CBSE Board Class 11 Math Sample Papers 2011

Sample Paper – 2011
Class – XI
Subject – Mathematics
Time: 3Hrs.                        Max. Marks: 100

General Instructions: (The question paper has two printed pages divided in 29 questions as under)

1.All the questions are compulsory.

2.The question paper has been divided in 3 sections A, B and C.
3.Section A contains 10 questions of 1 mark each.
4.Section B contains 12 questions of 4 marks each.
5.Section C contains 7 questions of 6 marks each.
6.There is no overall choice however internal choice has been provided in section B & C.

Use of calculators is not permitted.

Section – A

1.Write the set A= {1, 4, 9, 16…} in set builder form.

2.If (x+1, y -2) = (3, 1) find the value of x and y.

3.Find the value of tan

4.Convert the complex number in polar form.

5.Find the value of n if   

6.Find the sum of ‘n’ terms of the series: 

7.Find the equation of the line through (-2, 3) with slope  - 4. 

8.Write the converse of the following statement, “If a number n is even, then n2 is even”.

9.Write the contra positive of the statement “If a triangle is equilateral, it is isosceles”.

10.Evaluate    .                  

Section – B

11.For   U= { 1,2,3,4,5,6,7,8,9,10} A={2,4,6,8} B={2,3,5,7,8} verify DeMorgan’s Law     i.e. ( A U B)’ = A’ B’        and         (A B)’ = A’UB’

12.Let f(x) = x2 and g(x) = 2x + 1 be two real functions, find (f+g)(x), (f - g)(x), (f.g)(x) and  

13.Prove that   cotx.cot2x – cot2x.cot3x – cot3x.cotx = 1           

Or            

If tanx = find the value of sin   cosand  tan

14.If (x +iy)3 = u + iv prove that  4 (x2 – y2).

15.In how many of the distinct permutations of the letter MISSISSIPPI do the for  I’s not come together?        Or      P.T.O.      A committee of 7 members has to be formed from 9 boys and 4 girls. In how many ways can this be done, when the committee consists of (i) exactly 3 girls (ii) at least 3 girls (iii) at most 3 girls?

16.Find the term independent of ‘x’ in the expansion of   .

17.The sum of the first three terms of a G.P. is  and their product is – 1. Find the common ratio and the terms.

18.The lines through the points (4, 3) and (h, 1) intersect the line 7x – 9y – 19 = 0 at right angle. Find the value of ‘h’.       Or         Find the coordinates of the foot of the perpendicular from the point (-1, 3) to the line 3x – 4y= 16.

19.Find the equation of the circle passing through the points (4, 1) and (6, 5) whose centre lies on the line        4x + y =16.

20.Using section formula, prove that the three points (4, 6, 10), (2, 4, 6) and (14, 0,-2) are collinear.

21.Compute the derivative of tan x using first principle.

22.A box contains 10 red, 20 blue and 30 green marbles. 5 marbles are drawn from the box. What is the probability that (i) all will be blue (ii) at least one will be green.            

Section – C

23.A college awarded 38 medals on foot-ball, 15 in basket-ball and 20 in cricket. If these medals went to a total of 58 men and only 3 men received medal in all three sports, how many received medals is there in exactly two of the three sports.

24.Use mathematical induction for the series to prove that         1.3 + 3.5 + 5.7 +…..+ (2n – 1)(2n + 1)= n.             Or          12 + 32 + 52 + ……+(2n -1)2 =

25.Solve the following  system of inequalities  graphically:  x + 2y, x + y

26.The coefficient of the (r – 1)th, rth and ( r + 1)th terms in the expansion of (x + 1)n are in the ration 1:3:5. Find ‘n’ and ‘r’.

27.Find the coordinates of the foci, the vertices, the length of major ,minor axis, the eccentricity and the length of latus rectum for the ellipse 36x2 + 4y2 = 144.  Or         Find the equation of the hyperbola whose foci is ( 0,  passing through the point (2,3).

28.The ratio of the sums of m and n terms of an AP is m2 : n2. Show that the ratio of mth and nth term is           
(2m – 1 ): (2n – 1)