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
 Write the set A= {1, 4, 9, 16…} in set builder form.
 If (x+1, y 2) = (3, 1) find the value of x and y.
 Find the value of tan
 Convert the complex number in polar form.
 Find the value of n if
 Find the sum of ‘n’ terms of the series:
 Find the equation of the line through (2, 3) with slope – 4.
 Write the converse of the following statement, “If a number n is even, then n^{2} is even”.
 Write the contra positive of the statement “If a triangle is equilateral, it is isosceles”.
 Evaluate . Section – B
 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’
 Let f(x) = x^{2} and g(x) = 2x + 1 be two real functions, find (f+g)(x), (f – g)(x), (f.g)(x) and
 Prove that cot2x – cot2x.cot3x – cot3x.cotx = 1 Or
 If tanx = find the value of sin cosand tan
 If (x +iy)^{3} = u + iv prove that 4 (x^{2} – y^{2}).
 In how many of the distinct permutations of the letter MISSISSIPPI do the for I’s not come together? Or
 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?
 Find the term independent of ‘x’ in the expansion of .
 The sum of the first three terms of a G.P. is and their product is – 1. Find the common ratio and the terms.
 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.
 Find the equation of the circle passing through the points (4, 1) and (6, 5) whose centre lies on the line 4x + y =16.
 Using section formula, prove that the three points (4, 6, 10), (2, 4, 6) and (14, 0,2) are collinear.
 Compute the derivative of tan x using first principle.
 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
 A college awarded 38 medals on football, 15 in basketball 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.
 Use mathematical induction for the series to prove that 3 + 3.5 + 5.7 +…..+ (2n – 1)(2n + 1)= n. Or 1^{2} + 3^{2} + 5^{2} + ……+(2n 1)^{2} =
 Solve the following system of inequalities graphically: x + 2y, x + y
 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’.
 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 36x^{2} + 4y^{2} = 144. Or Find the equation of the hyperbola whose foci is ( 0, passing through the point (2,3).
 The ratio of the sums of m and n terms of an AP is m^{2 }: n^{2}. Show that the ratio of m^{th }and n^{th} term is (2m – 1 ): (2n – 1)
 Find the mean and the standard deviation using the short cut method.
X  60  61  62  63  64  65  66  67  68 
frequency  2  1  12  29  25  12  10  4  5 
Prepared by:
Name Chetan Jain
Email [email protected]
Phone No. 9929160320