General Instruction:

٠ All the questions are compulsory.

٠ 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.

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>A = \{1, 2\}</math> and <math>B = \{3, 4\}</math>, then how many subsets will <math>A \times B</math> have?
2. What connective word is used in the following statement 'ABC is an equilateral triangle, if and only if it is equiangular'.
3. Is 310 a term of the sequence 3, 8, 13, ...?
4. What is the eccentricity of the curve 4x3 + y2 = 100?
5. Write the contra-positive of the statement 'If you are born in India, then you are a citizen of India'.
6. Write the component statements of the compound statement If 2 > 3, then I am the king of India.

Section B

1. A relation R is defined from a set <math>A = \{2, 3, 4, 5\}</math> to a set <math>B = \{3, 6, 7, 10\}</math> as follows

<math>(x, y) \in R \iff x</math> divides y.' Express R as a set of ordered pairs and determine the domain 1/4

and range of R. Also, find R-1.

1. Prove that <math display="block">\frac{\sin(B-C)}{\cos B \cos C} + \frac{\sin(C-A)}{\cos C \cos A} + \frac{\sin(A-B)}{\cos A \cos B} = 0</math>
2. Prove that <math display="block">\frac{\cos 2.4 \cos 3.4 - \cos 2.4 \cos 7.4 + \cos .4 \cos 10.4}{\sin 4.4 \sin 3.4 - \sin 2.4 \sin 5.4 + \sin 4.4 \sin 7.4}</math>

0r Prove that <math>\cos^4 \frac{\pi}{8} + \cos^4 \frac{3\pi}{8} + \cos^4 \frac{5\pi}{8} + \cos^4 \frac{7\pi}{8} = \frac{5}{2}</math>

1. If z is a complex number such that <math>|z|</math>, then prove that <math>\left(\frac{z-1}{z+1}\right)</math> is purely imaginary.

1. A man wants to go on a country tour on a cycle to promote Eco-friendly atmosphere. He

wants to tour on a cycle and for that he wants to decorate his cycle with three green pieces of cloth. He has cloth of length 91 cm. He wants second length to be 3 cm longer than the shortest and the third length to be twice as long as the shortest. What are the possible length of the shortest cloth, if third piece is to be at least 5 cm larger than the second? What slogan would you like to give to the mission?

1. Find the equation of the line joining the point (3, 5) to the point of intersection of the lines

<math>4x + y - 1 = 0</math> and <math>7x - 3y - 35 = 0</math>.

0r

Find the equation of straight line parallel to <math>2x + 3y + 11 = 0</math> and the sum of its intercepts on the axes is 15.

1. Solve the equation <math>\cos \theta + \cos 3\theta - 2\cos 2\theta = 0</math>.
2. How many words with or without meaning, each of 2 vowels and 3 consonants can be formed from the letters of the word 'EMPATHY'? Do you agree that empathy is one value which everyone should acquire?
3. Find the equation of a circle whose centre is the point of intersection of the lines 2x - 3y +

2/4