Session Ending Examination 2015-2016 Set 2 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 5

1. A and B are two sets such that <math>A \subset B</math>. Find the value of <math>A \cup B</math>
2. Find the conjugate of <math>\frac{1}{3+4i}</math>.

Write the contra-positive of the following conditional statement. Tf my grandmother had wheels, then she would be a bus'.

1. Find the length of transverse axis of the hyperbola <math>9x^2 - 16y^2 = 144</math>.

Write the negation of the following statement Australia is a continent'.

1. Check whether the following statement is true or not. 'If x and y are odd integers, then xy is an odd integer'.

Section B

1. If <math>f: R \to R</math> is defined by <math>f(x) = x</math> and <math>g: R \to R</math> is defined by <math>g(x) = |x|</math>. Then, find

1. <math>f + g</math>
2. f - g
3. f.g

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(iv) or In a survey of 400 students in a school, 100 were listed as drinking apple juice, 150 as drinking orange juice and 75 were listed as drinking apple as well as orange juice. Find how many students were drinking neither apple juice nor orange juice?

1. Prove that <math>\cos 2\theta \cos \frac{\theta}{2} - \cos 3\theta \cos \frac{9\theta}{2} = \sin 5\theta \sin \frac{5\theta}{2}</math>

1. The longest side of a triangle is twice the shortest side and the third side is 3 cm longer

than the shortest side. If the perimeter of the triangle is at least 39 cm, then find the minimum length of the longest side.

1. To prove, <math>(\cos x - \cos y)^2 + (\sin x - \sin y)^2 = 4 \sin^2 \frac{x - y}{2}</math>

0r Prove that <math>\cos^3 A \cos 3A + \sin^3 A \sin 3A = \cos^3 2A</math>

1. Find real <math>\theta</math>, such that <math>\frac{3+2i\sin\theta}{1-2i\sin\theta}</math> is purely real.
2. The ratio of the sum of n terms of two AP's is (3n +1): (4n + 3). Find the ratio of their mth terms.
3. Find the mean and standard deviation for the following data using shortcut method.

X 60 61 62 63 64 66 65 67 68

<math>f_i</math> 2 1 12 29 25 10 12 4 S

1. How many words each of 3 vowels and 2 consonants can be formed from the letters of the word INVOLUTE?
2. Find the equation of the ellipse having axes along the coordinate axes and passing through the points (4, 3) and (-1, 4).

<math>\mathbf{Or}</math>

Find the equation of the circle which passes through the centre of the circle

<math>x^2 + y^2 + 8x + 10y - 7 = 0</math> and is concentric with the circle <math>2x^2 + 2y^2 - 8x - 12y - 9 = 0</math>.

1. Find the mean and standard deviation for the following data using shortcut method. Find

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