[certified.pagla]

Q. Suppose a, b and c are in AP and a^2, b^2 and c^2 are in GP. If a < b < c and a + b + c = 3/2 then what is the value of a ?

[ChAK_de_fatte]

Originally Posted by certified.pagla

Q. Suppose a, b and c are in AP and a^2, b^2 and c^2 are in GP. If a < b < c and a + b + c = 3/2 then what is the value of a ?

a=b=c=1/2 satisfy the eqns.

[ChAK_de_fatte]

Here's one.
find the number of numbers whose squares end in 24 between 330 and 520.
Plz post your approach puys.

[prateekg23]

Originally Posted by ChAK_de_fatte

a=b=c=1/2 satisfy the eqns.

its given that a<b<c therefore it cant be a=b=c=1/2

though i found the value of b=1/2 i m not able to find a.can some1 help

[bhupi3149]

Originally Posted by ChAK_de_fatte

Here's one.
find the number of numbers whose squares end in 24 between 330 and 520.
Plz post your approach puys.

is it 8 ????

[divishth]

Originally Posted by ChAK_de_fatte

Here's one.
find the number of numbers whose squares end in 24 between 330 and 520.
Plz post your approach puys.

8 Such Numbers

Approach

Looking For More Elegant Approach. But For Time Being
Those Numbers which end in 2 and 8 will give 4 in the end.
32^2 or 2^10 ends with 24
So, 332,432 will also end in 24
Also, 332+50, and 432+50 would also end the same way...Coz it is the property of squares that they repeat their last two digits after 50.

Similarly, 18^2 = x24
Hence, 68 would also leave xx24
And 368,418,468,518 would also leave xx24 in the end...

Hence 8 such Numbers.

[certified.pagla]

Originally Posted by ChAK_de_fatte

a=b=c=1/2 satisfy the eqns.

Look at the question. a<b<c

[uhhh...]

Originally Posted by certified.pagla

Look at the question. a<b<c

i just worked it out at a frantic pace.. so theres a high chance of being wrong

a=(1-2^0.5)/2

[certified.pagla]

Q. 1. Sum of the series 1^2 −2^2 +3^2 − 4^2 +.........+ 2001^2 −2002^2 + 2003^2 is?
A. 2007006
B. 1005004
C. 200506
D. None of the above

Q. 2. The number of ways in which a mixed double tennis game can be arranged
amongst 9 married couples if no husband and wife play in the same game is:
A. 1514
B. 1512
C. 3024
D. None of the above

[divishth]

Originally Posted by certified.pagla

Q. 1. Sum of the series 1^2 −2^2 +3^2 − 4^2 +.........+ 2001^2 −2002^2 + 2003^2 is?
A. 2007006
B. 1005004
C. 200506
D. None of the above

Answer is 2007006

1 + (3+2)(3-2) + (5+4)(5-4) + ....
1+ 5 + 9 + .......... + 4005
Sum = 1002/2 * (1+4005) = 2007006