Questions Paper (2014 - 15) Half Yearly CBSE Class XI Mathematics

GENERAL INSTRUCTIONS:

All questions are compulsory.

٠ The question paper consists of 26 questions divided into 3 section A, B and C. Section A comprises of 6 questions of 1 mark each, Section-B comprises of 13 questions of 4 marks each and section-c comprises of 7 questions of 6 marks each.

٠ There is no overall choice, however 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 calculators is not permitted.

(SECTION-A)

1. If <math>U = \{1,2,3,4,5,6,7,8,9\}</math>, <math>A = \{1,2,3,4\}</math>, <math>B = \{2,4,6,8\}</math>. Find (A-B).
2. If set A has 2 elements and set B has 3 elements, then how many relations from set A to Set B can be formed?
3. If <math>\sqrt{3}</math> cosec x = -2, find x.

Solve the following equation.

<math>X^2 + 3x + 9 = 0</math>

1. If <math>x \in N</math>, find the smallest value of x which satisfies the inequation.

<math>2x + \frac{5}{3} \ge \frac{5x}{3} + 1</math>

1. Find the equation of the line, which makes intercepts -3 and 2 on the x- and y- axes respectively.

SECTION-B

1/4

1. If <math>P(A) = P(B)</math> show that <math>A=B</math>

OR

Let A and B be sets; if <math>A \cap X = B \cap X = \emptyset</math> and <math>A \cup X = B \cup X</math> for some set X. show that <math>A = B</math>.

1. Find the domain and range of the function <math>f(x) = 1 - |x - 3|</math>
2. Let A = <math>\{1,2,3,4,5,6,7,8,9,10\}</math> a relation R from set A to A be define by R = <math>\{(x,y): y=x+5\}</math>
3. Write R in roster form
4. Find the domain of R.
5. Find the range of R
6. Depict R using an arrow diagram.
7. Prove that

<math>(\cos x + \cos y)^2 + (\sin x - \sin y)^2 = 4\cos^2\left(\frac{x+y}{2}\right)</math> OR For any ΔABC, prove that

-B COS 0+0 C Sin

1. Find Sini <math>\frac{x}{2}</math>, if tan <math>x = \frac{4}{3}</math> and x lies in quadrant IV.
2. Find the general solution for the equation <math>\sin 2x - \sin 4x + \sin 6x = 0</math>
3. For all <math>n \ge 1</math>, prove the following by using the principle of mathematical induction

<math>\frac{1}{1.2} + \frac{1}{2.3} + \frac{1}{3.4} + \dots + \frac{1}{n(n+1)} = \frac{n}{n+1}</math> 2/4