Download Assignment-3 Maths

DELHI PUBLIC SCHOOL
BOKARO STEEL CITY
ASSIGNMENT FOR THE SESSION 2010-2011
Class: XI
1.
Subject : Mathematics
If f is a function satisfying
Assignment No. 3
f(x + y) =f(x). f(y) for all x,y  N, such that f(1) = 3 and
n
 f(x)  120 .
Find the value of n.
x 1
2.
3
4
5.
6.
7.
8.
9.
10.
Two students A and B appeared in an examination. The probability that A will qualify the
examination
is 0.05 and B will qualify the examination is 0.10. The probability that both will qualify is 0.02.
Find the probability that
(i) Both A and B will not qualify the examination
(ii) At least one of them will not qualify the examination.
(iii) Only one of them will not qualify the examination
Find the probability that in a random arrangement of the letters of the word MISSISSIPPI, the 4`S
do not come together.
A die is thrown repeatedly until a six comes up. Find the sample space for this experiment.
If four digit number greater than 5000 are randomly formed from the digits 0,1.3,5,7, what is
the probability of forming a number divisible by 5 if (i) digit may be repeated (ii) Repetition
of digits not allowed.
A card is drawn from a pack of 52 cards and a gambler bets that, it is a spade or an ace. What are
the odds against his winning this bet?
If a, b, c, and d in any binomial expansion be the 6th, 7th, 8th, and 9th term in(x+)n respectively,
prove that :
b 2  ac 4a
.

c 2  bd 3c
Using Binomial theorem, prove that 32n+2 – 8n –9 is divisible by 64
1
If the 6th , 7th and 8th terms in the expansion of (x + a)n are 112, 7, and
respectively,
4
find the value of x, a and n.
Find n, if the ratio of the 5th term from the beginning to the 5th term from the end in the expansion
n

1 
of  4 2  4  is
3

11.
12
13
14.
15.
16.
6:1
The mean and standard deviation of 20 observations are found to be 10 and 2 respectively. On
rechecking, it was found that observation 8 was incorrect. Calculate the mean and standard
deviation in each of the following case : (i) If the wrong item is omitted (ii) If it is replaced by
12.
A rod of length 15 cm rests in between two coordinate axes in such a way that the end point A lies
on the x axis and end point B lies on the y axis. A point P (x,y) is taken on the rod such that AP =
6cm. Find the locus of P.
Using section formula, show that the points A(2, –3,4), B(–1, 2, 1 ) and C ( 0, 1/3,2) are collinear
Check the validity of the statement by Method of contradiction:The sum of an irrational and rational number is irrational
Verify by Method of contradiction that 7 is irrational.
The sum and sum of square corresponding to length x (in cm) and weight y (in gm) of 50 plants
products are given below:
50

1
xi  212,
50

1
yi  261,
50

x 2i  902 .8,
1
Which is more varying, length or weight?
50
 y 2i
1
 1457 .6
2c 2
ab
17.
Prove that the four lines ax  by  c  0 enclose a
18.
Referred to the principal axes as the axes of coordinates, find the equation of the hyperbola whose
foci are at (0,  10 ) and which passes through the point (2, 3)
Sum the following to n terms(i) 5 +7 +13 +31+85 +…………
19.
(ii)
rhombus whose area is
1
1
1


 .........
1.4 4.7 7.10
20.
(iii) 12– 22+ 32– 42+ 52 – 62 +……
The sum of two number of is 6 times their G.M, show that the numbers are in the ratio
(3  2 2 ) : (3  2 2 ) .
21.
If S1, S2, S3……………., Sn are the sum of n terms of, n G.P’s whose first term is 1 in each and
22.
23.
24.
25.
26.
27.
28.
29.
30.
31.
32.
33.
34.
35.
36.
37.
38.
39.
common ratios are 1,2,3……..n respectively, then prove that S1 +S2, +2S3+3S4, + …. .. +(n–1)Sn
n
n
n
n
= …1 + 2 + 3 +………..n .
If a, b, c, and d are different real numbers such that (a2+b2+c2) p2 –2(ab+bc+cd) p + (b2 +c2+d2)
 0, then show that a, b. c and d are in G.P
A beam is supported at its ends by supports which are 12 m apart. Since the load is connected at
its centre, there is a deflection of 3 cm at the centre and the deflected beam is in the shape of
parabola. How far from the centre is the deflection 1 cm?
Find the ratio in which the line joining the points (2,1,5) and (3, 4,3) is divided by plane 2x +
2y + 2z =1 Also find the coordinate of the points of division.
Show that the points (3, –2) (1, 0), (–1, –2) and (1, –4) are concyclic.
How many numbers greater than a million can be formed using the digits 1, 2, 0, 2, 4, 2, 4?
Prove that 33! is divisible by 215. What is the largest integer n such that 33! is divisible by 2n ?.
A committee of 7 has to be formed from 9 boys and 4 girls. In how many ways can this be done
when the committee consists of : ( 1) exactly 3 girls (ii) at least 3 girls (iii) at most 3 girls ?
Calculate the mean and standard deviation for the following distribution:
Marks
0-30
30-60
60-90
90-120
120-150
150-180
180-210
No. of students
2
3
5
10
3
5
2
If p, q, r are in G.P and the equation, px2 +2qx+r =0 and dx2 +2ex +f =0 have a common root, then
d e f
show that
, , are in A.P.
p q r
If S1, S2, and S3 be respectively the sum of n, 2nd 3n terns of a G. P, prove that S 1 (S3-S2) =
(S2,-S1)2
33. If n cr = n cr  1 and n pr = n pr 1 , find the value of r and n.
Find the coefficient of a4 in the product (1+2a) 4(2- a) 5 using binomial theorem.
How many five letter words containing 3vowels and 2 consonants can be formed using the letters
of the word EQUATION so that the consonants occur together?
A line is such that its segment between the lines 5x-y+4 =0 and 3x+4y-4 =0 is bisected at the
point (1, 5). Obtain its equation.
The opposite angular points of a square are (1, 2) and (5, 8). Find the co-ordinates of the other two
vertices.
Find the orthocenter, centroid, incentre and circum- centre of the triangle ABC whose sides have
the equations 3x-4y = 0,12y+5x =0 and y-15 =0
Find all points on x + y =4 that lie at a unit distance from the line 4x+3y =10
Prove that altitudes of a triangle are concurrent.
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