Download Half Yearly Examination 2015-2016 Class XI Mathematics Time 3

Half Yearly Examination 2015-2016
Class XI
Mathematics
Time 3 hrs
M.M 100
Note: Attempt all the questions
Section A (1X6 =6)
Q 1 If U = {1,2,3,4,5,6,7,8,9}
A= { 2,4,6,8} and B ={ 2,3,5,7} .Find A’∩ B’
11
Q2 Find the degree measure corresponding to the radian measure ( 16)
Q 3 Find the multiplicative inverse of 3- 4i
Q 4 Find solution of
3 ( 𝑥−2)
5
≤
5(2−𝑥)
3
Q 5Find coefficient of 𝑥 5 in ( 𝑥 + 3)8
Q6 If nth term of a series is n( n+1 ) .Find the sum of n terms of the series
Section B (4 X 13= 52)
Q 7Let A and B be sets: If A ∩X = B∩ 𝑋= ∅ and A U X = B U X for some set X .Show that A =B .
Q8 Find n , If the ratio of the fifth term from the beginning to fifth term from the end in the
1
expansion ( ∜2 + ∜3 ) is √6 : `1
Q 9 Between 1 and 31 , m numbers have been inserted in such way that the resulting sequence
is an A.P and the ratio of 7th and (m-1) th number is 5:9 .Find value of m .
Q 10 Find angles between the lines √3 x+ y = 1 and x+ √3 y =1
Q11The English alphabet has 5 vowels and 21 consonants. How many words with two different
vowels and two different consonant s can be formed from the alphabet?
Q 12 Find the real numbers x and y if ( x-iy ) ( 3+ 5i ) is the conjugate of ( -6 -24i)
−4
Q13 If tan x = 3
𝑥
𝑥
𝑥
where x is in second quadrant. Find Sin 2 , cos 2 and ten 2
𝜋
9𝜋
3𝜋
5𝜋
Q 14Prove that 2 cos 13 cos 13+ cos 13 + cos 13 = 0
Q 15 Find domain and range of the following real function
. f (x) =√9 − 𝑥 2
Q16 which of the following relations are function? Give regions if it is a function, determine it s
domain and range.
a) { ( 2,1) ,(5,1) ,(8,1), (11,1) ,( 14,1),(17,1) }
b) { (2,1),(4,2),(6,3),(8,4),(10,5),(12,6),(14,7) }
c) {(1,3),(1,5),(2,5)}
Q17 Find sets A ,B, and C such that A∩B ,B∩ 𝐶 and A∩ 𝐶are nonempty sets and ( A∩B)∩ C= ∅
Q18 Using principle of mathematical induction. Prove that
12 +32 +52 + ………………………+(2𝑛 − 1)2 =
𝑛(2𝑛−1)(2𝑛+1)
3
Q19 Find the direction in which a straight line must be drawn through the point (-1,2) so that its
point of intersection with the line x+y=4 may be at a distance of three units from the point .
Section C (6X7=42)
Q 20 In a survey of 60 people , it was found that 25 people read newspaper H ,26 read
newspaper T , 26 read newspaper I , 9 read both H and I , 11read both H and T , 8 read both T
and I , 3 read all three newspapers . Find
a) The number of people who read at least one of the newspapers.
b) The number of people who read exactly one newspaper
Q 21 a) Prove that Cot x Cot 2x-Cot 2x Cot 3x –Cot 3x Cot x =1
b) Find general solution of Cos 3x+ Cos x –Cos 2x =0
Q 22 Solve the following system of in equations graphically
2x+y≥4,
x+y ≤ 3, 2x-3y ≤ 6
Q 23 In how many ways can the letters of the word PERMUTATIONS be arranged, if the
a) Word start with P and end with S
b) Vowels are all together
c) There are always 4 letters b between P and S
Q 24 The coefficients of (r-1)th , rth and ( r+1) th terms in the expansion of (𝑥 + 1)𝑛 are in the
ratio 1:3:5 .Find n and r .
Q 25 Find the sum up to n terms of the series
3+7+13+21+31+……………………………
Q 26 Find the image of the point (3, 8) w.r.t the line x+3y =7 assuming the line to be plane
mirror .
End