Session Ending Examination (2015-2016) Set - 4 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 A

1. If <math>(x - 1, y + 3) = (2, x + 4)</math>, then find the values of x and y.
2. Rephrase the following sentence in conditional form 'Working hard ensures that you will pass the examination'.

How many three digit numbers are divisible by 7?

1. Find the length of latusrectum of the parabola <math>y^2 = -8x</math>.
2. Write the contrapositive of the following statement 'If a triangle is equilateral, then it is isosceles'.

Write the negation of the following statement, 'All Mathematicians are men'.

Section B

1. If f is a real function defined by <math>f(x) = \frac{x-1}{x+1}</math>, then prove that <math>f(2x) = \frac{3f(x)+1}{f(x)+3}</math>.
2. If <math>\tan \theta = \frac{\sin \alpha - \cos \alpha}{1}</math>, then show that <math>\sin \alpha + \cos \alpha = \sqrt{2} \cos \theta</math>.

1/4

1. If <math>\tan x = \frac{3}{4}</math>, <math>\pi < x < \frac{3\pi}{2}</math>, then find the values of <math>\sin \frac{x}{2}</math>, <math>\cos \frac{x}{2}</math> and <math>\tan \frac{x}{2}</math> or Prove that <math>\cot \frac{\pi}{21} = \sqrt{2} + \sqrt{3} + \sqrt{4} + \sqrt{6}</math>
2. If <math>\alpha</math> and <math>\beta</math> are different complex numbers with <math>|\beta|=1</math>, then find <math>\frac{|\beta-\alpha|}{|1-\alpha|\beta|}</math>

1. To pass in a subject, one must obtain an average of 33 out of 100 or higher to pass in the

subject in five examinations. If a student's marks in the four examinations are 28, 31, 40 and 37, then find the minimum marks a student must obtain to pass in the subject.

A student obtained 42 marks in the fifth exam. Do you think student has passed in the subject? What value system does he possess?

1. A group consists of 4 girls and 7 boys. In how many ways can a team of 5 members be selected, if the team has
2. no girl?
3. at least one boy and one girl?

1. Find the equation of a line which passes through the point of intersection of lines 3x + y -

<math>7 = 0</math> and <math>x + 2y + 5 = 0</math> and is perpendicular to the line <math>5x - 2y + 6 = 0</math>. or If P and P' are perpendiculars from the origin on the straight lines whose equations are <math>x\sec\theta + y\csc\theta = a</math> and <math>x\cos\theta - y\sin\theta = a\cos 2\theta</math>, then prove that <math>4P^2 + (P')^2 = a^2</math>

14. Prove that <math>\sin 20^{\circ} \sin 40^{\circ} \sin 60^{\circ} \sin 80^{\circ} = \frac{3}{10^{\circ}}</math>

1. Four students in traditional dresses represent four states of India, standing at the points

represented by O(0, 0, 0), A(a, 0, 0), B(0, b, 0) and C(0, 0, c). Find the place, in terms of coordinates, where a girl representing 'BHARATMATA be placed so that girl is equidistant from the four students. What message does it convey?

1. Find the equation of circle which passes through (3, -2), (-2, 0) and has its centre on the line <math>2x - y = 3</math>.

or

Find the equation of the ellipse whose axes are along the coordinate axes, vertices are 2/4