Session Ending Examination 2015-2016 Set-1 Class XI (Mathematics)

Time: 3 Hrs M.M: 100

General Instructions:

1. All the questions are compulsory.
2. The Question Paper consists of 26 Questions divided into three sections A, B and C
3. Section-A comprises of 6 questions of one mark each.
4. Section-B consists of 13 questions of four marks each.
5. Section-C comprises of 7 questions of Six marks each.
6. There is no overall choice. However, an internal choice has been provided in 4 questions of four marks each and 2 questions of six marks each. You have to attempt only one of the alternatives in all such questions.
7. Use of calculator, is not permitted.

Section

1. If R is a relation from set A having 3 elements to a set B having 2 elements, then find the number of relations from A to B.
2. Find the value of <math>(1+i)(1+i^2)(1+i^3)(1+i^4)</math>.
3. Write the converse of the following statement 'If a number n is even, then <math>n^2</math> is even'.

Express the following statement by appropriate symbol 'She is rich and beautiful.'

1. Find the centre and radius of the circle <math>2(x+1)^2 + 2y^2 = 25</math>.
2. Write the negation of the following statement 'Every natural number is an integer'.

Section B

1. If R is a relation in N, defined as R = <math>\{(x, y) \in N \times N : x + 2y = 39\}</math>. Then, find the domain and range of R.

0r If A= {1, 2, 3, 4},B = {0, 7} and C = {4}, then verify that <math>A \times (B \cup C) = (A \times B) \cup (A \times C)</math>. 1/4

1. Prove that: <math display="block">\frac{\sin(B-C)}{\cos B \cos C} + \frac{\sin(C-A)}{\cos C \cos A} + \frac{\sin(A-B)}{\cos A \cos B} = 0</math>
2. Prove that: <math display="block">\frac{\sin 5x - 2\sin 3x + \sin x}{\cos 5x - \cos x} = \tan x</math>

Find the square roots of 9 + 40i.

1. A milk of 80% concentration is diluted at home by the seller by adding some water to it,

so that milk concentration is reduced between 65% to 70%. If 640 L of milk of 80% concentration is available, then how much water has been added? Which value system, the seller is lacking?

1. How many words can be formed from the letters of the word 'DAUGHTER', so that vowels are always together?

or

In an examination, a question paper consists of 12 questions divided into two parts, i.e., Part I and Part II, containing 5 and 7 questions, respectively. A student is required to attempt 8 questions in all, selecting atleast 3 from each part. In how many ways, can a student select the questions?

1. Find the general solution of <math>\sec^2 2x = 1 - \tan 2x</math>.
2. Find the equation of the straight line which has Y-intercept equal to <math>\frac{4}{3}</math> and is perpendicular to <math>3x-4y+11 = 0</math>.
3. An equilateral triangle is inscribed in a parabola <math>y^2 = 4\alpha x</math>, whose vertex is at the vertex of the parabola. Find the length of its side.

Or Find the equation of circle of radius 5, whose centre lies on X-axis and passes through the point (2,3).

16. Using section formula, show that the points A (2, -3, 4), B (-1, 2,1) and C <math>\begin{pmatrix} 0, \frac{1}{3}, 2 \end{pmatrix}</math> are collinear.

Calculate the mean deviation from the median for the following distribution.

<math>X_i</math> 10 15 20 25 30 40 35 45 2/4