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Army Public School
Annual Examination
Mathematics: Class-XI
Time:3 hrs
M.M.:100
General Instructions
1. All questions are compulsory
2. The question paper consists of 29 questions divided into three sectionsA, B, C. Section A comprises of 10 questions of 1 mark each. Section B
comprises of 12 questions of 4 marks each. Section C comprises of 7
question of 6 marks each.
3. There is no overall choice. However, internal choice has been provided
in 4 questions of 4 marks each and 2 questions of 6 marks each.
4. Use of calculator is not permitted.
SECTION-A
1. Write in set builder form of S={1, 3, 9, 27} .
2. If   1, y     ,  . Find x and y.
3  3 3
3
3. Convert in radian -22o 30’ .
4. Find the principal solution of secx= -2.
5. Find the new coordinates of the point (3, -4) if the origin is shifted to
(1,2) by a translation .
6. What is the 20th term of the sequence defined by
an=(n-1)(2-n)(3+n)
7. If A={-1, 0,{1}} , find n( P(A)) .
8. Three coins are tossed once. Write the probability of getting exactly 2
tails.
x
2
5 1
9. Find the domain of f ( x) 
( x  2)
.
x2  4
10.Find the component statements of the compound statement:
All rational numbers are real and all real numbers are complex.
SECTION-B
11.Find the number of arrangements of the letters of the word
‘INDEPENDENCE’. In how many of these arrangements
i) Do the word start with P.
ii) Do all vowels always occur together.
iii) There are always 4 letters between P and C .
12.The letters of the word ‘SERIES’ are written in all possible orders and
these words are written out as in a dictionary. Find the rank of the word
‘SERIES’ .
13.Find n, if the ratio of the fifth term from the beginning to the fifth term
from the end in the expansion of
1 
4
 2 4 
3

n
is
6:1
14.The sum of two numbers is 6 times their geometric mean, show that
numbers are in the ratio (3+22): (3-22) .
Or
150 workers were engaged to finish a job in a certain number of days.
4 workers dropped out on second day, 4 more workers dropped out
on third day and so on. It took 8 more days to finish the work. Find
the number of days in which the work was completed.
15.Find the equation of the circle passing through the points (4,1) and (6,5)
and whose centre is on the line 4x + y = 16 .
Or
Find the coordinates of the foci, the vertices, the length of major and
minor axes and the eccentricity of the ellipse 9x2 + 4y2=36.
16.Find the coordinates of the points which trisect the line segment joining
the points P(8,3,-4) and Q(2,-5,5).
17.If α and β are different complex numbers with β =1 then find
 
1 
Or
Solve : 3 x2 –2 x+33=0 .
18.In an entrance test that is graded on the basis of two examinations, the
probability of a randomly chosen student passing the first examination is
0.8 and the probability of passing the second examination is 0.7. The
probability of passing atleast one of them is 0.95. What is the probability
of passing both the examinations?
19.Prove that: 2Cos

13
.Cos
9
3
5
 Cos
 Cos
0
13
13
13
20.Prove that: Cos6x=32cos6x-48cos4x+18cos2x-1.
Or
Prove that:
x
9x
5x
Cos2x.Cos  Cos3x.Cos
 Sin5x.Sin
.
2
2
2
21.Prove that (by using PMI)
2.7n+3.5n-5 is divisible by 24, for all nN.
22. The Cartesian product A X A has 9 elements, among which are found
(- 1, 0) and (0, 1). Find set A and remaining elements of set A X A.
SECTION-C
23. Solve the following system of inequalities graphically
x+y≤5,
4x+y≥4,
x+5y≥5,
x≤4,
y≤3.
24. Find the derivative of function sin( x  1) w.r.t. x from the first
principle .
Or
x 2

1
lim  2
 3

2
x 1 x  x
x  3x  2 x 

2
i) Evaluate
ii) Check whether limit of the following function exist or not
x
 , x0
f ( x)   x
0,
x0

(4+2)
25. The sum of three numbers in G.P is 56. If we subtract 1,7,21 from
these numbers in that order, we obtain an arithmetic progression.
Find the numbers.
26. The mean and standard deviation of 20 observations are found to be
10 and 2 respectively. On rechecking it was found that an observation
8 was incorrect. Calculate the correct mean and standard deviation if
the wrong item is replaced by 12.
Or
Find the mean , variance and standard deviation using short-cut
method
x
f
0-30
9
30-60
17
60-90
43
90-120 120-150 150-180
82
81
44
180-210
24
27. F ind the equation of the line through the intersection of 5x-3y=1 and
2x+3y-23=0 and perpendicular to the line 5x-3y-1=0.
28. A market research group conducted a survey of 1000 consumers and
reported that 720 consumers like product A and 450 consumers like
product B. What is the least number that must have liked both
product?
What strategy should be taken by any company so that the consumers
will like their new product (atleast two points).
(4+2)
29. For any triangle ABC, prove that
aSin(B-C)+bSin(C-A)+cSin(A-B)=0