1. No category


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.
i) Do the words start with P
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