The document is the instructions for a mathematics exam consisting of 3 sections (A, B, C) worth a total of 100 marks. Section A has 6 single-mark questions. Section B has 13 four-mark questions. Section C has 7 six-mark questions. Calculators are not permitted. Questions cover topics of relations, geometry, complex numbers, probability, and series.

1. KENDRIYA VIDYALAYA SANGATHAN
SESSION ENDING EXAMINATION CLASS XI
SUBJECT – MATHEMATICS
MAXIMUM TIME ALLOWED: 3 HRS MAXIMUM MARKS: 100
General instructions:
a) All questions are compulsory.
b) The question paper consists of 26 questions divided into three sections
A,B,C. Sections A comprises of 6 questions of one mark each, section B
comprises of 13 questions of four mark each and section C comprises of
7questions of six mark each.
c) All questions in section A are to be answered in one word, one sentence or as
per the exact requirement of the question.
d) There is no overall choice. However internal choice has been provided in four
questions of four marks each and two questions of six mark each. You have
to attempt only one of the alternatives in all such questions.
e) Use of calculators is not permitted. You may ask for logarithm tables, if
required.
SECTION – A
1. Let A = {1, 2}. Find the number of relations on A. 1
2. How many points on a circle can be joined to get 10 chords? 1
3. Find the length of the latus rectum of the parabola 1
4. Write down the contra positive of the statement: 1
If a number is divisible by 9, then it is divisible by 3.
5. Write the converse of the statement: 1
If two lines are parallel, then they do not intersect in the same plane.

2. 6. State whither the ‘OR’ used in the statement is ‘exclusive’ or ‘inclusive’
“Sun rises or Moon sets”. 1
SECTION – B
7. If U={ 1,2,3,4,5,6,7}, A ={2,4,6} and B={2,3,5}. Verify that
i) ( )
ii) 4
8. Let ( ) be a function from R to R. Determine the range of 4
9. In any Prove that : ( ) where a,b,c are sides
opposite to angles A, B and C respectively. 4
OR
Two ships leave a port at the same time. One goes 24 km per hour in the
direction and other travels 32 km per hour in the directions . Find
the distances between the ships at the end of 3 hours.
10. Prove that . 4
11. Convert the complex number
√
into polar form. 4
OR
Find the square root of the complex number
12. In how many ways a discipline committee of 6 members can be selected from
a group of 4 girls and 7 boys if the committee has 2 girls?
In your view how many girls and boys should be taken in the committee? 4

3. 13. The sum of first three terms of a G.P is and their product is -1. Find the
common ratio and the terms. 4
14. Find the image of the point (3, 8) with respect to the line assuming
the line to be a plane mirror. 4
OR
Find the direction in which a straight line must be drawn through the point (-1, 2)
so that its point of intersection with the line x + y = 4 may be at a distance of
3 units from this point.
15. An arch is in the form of a semi-ellipse. It is 8m wide and 2m high at the
centre. Find the height of the arch at a point 1.5 m from one end. 4
OR
Find the equation of the circle with radius 5 whose centre lies on x-axis and
passes through the point (2, 3).
16. Using section formula, prove that the three points (-4, 6, 10) , (2,4, 6) and
(14, 0,-2) are collinear 4
17. Find the mean and variance for the following frequency distribution:
Classes 25-35 35-45 45-55 55-65 65-75
Frequencies 21 20 16 25 18
4
18. A box contains 6 red marbles, 5 blue marbles and 4 green marbles.

4. 3 marbles are drawn from the box, what is the probability that
a) all will be blue?
b) at least one will be green? 4
19. In a class of 60 students, 30 opted for NCC, 32 opted for NSS and 24
opted for both NCC and NSS. If one of these students is selected at
random ,find the probability that
a) The student opted for NCC or NSS
b) The student has opted NCC but not NSS
c) What is the importance of opting NCC or NSS? 4
SECTION – C
20. In a survey of 25 students, it was found that 15 had taken mathematics,12
had taken physics and 11 had taken chemistry, 5 had taken mathematics and
chemistry,9 had taken mathematics and physics,4 had taken physics and
chemistry and 3 had taken all the three subjects. Find the number of students
that had taken:
a) at least one of the three subjects.
b) only one of the subjects.
c) none of the three subjects. 6
21. a) Solve: 3

5. b) If 3
22. Using principle of mathematical induction, prove that:
( )( ) ( )
for all 6
23. Solve the following system of linear inequalities graphically:
6
24. The coefficients of three consecutive terms in the expansion of ( ) are
in the ratio 1:7:42. Find n and r. 6
OR
Find n, if the ratio of the fifth term from the beginning to the fifth term from the
end in the expansion of (√
√
) is √
25. Sum the series: 1 + 3 + 6 + 10 + ……..up to n terms. 6
OR
If +…………… +……………
then prove that, +……………
26. a) Evaluate
( )
. 3
b) Differentiate with respect to where 3