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MODEL TEST PAPER No. 1HALF YEARLY EXAM 2008-09

CLASS XI (MATHS)Time : 3 hrs. M.M. 100

General Instructions :

1. All questions are compulsory.2. The question paper consists of 29 questions divided into three sections A,

B and C. Section A comprises of 10 questions of one mark each, SectionB comprises of 12 questions of four marks each and Section Comprisesof 07 questions of six marks each.

3. All questions in Section A are to be answered in one word, one sentence

or as per the exact requirement of the question.4. There is no overall choice. However, interval choice has been provided in

04 questions of four marks each and 02 questions of six marks each. Youhave to attempt only one of the alternatives in all such questions.

5. Use of calculations is not permitted. You may ask for logarithmic tables, ifrequired.

SECTION A

Q.1 Find the power set of { }cba ,,

Q.2 For any non empty set A & B show that (A-B) UB = AUB

Q.3 If ( ){ }NyyyxyxR

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Q.8 If310 cc

nn = find n & also2c

n

Q.9 How many terms of the sequence 2,8, 16........... must be taken to make

the sum 2186?

Q.10 Reduce the equation of line 2x-3y+4=0 to slope intercept form. Find its Y

intercept & slope.

SECTION B

Q.11 Out of 120 students who secured Ist class marks in Maths or in English,

75 students obtained Ist class in Maths and 15 in English. How many got

Ist class marks in English only?

Q.12 Find domain and range of

21)( xxf = from RR

or

If the function f : RR is defined by

>

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Q.15 Prove that 224

tan4

tan Sec=

+

+

Q.16 Using principle of mathematical induction prove that

12 + 32 + 52 + ...........+ (2n-1)2 = Nnnnn

+

3

)12()12(

Q.17 Prove that 2.7n + 3.5n 5 is divisible by 24 NnV

Q.18 Prove that there is no term involving x5 in the expansion of

7

2

3 5

+x

x

Q.19 The sum of first p, q, r terms of an AP are a,b,c respectively show that

0)()()( =++ qpr

cpr

q

brq

p

a

Q.20 How many different words can be formed with the letter of the word

`BHARAT? How many of them.

i) will not have B, H together?

ii) will begin with B and end with T?

Q.21 In a school there are 15 teachers (including physical education teacher)

and 5 captains of different games. The Principal wants to form a game

committee consisting of physical education teacher, 2 other teachers and

2 captains. In how many ways can he do it?

Q.22 Find the equation of line through the inter-section of lines 3x+4y-7=0 and

x-y+z=0 and which is parallel to the line 5x-y+11=0

or

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Find the equation of the line which passes through the intersection of the

lines 3x-2y-2=0 and 2x-y-1=0 and which is at a distance of 2 units form

the point (1,0).

SECTION C

Q.23 There are 200 individuals with a skin disorder 120 had been exposed to

chemical A, 50 to chemical B and 30 to both chemicals A & B find the

number of individuals exposed to

i) chemical A but not chemical B

ii) chemical B but not chemical A

iii) chemical A or chemical B

Q.24 Prove that the

Sin10 Sin50 Sin60 Sin70 =16

3or

28

78

58

38

2222=+++ CosCosCosCos

Q.25 Let Z1 and Z2 be the two complex numbers such that

|Z1+Z2| = |Z1-Z2| prove that arg (Z1) arg(Z2) = /2

Q.26 Solve the system of equation graphically

0,0,3,22 + yxyxyx

Q.27 Find n, if the ratio of the fifth term from beginning to the fifth term

from the end in the expansion ofn

+

4

4

3

12 is 1:6

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Q.28 Find the sum to n terms of the series 0.5 + 0.55 + 0.555+.........to n

terms

Q.29 If p is the length of the perpendicular segment from the origin on the

line whose intercepts on the axes are a & b, show that.

222

111

bap+= or

Find the equation of the lines which passes through the point (-3,2)

make an angle of 45 with the line 3x-4y+2=0

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