Mathematics
QUESTION PAPER

 Time : 3 Hours Maximum Marks : 100

General Instructions :
(i) All the questions are compulsory.
(ii) The question paper consists of 26 questions divided in 3
Sections A, B and C. Section A comprises 6 questions of 1 mark each,
Section B comprises 13 questions of 4 marks each and
Section C comprises 7 questions of 6 marks each.
(iii) All the questions in section A are to be answer in minimum requirement. There will be no fractional marking in any condition in this section.
(iv) There is no overall choice however, internal choice has been provided in 4 questions of section B and in 2 questions of section C. You have to attempt only one of the alternatives in all such questions.
(v) Use of any electronic gazette is not permitted for calculations except log table if required.

SECTION – A

Q.1. Two sets A and B are such that Q.2. Write the value of Q.3. For what values of r, 5Pr = 5Cr?

Q.4. Is the statement p: ‘100 is divisible by 2, 3 and 5’. true?

Q.5. Identify the ‘or’ as inclusive / exclusive:
“To apply for driving license you need a ration card or a passport”

Q.6. Write contra positive statement of :
“If a number n is even than its square is even.”

SECTION - B

Q.7. For set A = {3,6,9,12,15,18,21} and B={4,8,12,16,20} find:
(i) A ∪ B
(ii) A ∩ B
(iii) A- B
(iv) B - A.

Q.8. Let n(A) = 3, n(B) = 2 and {(x,1), (y,2), (z,1)} ⊂ A X B find sets A and B where x, y and z are distinct elements.

Q.9. Show that: Q.10. Prove that 7n – 3n is divisible by 4. Q.11. Prove that 1 + 3 + 5 +…+(2n – 1) = n2 Q.12. Write 1 + i in polar form.

Q.13. Draw the graph of inequalities given below and shade the common solution area: Q.14. Using binomial theorem expand Is there any term which is free from x?

Q.15. If the sum of an infinite G.P. is 15 and that of squares of its terms is 45, find the G.P.

Or Q.16. An equilateral triangle is inscribed in a parabola y2 - 4√3 x whose one vertex is at the vertex of parabola. Find the length of side of the triangle.

Or

Find the equation of a circle, coordinates of end points of whose one of the diameter are (– 1, 3) and (7, – 8).

Q.17. Write the type of triangle made by the vertices (1,2,3) , (2,3,1) and (3,1,2).

Q.18. Or

A particle moves along a path whose equation is given by s = t3 – 3t2 +3t + 5 at any time t seconds. At what time its velocity will be zero?

Q.19. In a lottery, a person chooses six different numbers at random from 1 to 20 and if these six numbers match with the six no’s already fixed by lottery committee, he wins the prize. Write the probability of not winning the prize by him in this game? What are the social impacts of playing such games? How does it affect one’s family life?

SECTION - C

Q.20. In a survey of 60 students, it was found that 25 students were sick of use of internet, 26 students remain busy on facebook with their mobile, and 26 prefer to read extra books. 9 students prefer to surf internet and facebook, 8 students prefer to remain busy with facebook and extra books, 11 students prefer to surf internet and remain busy with extra books and 3 students are engaged in all three activities.
(i) In which activity in your opinion should a student pay more attention?
(ii) How many students surf internet only? Do you think they are wasting their time?
(iii) Suggest time limit for each activity.

Q.21. Find the general solutions of trigonometric equation: 2 sin2 x = 3cosx.

Q.22. IQ of a person is given by formula where M.A. is mental age and C.A. is chronological age of person. If for a group of 12 year children, find the range of their mental age.

Q.23. Find the number of arrangements of the letters from the word ‘REPUBLIC’. How many arrangements start with a vowel? What is the significant of Republic Day in India?

Q.24. Find the image of point (3, 8) in the mirror line whose equation is given by x + 3y = 7.

Or

Find the equation of a line which is mid parallel to lines 3x + 2y + 6 =0 and 9x + 6y = 7.

Q.25. Use first principle to find the derivative of
(i) sin2
(ii) ex

Or

Find the derivative of Q.26. Calculate the standard deviation from the table. 