Question Paper (2014-2015) set 2 CBSE Class XI Mathematics

General Instruction:

٠ All the questions are compulsory.

۰ The Question Paper consists of 26 Questions divided into three sections A, B and C

٠ Section-A comprises of 6 questions of one mark each.

٠ Section-B consists of 13 questions of four marks each.

٠ Section-C comprises of 7 questions of Six marks each.

٠ 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.

use of calculator is not permitted.

SECTION

1. If <math>X = \{a, b, c, d\}</math> and <math>Y = \{f, b, d, g\}</math>. find find X - Y.
2. Solve <math>3x - 7 > 5x - 1</math>.
3. Find the centre and radius of the circle: <math>(x + 5)^2 + (y - 3)^2 = 36</math>
4. Write the contrapositive of the statement

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

Write the negation of the statement.

"All triangles are not equilateral triangles".

1. Write the converse of the statement

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

SECTION - B 1/4

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

Write down the domain and range.

1. Prove that

<math>\sin^2 6x - \sin^2 4x = \sin 2x \sin^{10}x</math> OR <math>\sin 2x + 2\sin 4x + \sin 6x = 4\cos^2 x \sin 4x</math>

1. Find the general solution of the equation <math>sec^22x = 1 - tan2x</math>
2. Prove by using Principal of Mathematical Induction for all <math>n \in N</math>

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

OR Prove by using Principle of Mathematical induction for all <math>n \in \mathcal{N}</math> -8n - 9 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 If the different permutations of all the letters of word; EXAMINATION' are listed as in a dictionary, how many words are there in this list before the first word starting with E?

1. If the first and the nth terms of a G.P. are 'a' and 'b', respectively, and if P is the product of the first n terms, prove that <math>p^2 = (ab)^n</math>
2. Find the equation of the line passing through the mid-point of (-2, 4), (-4, 6) and perpendicular to the line through the point (2, 5) and (-3, 6).
3. Find the coordinates of the focus, axis of the parabola, the equation of the directrix and

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