CBSE Board Class 11 Math Sample Papers 2008

SAMPLE PAPER – 2008
CLASS - XI
SUBJECT - MATHEMATICS

SECOND ASSESSMENT [2007-2008]
Time allowed: 3 hrs                     M.Marks:100

           General Instructions:
      
1.All questions are compulsory.
2.The question paper consists of 29 questions divided into three sections A, B and C.
3.Section A contains 10 questions of 1 mark each, Section B is of 12 questions of 4 marks each and Section C is of 7 questions of 6 marks each.
4.There is no overall choice. However, internal choice has been provided in four questions of four marks and two questions of six marks each.
5.In question on construction, the drawing should be neat and exactly as per the given measurements.
6.Use of calculators is not permitted. However you may ask for mathematical tables.

SECTION – A

1.Write the set in the set builder form.

2.A relation R is defined on the set of integer as R =find R.

3.Let f(x)= and g(x)=x-1 be two functions defined in the domain R. find
a)fg(x) b)

4.In a circle of diameter 60cm, the length of a chord is 30cm.find the length of minor arc of the chord.

5.Find the multiplicative inverse of 2-3i

6.Evaluate

7.Find the positive integer n, so that

8.Given P(A)= and P(B)=.Find P(A or B).If A and B are mutually exclusive  events.

9.Consider the experiment in which a coin is tossed repeatedly until a head comes up. Describe the sample space.

10.Write the contra positive of the statement, “If the diagonals of quadrilateral bisect each other, then it is a parallelogram”.

SECTION – B

11.Let f=be a function from R into R. Determine the range of f.

12.If sinx=find the value of

13.Prove that cos2xcos

14.Prove by mathematical induction
      
15.Convert the complex number  into polar form.

OR
            Solve x2-(3 

16.If P(11,r)=P(12,r-1),find r

OR
 
In how many distinct permutations of the letters in MISSISSIPPI do the four I’s not come together.


17.A group consists of 4 girls and 7 boys. in how many ways can a team of 5 member be selected if the team has
a)no girl
b)at least one boy and one girl
c)at least three girls

18.Find the sum to n terms of the series: 5+11+19+29+41……………………

19.The sum of two number is 6 times their geometric means, show that numbers are in the ratio (3+2

20.Find the coordinates of point on y –axis which are at a distance of 5 from the point  P(3,-2,5)

21.If y= then prove that cosx
OR
Compute the derivative of cotx, with respect to x from first principle.


22.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 neither NCC nor NSS
c)the student has opted NSS but not NCC
OR
A and B are two events such that P(A)=0.25,P(B)=0.50 and P(A


SECTION – C

23.In a survey of 100 persons it was found that 28 read magazine A,30 read magazine B,42 read magazine C,8 read magazines A and B,10 read magazines A and C,5 read magazines B and C and 3 read all three magazines. Find:
a)How many read none of three magazines?
b)How many read magazine C only?

24.Solve the following system of inequalities graphically
x+2

25.If the third, fourth and fifth  terms in the binomial expansion (x+a)n are 84,280 and 560 respectively, find x, a and n

26.Find the image of the point (3,8) with respect to the line x+3y=7 assuming the line to be a plane mirror.

27.Show that the points (5,5),(6,4),(-2,4) and (7,1) all lie on a circle, and find its equation, centre and radius.
OR
Find the eccentricity, coordinates of foci, coordinates of vertex, coordinates of centre, length of latusrectum of the following ellipse. 25x2+16y2=400

28.Calculate mean, Variance and Standard deviation for the following distribution