The number of arrangement in which A and B are not together
= Total number of arrangement - Number of arrangement in which A and B are together
= 4! - 3! x 2! = 24 - 12 = 12
If x = ?a + |
|
, y = ?a - |
|
, then the value of |
?a |
?a |
0.8268 = (8268 - 82)/9900
= 8186/9900
= 4093/4950
This is an AP with a = 1 and d = 7
? 11th term = a + (n - 1) x d = 1 + (11 - 1) x 7
= 1 + 10 x 7 = 71
Total age of 4 member = 25 x 4 = 100 yr
Total age of 5 members including the head
= 5 x (25 + 25 x 20/100)
= 5 x 30 = 150 yr
? Age of the head = 150 - 100 = 50 yr
To reach the winning post B will have to cover the distance (440 ? 40) = 400 m.
Hence,
time taken by B to cover 440 meter = 55
time taken by B to cover 1 meter = 55 / 440
time taken by B to cover 400 meter = 400 x 55 / 440 = 40 x 55/44 =10 x 55/11 = 10 x 5
time taken by B to cover 400 meter = 50 Sec.
Since, A reaches the winning post in 51 sec. while B in 50 sec.
So, B will win by 1 second.
Let us assume length of pole is L.
Length of the pole in Mud is = L x 4/7 = 4L/7
Length of the Pole which is pulled out = L x 1/3 = L/3
Length of the pole is still in mud = Length of the pole in Mud - Length of the Pole which is pulled out
Length of the pole is still in mud = 4L/7 - L/3
According to question,
Length of the pole is still in mud = 250
4L/7 - L/3 = 250
(4L x 3 - L x 7)/7 x 3 = 250
12L - 7L = 250 x 21
5L = 250 x 21
L = 250 x 21/5
L = 50 x 21
L = 1050
Let MP of the article = ? N
? C P of the article = (N x 64) / 100 = ? 16N/25
And SP of the article = [N x (100 - 12)]/100 = ? (N x 22)/25
? profit = [ 22N/25 - 16N/25 ] = ? 6N/25
Hence, profit per cent = [(6N/25) / (16N/25)] x 100%
= (6 x 100)/16 = 37.5%
As we know from the algebra formula,
(a ? b)3 = a3 ? b 3 ? 3ab (a ? b) .......................(1)
As per given question,
a3 ? b 3 = 56 and a ? b = 2
Put these value in above equation (1) . We will get,
? 23 = 56 ? 3ab x 2
? 8 = 56 ? 3ab x 2
? 8 = 56 ? 6ab
? 6ab = 56 ? 8 = 48
? ab = 8 ...................... (i)
? a2 + b2 = (a ? b)2 + 2ab
? a2 + b2 = (a ? b)2 + 2ab
Put the value of
? a2 + b2 = 22 + 2 x 8
? a2 + b2 = 4 + 16 = 20
First we find the probability that the plane is not hit
= (1 - 0.4) ( 1 - 0.3) (1 - 0.2) (1 - 0.1)
= 0.6 x 0.7 x 0.8 x 0.9 = 0.3024
? probability that the plane is hit = 1 - 0.3024
= 0.6976
Comments
There are no comments.Copyright ©CuriousTab. All rights reserved.