Session Ending Examination 2014-2015 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 - A

1. If <math>X = \{a, b, c, d\}</math> and <math>Y = \{f, b, d, g\}</math>. find X - Y.

1. Solve <math>3x - > 5x - 1</math>.

3. Fine the centre and radius of the circle: <math>(x+5)^2 + (y-3)^2 = 36</math>

1. Write the contrapositive of the statement

"If x is a prime number, then x is odd."

Write the negation of the statement. 1/5

"All triangles are not equilateral triangles".

Write the converse of the statement

If a rectangle 'R' is square, then R is a Rhombus."

SECTION - B

1. Define a relation R on the set N of natural numbers by <math>R=\{(x,y); y=x+5, x \text{ is natural } \}</math> number less than 4, <math>x, y \in N</math> }
2. roster form and
3. an arrow diagram.

Write down the domain and range.

1. Prove that

<math>\sin^2 6x - \sin^2 4x = \sin 2x \sin 10x</math> Or <math display="block">\sin 2x + 2\sin 4x + \sin 6x = 4\cos^2 x \sin 4x</math>

1. Find the general solution of the equation <math>\sec^2 2x = 1 - \tan 2x</math>
2. Prove by using Principal of Mathematical Induction for all <math>n \in N</math>

<math>1.2 + 2.2^2 + 3.2^3 + \dots + n.2^n = (n-1)2^{n-1} + 2</math>

OR Prove by using Principle of Mathematical induction for all <math>n \in \mathbb{N}</math> <math>3^{2n-2} - 8n - 9</math> is divisible by 8.

1. In how many ways can a student choose a program of 5 courses. If 9 courses are

available and 2 specific courses are compulsory for every student? OR 2/5