Sample Paper of Mathematics 2014 for class 11, CBSE. Paper No.1

Sample Paper – 2014
Class – XI
Subject – Mathematics

Time: 3Hrs.                                                                                                                  Max. Marks: 100

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

• All the questions are compulsory.

• The question paper has been divided in 3 sections A, B and C.

• Section A contains 10 questions of 1 mark each.

• Section B contains 12 questions of 4 marks each.

• Section C contains 7 questions of 6 marks each.

• 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                                                                    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 cot2x – cot2x.cot3x – cot3x.cotx = 1                                                                                                                                                                              Or                                                                                   
14.  If tanx = find the value of sin   cosand  tan
15. If (x +iy)³ = u + iv prove that 4 (x² – y²).
16. In how many of the distinct permutations of the letter MISSISSIPPI do the for I’s not come together?                                                                                                   Or                                                                  
17. 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?
18. Find the term independent of ‘x’ in the expansion of .
19. The sum of the first three terms of a G.P. is and their product is – 1. Find the common ratio and the terms.
20. 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                                                                              
21. Find the coordinates of the foot of the perpendicular from the point (-1, 3) to the line 3x – 4y= 16.
22. Find the equation of the circle passing through the points (4, 1) and (6, 5) whose centre lies on the line 4x + y =16.
23. Using section formula, prove that the three points (4, 6, 10), (2, 4, 6) and (14, 0,-2) are collinear.
24. Compute the derivative of tan x using first principle.
25. 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
26. 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.
27. Use mathematical induction for the series to prove that  3 + 3.5 + 5.7 +…..+ (2n – 1)(2n + 1)= n.                                                                                                                                                                                               Or                                                                                                                          1² + 3² + 5² + ……+(2n -1)² =
28. Solve the following system of inequalities  graphically:  x + 2y, x + y
29. The coefficient of the (r – 1)^th, r^th and ( r + 1)^th terms in the expansion of (x + 1)ⁿ are in the ration 1:3:5. Find ‘n’ and ‘r’.
30. 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).
31. The ratio of the sums of m and n terms of an AP is m² : n². Show that the ratio of m^th and n^th term is (2m – 1 ): (2n – 1)
32. Find the mean and the standard deviation using the short cut method.

Prepared by: 

Name  Chetan Jain

Email   jainchetan2004@yahoo.com

Phone No.      9929160320