameter each.
Find the number of spheres so formed.
14.Prove that:
16.Prove that the points 
are
vertices of a right isosceles triangle.
17. The
line joining the points 
and 
is
trisected at the points P and Q. If point P lies on the line
,
find the value of k.
18.If the
mean of the following data is 
find
the value of 
:
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20.A bag contains 
red,
white
and 
black
balls. A ball is drawn at random from the bag. Find the probability that the
drawn ball is:
(i) Red or white (ii) Not black (ii) Neither white nor black.
| Section A | Section B | Section C |
