Class – XI Subject – Mathematics
Class – XI
TIME ALLOWED:3 HRS
M.M.:
100
GENERAL INSTRUCTIONS:
Ø
All questions are
compulsory.
Ø
Section A
consists of ten questions of 1 mark each.
Ø
Section B
consists of twelve questions of 4 marks each.
Ø
Section C
consists of seven questions of 6 marks each.
Ø
Use of
calculators is not permitted. However you may ask for logarithimic tables if
required.
Ø
No step marking
for 1 mark questions of Section A.
SECTION A
Question
1: If D,G and R denote
respectively the number of degrees, grades and radians in an angle, then find
the value of D/100 in grades and in radians.
Question
2: Find the value of sin (11/3).
Question
3: Find the value of (1+i) (1+i^{2})
(1+i^{3}) (1+i^{4}).
Question
4: If ^{22}P_{r+1}:
^{20}P_{r+2}=11:52, find the value of r.
Question
5: Find the sum of the
following series.
(a^{2}b^{2}),(ab),(ab/a+b),……..to
n terms.
Question
6: Write down the equation of
a line parallel to yaxis at a distance of 5 units on the left hand side of it.
Question
7: Evaluate: lim
x√xa√a
x→a xa
Question
8: If y=1+ x + x^{2}+
x^{3 }+……..,show that dy = y.
1!
2! 3! dx
Question
9: Sample A has a mean
bursting pressure of 21 kg and S.D. 4.87. Sample B has mean bursting pressure
of 21.81 kg and S.D. 7.07.Which sample has the highest average bursting
pressure? Which has more uniform pressure?
Question10: Three dice are thrown together. Find the probability
of getting a total of at least 6.
SECTION
B
Question
11: If tan θ =√1e tan ,
then find the value of cos in terms of θ
and e.
2 1+e
_
Question
12: Find all nonzero complex
number z satisfying z =iz^{2}.
Question
13: Solve:  x+3  + x
> 1.
x+2
Question
14: How many fiveletter
words can be formed using the letter of the word ‘INEFFECTIVE’?
Question
15: If a_{1,}a_{2},a_{3},a_{4}
be the coefficients of four consecutive terms in the expansion of (1+x)^{n},
then prove that : a_{1 }_{ } + a_{3} = 2 a_{2 }_{ }
_{ } a_{1 }+a_{2 }a_{3} + a_{4 }a_{2} + a_{3}
Question
16: In an increasing G.P.,
the sum of the first and the last term is 66, the product of the second and the
last but one is 128 and the sum of the terms is 126. How many terms are there
in the progression?
Question
17: One side of a square
makes an angle θ with xaxis and one vertex of the square is at the origin.
Prove that the equations of its diagonals are x(sinθ+cosθ)=y(cosθsinθ) and
x(cosθsinθ)
+ y(sinθ+cosθ)=a, where a is the length of the side of the square.
Question
18: Find the equation of a
circle which passes through the point (2,0) and whose centre is the limit of
the point of intersection of the lines 3x+5y=1 and (2+c)x+5c^{2}y=1 as
c→1.
Question
19: If b,c,d be the ordinates
of a vertices of the triangle inscribed in a parabola y^{2}=4ax, then
show that the area of the triangle is 1 (bc) (cd) (db).
8a
Question
20: Evaluate the following
limit:
lim (x+y) sec(x+y) – xsecx
y→0 y
Question
21: Find the derivative
of ^{3}√sin x by first principle.
Question
22: Five persons entered the
lift cabin on the ground floor of an 8floor house. Suppose that each of them
independently and with equal probability can leave the cabin at any floor
beginning with the first. Find out the probability of all five persons leaving
at different doors .
SECTION C
Question
23: In a survey of 25
students, it was found that 15 had taken mathematics, 12 had taken Physics and
11 had taken Chemistry, 5 had taken Mathematics and Chemistry, 9 had taken
Mathematics and Physics, 4 had taken Physics and Chemistry and 3 had taken all
the three subjects. Using the properties of sets find the number of students
that had:
(i)
only Chemistry.
(ii)
only Mathematics.
(iii)
only Physics.
(iv)
Physics and
Chemistry but not Mathematics.
(v)
Mathematics and
Physics but not Chemistry.
(vi)
only one of the
subjects.
Question
24: (i) The sum of n, 2n, 3n
terms of an A.P. are S_{1},S_{2},S_{3} respectively.
Prove
that: S_{3}= 3 ( S_{2} S_{1})
(ii) The midpoints of the sides
of a triangle are (1,5,1) , (0,4,2) and
(2,3,4). Find its
vertices.
Question
25: If sin (θ+) = 1m , then find the value of tan (/4 θ) tan (/4).
cos (θ) 1+m
Question
26: Find the sum of first n
terms of the following series:
(i) 5+11+19+29+41+……. (ii) 5+7+13+31+85+……
Question
27: Suppose that samples of
tyres from two manufactures, A and B, are tested by a prospective buyer for
bursting pressure, with the following results:
Bursting
Pressure in kg

Number
of bags manufactured by manufacturer


A

B


510

2

9

1015

9

11

1520

29

18

2025

54

32

2530

11

27

3035

5

13

Which
set of tyres has the highest average bursting pressure? Which has more uniform
pressure?
Question
28: Find the equation of the
ellipse whose axes are parallel to the coordinare axis having its centre at the
point (2,3) one focus at (3,3) and one vertex at (4,3).
Question
29: (i) Prove that: 2.7^{n} + 3.5^{n}
– 5 is divisible by 24 using P.M.I. for all n € N.
(ii) Find the domain and
range of the function given by: f(x) = 1 x3.
Read more topics.
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Read more topics.
Seriesformulas
Thebinomialtheorem
Analytictrigonometrydoubleanglehalf angle
solvedproblemsonlimitsandcontinuity
geometricprogressions
Rationalizingdenominatorofradicals
Basicpointformulasdistancemidpoint
Twopointformnormalform parametric
limitquestions
setrelationfunctionpart1
permutationcombination
straightlines
Threediamensionalgeometry
complexnumbersandquadraticequations
Trignometry
hyperbola
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