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,...
Thursday, 29 November 2012
A man covers a certain distance by car driving at 100km/h and he returns back to the starting point riding on a scooter at 45 km/h. Find his average speed for the whole journey.
A man covers a certain distance by car driving at 100km/h and he returns back to the starting point riding on a scooter at 45km/h. Find his average speed for the whole journey.
Sol
Average Speed = 2x100x45/100+45 km/h
= 62.06 km...
Tuesday, 27 November 2012
Solved Question of Ex.10.2 of Class 11th............Q.No..20
Solved Question of Ex.10.2 of Class 11th............
Q.No..20......................
keywords : CBSE, coordinate geometry, Geeks Networks, NCERT solved answers, slope of line, solved answers of mathematics of 11th class, Straight Lines,
...
Sunday, 25 November 2012
Q.No. 18 of Ex. 10.2 of Class 11th
Q.No. 18 of Ex. 10.2 of Class 11th.............
Sol :
Keywords : CBSE, coordinate geometry, Geeks Networks, mathsmania, NCERT solved answers, slope of line, solved answers of mathematics of 11th class, Straight Lines,...
The two adjacent sides of a parallelogram are 5 cm and 4 cm respectively, and if the respective diagonal is 7 cm then find the area of the parallelogram?
The two adjacent sides of a parallelogram are 5 cm and 4 cm respectively, and if the respective diagonal is 7 cm then find the area of the parallelogram?
Sol :
We know that
Required Area = 2 Sqrt{s(s-a)(s-b)(s-D)
Where S = a+b+D/2
...
Thursday, 15 November 2012
The perpendicular from the origin to a line meet at the point (-2,9), find the equation of the line.
The perpendicular from the origin to a line meet at the point (-2,9), find the equation of the line.
Sol:
Keywords : Area of Triangle, CBSE, coordinate geometry, Geeks Networks, NCERT solved answers, slope of line, solved answers of mathematics of 12th class, Straight Lines, ...
Find the equations of the lines passing through the point (2,2),such that the sum of their intercepts on the axes is 9.
Q.No.13 of Exercise 10.2 of Class 11th
Find the equations of the lines passing through the point (2,2),such that the sum of their intercepts on the axes is 9.
Sol :
keywords : CBSE, Calculus, Area of Triangle, base, Geeks Networks, integrations, NCERT solved answers, slope of line, Software, Straight Lines, solved answers of mathematics of 11th class, solved answers of mathematics of 12th class,...
Wednesday, 14 November 2012
Find the equation of a line that cuts off equal intercepts on the co-ordinate axes and passes through (2,3).
Q.No 12 of Exercise 10.2 of Class 11th
Find the equation of a line that cuts off equal intercepts on the co-ordinate axes and passes through (2,3).
Sol :
Keywords : CBSE, Geeks Networks, solved answers of mathematics of 11th class, Straight Lines, NCE...
Tuesday, 13 November 2012
Solved Question of Exercise 7.2 of Class 12th........................Q.No.36............Integrate This................
Solved Question of Exercise 7.2 of Class 12th........................
Q.No.36............
Integrate This................
Sol :
...
Solved Question of Exercise 7.2 of Class 12th........................Q.No.35............Integrate This................
Solved Question of Exercise 7.2 of Class 12th........................
Q.No.35...........
Integrate This................
Sol :
...
Solved Question of Exercise 7.2 of Class 12th.............Q.No.34......................Integrate This
Solved Question of Exercise 7.2 of Class 12th.............
Q.No.34......................
Integrate This............................
Sol :
...
Solved Question of Exercise 7.2 of Class 12th.............Q.No.33......................Integrate This
Solved Question of Exercise 7.2 of Class 12th.............
Q.No.33......................
Integrate This...............
Sol :
...
Solved Question of Exercise 7.2 of Class12th............Q.No.32........Integrate this..............
Solved Question of Exercise 7.2 of Class12th............
Q.No.32........
Integrate this..............
Sol
...
Solved Question of Exercise 7.2 of Class 12th.............Q.No.31.......Integrate this
Solved Question of Exercise 7.2 of Class 12th.............
Q.No.31
Integrate this.................
Sol :
...
Monday, 12 November 2012
Q.No.30 of Exercise.7.2 of Class 12th...........Integrate this.............
Q.No.30 of Exercise.7.2 of Class 12th...........
Find the Integration of Sinx/1+cosx
Sol :
...
Q.No. 29 of Exercise.7.2 of Class 12th..........Find the Integration of cotx.log(sinx).
Q.No. 29 of Exercise.7.2 of Class 12th
Find the Integration of cotx.log(sinx).
Sol :
...
Saturday, 10 November 2012
Friday, 9 November 2012
A line perpendicular to the line segment joining the points(1,0) and (2,3) divides it in ratio 1:n. Find the equation of the line.
Q.No. 11 of Ex. 10.2 of Class 11th
A line perpendicular to the line segment joining the points(1,0) and (2,3) divides it in ratio 1:n. Find the equation of the line.
Sol :
...
The Vertices of a triangle PQR are P(2,1), Q(-2,3) and R(4,5). Find the equation of the median through the vertex R.
Q.No. 9 of Ex. 10.2 of Class 11th.
The Vertices of a triangle PQR are P(2,1), Q(-2,3) and R(4,5). Find the equation of the median through the vertex R.
Sol :
...
Sunday, 4 November 2012
Find the Equation of the line passing through (-3,5) and perpendicular to the line through the points (2,5) and (-3,6).
Ex 10.2 of Class 11th
Q. No. 10
Find the Equation of the line passing through (-3,5) and perpendicular to the line through the points (2,5) and (-3,6).
Sol :
...
Find the Equation of a line whose perpendicular distance from the origin is 5 units and the angle made by the perpendicular with positive x-axis is 30.
Ex 10.2
Q. No. 8
Find the Equation of a line whose perpendicular distance from the origin is 5 units and the angle made by the perpendicular with positive x-axis is 30.
Sol :
...
Saturday, 27 October 2012
Find the Equation of the line AB when it meets x-axis at (-3,0) with slope = -2
Find the Equation of the line AB when it meets x-axis at (-3,0) with slope = -2
Sol :
Normal
0
false
false
false
EN-US
X-NONE
X-NONE
...
Friday, 26 October 2012
Find the Equation of the line which is passing through the point (0,0) with slope m.
Sol :
Normal
0
false
false
false
EN-US
X-NONE
X-NONE
...
Tuesday, 23 October 2012
Find the Equation of the line which is passing through (-4,3) with slope 1/2
Find the Equation of the line which is passing through (-4,3) with slope 1/2
Sol :
We know that Equation of line will be (y-y1)
= m(x-x1) when slope of line and a point is given.
Normal
0
false
false
false
EN-US
X-NONE
X-NONE
...
