 # - Chinmaya Vidyalaya

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CHINMAYA VIDYALAYA / B S CITY
(CBSE NEW GENERATION SCHOOL)
ANNUAL MODEL QUESTION PAPER -2014-2015
CLASS : XI
F.M. - 100
SUBJECT : MATHEMATICS
TIME : 3Hrs
General Instructions
a) Section ‘A’ contains 6 questions carry 1 mark each.
b) Section ‘B’ contain 13 question carry 4 marks each.
c) Section ‘C’ contain 7 question carry 6 marks each.
SECTION-A
1. If y  (1  TanA)(1  TanB), Where AB   4 , Find (1  y)1 y
2. If (a  ib)5    i , then (b  ai)8      
x
it (1  x) tan
3. Find x 
1
2
4. If two coins are tossed once, find the probability of getting at most two heads.
5. By using counter-example, show that the following statement is not true.
P: : The equation x2 – 1 = 0 does not have a root lying between 0 and 2.
6. . Write the negation of the statement “All politician are corrupt.
SECTION-B
7. A relation R is defined on the set z of integers as ( x, y)  R  x2  y 2  25 . Find
8.
(i) R (ii) R-1 (iii) domain of R (iv) Range of R-1
Find the domain of the function
t ( x) 
1
 x2
log10 (1  x)
OR, Draw the graph of the functions
 x2 ,
x0

f ( x )   x, 0  x  1
1 , 1 x  
 x
a b
a cos 
tan 0 2, then prove that cos  
ab
a  b cos 
10. Solve : tan   tan 2  tan 3  0 OR Solve: tan   tan(   3 )  tan(  2  3 )  3.
i 1
11. Write the complex number
in polor form.

cos 3  Sin  3
9. If tan 0 2 
12. Solve : (2  i) x2  (5  i) x  2(1  i)  0
13. Prove by principle of mathematical induction : 11n2  122n1 is divisible by 133.
14. Let S be the sum, P the product and R the sum of reciprocals of n terms of a GP. Prove that
S
P 2    OR P2RN=Sn
R
OR
If a,b,c be the pth,qth and rth terms of both AP and also of GP, prove that
abc  bca  cab  1
15. Find the number of arrantgments of the letters of the word ‘INDEPENDENCE’. In how
many of these arrangements.
ii) Do the vowels never occur together.
iii) Do the words being with I and end with P ?
16.
Prove that the first order equation in x and y always represents a straight line.
17. Find the equation of a circle which passes through the point (2,0) and whose centre
is the limit point of intersection of the lines 3x  5 y  1 and (2  c) x  5i 2 y  1 c  1 .
Find the difference co-efficient of y  x tan x by first principle.
18.
OR
Find the d.c. of y  tan x by first principle.
19. Two cards are drawn at random from a well-shutled pack of 52 cards. What is the
probability that either both are red or both are Jacks ?
PART-C
20.
(i) For any three sets A, B and C, prove that
A  ( B  C )  ( A  B)  ( A  C )
(ii) Draw appropriate venn-diagrams for
(a) A ' ( B  C )
(b) A  ( B  C )
21. If A+B+C = 0, prove that cos2 A  Cos 2 B  Cos 2C  H 2 cos A cos BCosC
22.
Solve the following an equation by graphical method :
3x  y  6  0,4 x  9 y  36  0,4 x  3 y  12, x  3 y  6, x  0, y  0.
23.
Find the sum of the first n terms of the series
3+7+13+21+31 + - - - - - 24.
Find the centre, lengths of major and minor areas, co-ordinaters of vertices,
eccentricity, co-ordinates of foci and length of latus rectuem of the ellipse
25x2  9 y 2  150 x  90 y  225  0
OR
Find the standard equation of the hyperbola.
25.
If a,b,c and d, in nay binomial expansion be the four consecutive terms then prove
b 2  ac 4a
that 2

c  bd 3c
OR,
th
th
th
If r , (r + 1) and (r + 2) terms in the expansion of (1+x)n are in AP, show that
n2  n(ur  1)  ur 2  2  0
26. Calculate the mean deviation about median age for the age distribution of 100 persons
given below
Age
Numbers
16-20
5
21-25
6
26-30
12
31-35
14
---xxx----
36-40
26
41-45
12
46-50
16
51-55
9
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