Show that :
cos(36 - A) cos(36 + A) + cos(54 + A) cos(54 - A) = cos2A
Sol :
L.H.S. = cos(36 - A) cos(36 + A) + cos(54 + A) cos(54 - A)
= 2/2 cos(36 - A) cos(36 + A) + 2/2 cos(54 + A) cos(54 - A)
= 1/2{cos(36 -A +36 +A) + cos(36-A-36-A)} + 1/2{cos(54+A+54-A) + cos(54+A-54+A)}
= 1/2 {cos72 + cos(-2A)} + 1/2 {cos108 + cos2A}
...
Friday, 28 December 2012
Monday, 24 December 2012
The mean and variance of 5 observations are 15 and 6 respectively.If three observations are 11,15,18, find the remaining observations.
The mean and variance of 5 observations are 15 and 6 respectively.If three observations are 11,15,18, find the remaining observations.
Sol :
Keywords : statistics,CBSE, Geeks Networks, NCERT solved answers, solved answers of mathematics of 11th class,...
Saturday, 15 December 2012
profiles of users in computer system
Simply, Profile is used for desktop related settings.
There are three types of profile :-
Local Profile
Roaming Profile
Mandatory Profile
1. Local Profile :- It is automatically provided by Operating System. When we create a user , he gets local profile by default.
2. Roaming Profile :- It is manually created by administrator of Domain Controller (DC).With this profile , If user will change anything in his desktop,he will get that changes in entire domain.
3. Mandatory Profile :- This Profile is also manually created by Network...
In a parallelogram, The lengths of adjacent sides are 15 cm and 17 cm respectively. If the length of one diagonal is 18 cm, find the length of the other diagonal........
In a parallelogram, The lengths of adjacent sides are 15 cm and 17 cm respectively. If the length of one diagonal is 18 cm, find the length of the other diagonal........
Sol :
In a parallelogram, the sum of the squares of the diagonals = 2 x ( the sum of the squares of the two adjacent sides).
Or (D1)^2 + (D2)^2 = 2{(a)^2 + (b)^2}
Or 18^2 + (D2)^2 = 2 { 15^2 + 17^2 }
Or ...
Monday, 10 December 2012
Find the no. of Diagonals of a Polygon of 15 sides....
Find the no. of Diagonals of a Polygon of 15 sides....
Sol :
A polygon of n sides will have n vertices . A diagonal or a side of the polygon will be formed by joining any two vertices of the polygon..
No. of Diagonals of the polygon + No. of sides of the polygon = C(n,2) - n
...
Saturday, 1 December 2012
Given 7 flags of different colours, how many different signals can be generated if each signal requires the use of two flags, One below the other ?
Given 7 flags of different colours, how many different signals can be generated if each signal requires the use of two flags, One below the other ?
Sol :
First place can be filled up in seven ways. After filling first place , we have left with 6 flags.
Therefore The second place can be filled up in six ways...
The total number of signals which can be generated = 7 x 6 ways = 42 ways...........
How many 3-letter code words are possible using the first 10 letters of the English alphabet, if no letter can be repeated ?
How many 3-letter code words are possible using the first 10 letters of the English alphabet, if no letter can be repeated ?
Sol :
First letter of the code word can be selected in 10 ways. After the selection of the first letter, we have nine letters. Hence, the second letter can be selected in nine ways. According to Fundamental principal of Counting(FPC), first two letters can be selected in 10 x 9 ways.
Similarly third letter can be selected in eight ways . According to FPC , number of ways of selecting Three letters out of ten letters...
How many 3-digit even numbers can be formed from the digits 1,2,3,4,5 and 6 if the digits can be repeated?
How many 3-digit even numbers can be formed from the digits 1,2,3,4,5 and 6 if the digits can be repeated?
Sol :
Let 2 be fixed at unit's place . The ten's place can be filled up in six ways. The hundred's place can also be filled in six ways.
No. of numbers that can be formed when 2 is at unit's place = 6x6 = 36.
Similarly when 4 is at unit's place, the number of numbers that can be formed = 36.
Again when 6 is at unit's place, The number of numbers that can be formed = 36.
Therefore The total numbers of...
How many 3-digit numbers can be formed from the digits 1,2,3,4 and 5 when repetition of digits is allowed and if repitition of digits is not allowed.......
How many 3-digit numbers can be formed from the digits 1,2,3,4 and 5 when repetition of digits is allowed and if repetition of digits is not allowed.......
Sol :
When Repetition is allowed :
There are five digits, 1,2,3,4 and 5. Every digit can be selected any number of times. Hence , we can select first digit five times. The second digit 5 times and the third digit five times.
Therefore the number of ways in which the selection of three digits can be made 5x5x5x ways = 125 ways.
When repetition is not allowed ...
Reduce the Equation 5y+3 = 0 into intercept form and find its intercept on the axes.................
Reduce the Equation 5y+3 = 0 into intercept form and find its intercept on the axes.................
Sol :
We have 5y + 3 = 0
Or 5y...
Reduce the Equation 3x+2y-12=0 into intercept form and find its intercepts on the axes...........
Reduce the Equation 3x+2y-12=0 into intercept form and find its intercepts on the axes...........
Sol :
here 3x+2y-12=0
Or 3x+2y = 12
Dividing by 12 we get,
...
Reduce the Equation 6x+2y-5=0 into slope-intercept form and find its slope and intercept........
Reduce the Equation 6x+2y-5=0 into slope-intercept form and find its slope and intercept........
Sol :
Here Equation is
6x+2y-5=0
Or ...
Reduce the equation x+7y = 0 into slope intercept form and find its slope and the intercept.....
Reduce the equation x+7y = 0 into slope intercept form and find its slope and the intercept.....
Sol :
x + 7y = 0
Or 7y = -x
Or y = -1/7x + 0
Therefore Slope = -1/7 and Intercept = 0
Keywords : CBSE, coordinate geometry, Geeks Networks,...
