Post mathematic related questions here

[powerhoney]

In 8x8 chessboard we have only ONE 8x8 square.
There are FOUR 7x7 squares. There are NINE 6x6 squares, and so on

In 8x8 chessboard we have 1^2 + 2^2 + 3^2 + 4^2 + 5^2 + 6^2 + 7^2 + 8^2 square

Hence in NxN chessboard chessboard
the total number of squares = 1^2 + 2^2 + 3^2 + ... + N^2

Also NxN chessboard chessboard
the total number of rectangle = [C(n+1,2) ] ^2

Good... There were no new questions being posted so I posted that one...

 

[rst]

A vertical pole with height more than 100 m consists of two parts, the lower being on third of the whole.
At a point on a horizontal plane through the foot and 40 m from it, the upper part subtends an angle whose tangent is 1/2.
what is the height of the pole ?

a)110 m
b)200m
c)120 m
d)150m

 

[rst]

If m, n are integers, then what is the value of
int (0,1) sinmx sinnx dx (here int is integration, 0 is lower limit and 1 is upper limit).if m ≠n
A)2/π
B)4/π
C)0
D)1

 

[rst]

What is the least value of 3sin^2 x + 4 cos^2 x
A)1
B)2
C)3
D)4

 

[anirbandd]

^3 for x=pi/2

 

[rst]

^3 for x=pi/2

Answer is correct
3sin^2 x +4cos^2 x
=3+cos ^2 x

-1≤Cosx≤1
0≤cos^2 x ≤1 (as cos^2x can't be negative)
3≤cos^2 x+3≤4

So least value is 3

 

[rst]

If equation ax^2+bx+c=0, a>0, has two distint real roots p and q such that p<-5 and q>5 then
A)c>0
B)c=0
C)c=(a+b)/2
D)c<0
E)c= a+b

 

[anirbandd]

^thats easy..

its D. c<0

 

[rst]

if angle between the curves y=2^x and y= 3^x is p then value of tanp is
a)log(3/2) /[1+6(log2)(log(3)]
b) 6/7
c)1/7
d)log6 / [1+(log2)(log3)]

 

[anirbandd]

whats the soln??

they meet at x= - ∞, but at -∞ it becomes 0..

 

[Neo]

if angle between the curves y=2^x and y= 3^x is p then value of tanp is
a)log(3/2) /[1+6(log2)(log(3)]
b) 6/7
c)1/7
d)log6 / [1+(log2)(log3)]

A. Simply find tan(A-B)

 

[rst]

A. Simply find tan(A-B)

answer is correct

can you explain a little bit

 

[anirbandd]

answer is correct

can you explain a little bit

+1.

Im a lil confused

 

[Neo]

Find tanA = dy/dx for the graphs. Find tan (A-B) using the identity. Put x=0 at last because the graphs meet at it.

What class you guys in btw?

 

[rickenjus]

Guys, I have doubt over this Question. It is from 11th class RD Sharma. Permutation -> Exercise - 16.2 -> Q24.

Below is a part of the Question.

Q. How many 3 digit odd numbers can be formed using 0,3,5,7, repetition not allowed.

Sol. What I did.

_ _ _
3 X 3 X 1

For Hundredth place - It can be filled in 3 ways (any of 3,5,7), we cannot use 0.
For Tens place - It can be filled in 3 ways (0,3,5,7) as one of 3,5,7 already filled in hundredth place).
For Ones place - It can be filled in 1 way as two digits of 3,5,7 already used in above two places and it cannot use 0.

And solution I found on book says this: -

It fills Hundredth first, then Ones and then Second.

*i.imgur.com/T5f2zsO.png
_ _ _
3 X 2 X 2

What is that I'm not understanding or doing wrong??

 

[rst]

Guys, I have doubt over this Question. It is from 11th class RD Sharma. Permutation -> Exercise - 16.2 -> Q24.

Below is a part of the Question.

Q. How many 3 digit odd numbers can be formed using 0,3,5,7, repetition not allowed.

Sol. What I did.

_ _ _
3 X 3 X 1

For Hundredth place - It can be filled in 3 ways (any of 3,5,7), we cannot use 0.
For Tens place - It can be filled in 3 ways (0,3,5,7) as one of 3,5,7 already filled in hundredth place).
For Ones place - It can be filled in 1 way as two digits of 3,5,7 already used in above two places and it cannot use 0.

And solution I found on book says this: -

It fills Hundredth first, then Ones and then Second.

*i.imgur.com/T5f2zsO.png
_ _ _
3 X 2 X 2

What is that I'm not understanding or doing wrong??

Book solution is correct

As Tens place can be filled in any way
So it will be filled last

Hundreds and Ones places can be filled in specific way
So they are filled first

 

[rickenjus]

[MENTION=158560]rst[/MENTION] - ya thanks... got perfect explanation on stackexchange.

 

[rst]

let AB be diameter of circle and AC be the chord.let a tangent is drawn from C to meet AB produced at D. If angle BAC= 30 .Prove that
BC= BD

 

[doomgiver]

*i.imgur.com/kPWFYcl.png




angle ACB = right angle coz thales theorem. i dunno what else to do.

http:/ /www. math10.com/en/geometry/geogebra/geogebra. html
remove spaces.
tool used for pic ^^

 

[rst]

By diagram it is clear

But is there any method to prove it