isi 2004 maths

[seema]

25. If a2 x2 + 2bx + c = 0 has one root greater than unity and the other less
than unity, then
(A) a2 + 2b + c = 0
(B) a2 + 2b + c > 0
(C) 2b + c < 0
 (D) 2b + c > 0


15. The sum of the infinite series ...1+3/4+ 7/16+15/64+31/256+....is
(A) 2/3
(B) 4/3
(C) 8/3
(D) none of these.

[neha]

15. The sum of the infinite series ...1+3/4+ 7/16+15/64+31/256+....is
(A) 2/3
(B) 4/3
(C) 8/3
(D) none of these.

solution: take Sn= 1+3/4+ 7/16+15/64+31/256+....

multiplying both sides by 2 gets us to
             2Sn= 2+ 6/4 + 14/16 +  30/64  +...
               Sn=      1    + 3/4   +    7/16  +....

by subtracting the two, we get

Sn= 2 + 2/4 + 2/16+ 2/64 +..... ,, which is an infinite g.p,, so the answer should be 8/3.

[neha]

For the second question ,, I am getting  a2^2-4a2c >0 which is not in any of the options given,,,, whats d correct answer by d way??

[neha]

pardon,,, i am getting a^4-a^2.c >0 which is still not there :(

[Ram]

For the 1st question we can take one root as 4 and the other as -3 (am just taking some random values) now the quadratic expression is (x-4)(x+3)=0 => x2-x-12=0 and now compare this with a2 x2 + 2bx + c = 0 we get a2=1, 2b=-1, c=-12 now check the options...
only option c is correct...