Question Paper (2016-2017) CBSE Class XI Mathematics

General Instruction:

٠ All sections are compulsory

۰ The question paper of 28 questions divided into four sections A, B, C and D. Section A comprises of 4 questions of one mark each, Section B of 7 questions of two marks each, Section C comprises of 11 questions of three marks each and Section D comprises of 6 questions of four marks each.

٠ There is no overall choice. However, an internal choice has been provided in three questions of three marks each and three questions of four 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>A = \{(x, y) : x^3 + y^2 = 25 \text{ where } x, y \in \mathbb{N} \}</math>, write a set of all possible ordered pairs.
2. Find the value of X-y if <math>X=\{a,b,c,d\}</math> and <math>Y=\{b,d,f,g\}</math>.

Solve 24 x < 100 where x is an integer.</li>

4. If <math>\frac{1}{6!} + \frac{1}{8!} = \frac{1}{9!}</math>, find the value of x.

SECTION B

1. Find the multiplicative inverse of <math>4 - \sqrt{-9}</math>.
2. Prove that <math>tan 15^{\circ} + cot 15^{\circ} = 4</math>.
3. If <math>A = \{1, 2, 3\}, B = \{4, 5, 6\}</math> and verify that <math>A \cup (B \cap C) = (A \cup B) \cap (A \cup C)</math>.
4. Solve <math>\frac{x}{4} > \frac{5x-2}{3}</math> <math>\frac{7x-3}{5}</math> and graph the solution set on the number line.

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1. If <math>{}^{34}C_{r-6} = {}^{34}C_{2r-2}</math>, find r.
2. How many different words can be formed with the letters of the word 'BHARAT'? How many of these begin with B and end with T?
3. Let <math>f\left(x+\frac{1}{x}\right)=x^2+\frac{1}{x^2}</math>, <math>x\neq 0</math> then find the value of f(x).

SECTION C

1. From the adjoining venn diagram, write the value of the following:
2. A'
3. B'
4. (A∩B)'

1. Let X and Y be two sets. <math>X = \{x: x \text{ is a nutural number and } 1 < x \le 6\}</math>, : 16, Y = <math>\{X: x \text{ is } 1\}</math>

natural number and <math>6 < x < 10</math>. Find the value of:

1. X ∩ Y
2. X∪Y
3. Let R be the relation on the set N of natural numbers defined by a + 3b + = 12. Find:
4. R
5. Domain of R
6. Range of R

Here, <math>a,b \in N</math>

1. Find the domain of the real function F given by:

<math display="block">F(x) = \frac{1}{\sqrt{[x]^2 - [x] - 6}}</math> 2/4