GGRO-1103

Please check total printed pages before start:- 4 Roll No. : ______

PIL DIDELL BIEM GV

SESSION ENDING EXAMINATION 2014-15 SUBJECT - MATHEMATICS

CLASS - XI

Time: 3:00 Hrs. M.M. 100 MARKS

General Instructions:

tested interest acressed and in the Arrest

1. All questions are compulsory.

1. The question paper consists of 26 questions divided into three sections A, B and C. Section A comprises 6 questions one mark each, Section B comprises 13 questions of four marks each And Section C comprises 7 questions of six marks each.

1. All questions of section A are to be answered in one word o, one sentence or as per exact Requirement of the question.
2. There is no overall choice. However, an internal choice has been provided in four questions of four marks each and two questions of six marks each.
3. Use of calculator is not permitted.

SECTION A

VSHIZ I WA

Question numbers 1 to 6 carry 1mark each.

1. If <math>X=\{a,b,c,d\}</math> and <math>Y=\{f,b,d,g\}</math>, find Y-X.
2. Find multiplicative inverse of - i.

4220

/3. Solve 24x < 100 when x is a natural number.

1. Evaluate 7!-5! .

_5. Find the radius of the circle <math>x^2+y^2-4x-8y-45=0</math>

_6. <math>P(A) = \frac{3}{5}</math>, find P (not A)

XEND TOO IT TOO nod symbosines to any north land date we is

[P.T.O.]

2

ggro-1103

SECTION -B

Question numbers 7 to 19 carry 4 marks each.

1. In a survey of 400 students in a school, 100 were listed as taking apple juice, 150 as taking orange juice and 75 were listed as taking both apple as well as orange juice. Find how many students were taking neither apple juice nor orange juice.

_8. Let A= {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}. Let R be a relation defined on A by <math>R = \{(x, y) : y = 2x \ x, y \in A \}</math> Write R in the Roster form. Also write the domain, co-domain and range of R.

1. Prove that <math>Cot4x(Sin5x + Sin3x) = Cotx(Sin5x - Sin3x)</math>

OR Prove that <math>Cos20^{\circ} Cos40^{\circ} Cos60^{\circ} Cos80^{\circ} = \frac{1}{100}</math>. 16

1. Prove that <math>(\cos x + \cos y)^2 + (\sin x - \sin y)^2 = 4 \cos^2 \left(\frac{x+y}{x-y}\right)^2</math> (2)

OR Solve :- <math>Sin2x - Sin4x + Sin6x = 0</math>

1. Using principal of mathematical induction, Prove that 41ⁿ-14ⁿ is a multiple of 27.

i-1 _12. Convert into polar form <math display="block">z = \frac{1}{\cos\left(\frac{\pi}{3}\right) + i\sin\left(\frac{\pi}{3}\right)}</math> OR Find the square root of complex number -5-12i

_13. Find all pairs of consecutive odd natural numbers, both of which are larger than 10 , such that their sum is less than 40. [P.T.O.]