[prade]

Originally Posted by gugu

Solve the sums on Quadratic Equations:-
1. If both the roots of the quadratic eqn. ax^2+bx+c=0 lie in the interval (0 3) then ‘a’ lies in

2. Value of the expression (x^2-x+1)/(x-1) cant be between (a) 1, 3 (b) -1, -3 (c) 1, -3 (d) -1,3.
3. If one root of the eqn (I-m)x^2 + Ix + 1=0 is double of the other & is real, find the greatest value of m.

qn 2

y = (x^2-x+1)/(x-1)

=> x^2 - (y+1)x +(1+y) = 0

=> (y+1)^2 - 4(y+1) >= 0
y< -1 and y >3

hence answer option D

[M A V E R I C K]

Originally Posted by prade

qn 2

y = (x^2-x+1)/(x-1)

=> x^2 - (y+1)x +(1+y) = 0

=> (y+1)^2 - 4(y+1) >= 0
y< -1 and y >3

hence answer option D

well, what the heck,

am i just a speck in the galaxy?

so, i decide to spot / post on PG

:sad: [25-07-2006 01:26 PM] M A V E R I C K: http://www.kozmikhoroscopes.com/cobain.htm [25-07-2006 01:25 PM] thewebdon: rani_das kaun ha ? :neutral:

[prade]

3. If one root of the eqn (I-m)x^2 + Ix + 1=0 is double of the other & is real, find the greatest value of m.[/quote]

let y and 2y be the roots of the eqn

then 3y = -I/ (I-m)
2y^2 = 1/(I-m)

=> 9(I-m) = 2 I^2
=> 2I^2 -9I + 9m = 0
for real I

81-4.9.2m>= 0
=>m<= 9/2

hence greates value of m is 9/2

[prade]

Originally Posted by gugu

Solve the following sum:-

1. If x+y+z=5 & xy+ yz +zx =3 then the least & largest value of x is:-
(a) 10/3 , 5 (b) -1, 13/3 (c) 17/3 , 7 (d) None of These.

y = 5-(x+z)

substituting this in xy+ yz +zx =3

=> x(5-(y+z)) + (5-(x+z))z + zx = 3
=> z^2 -(5-x)z + x^2 -5x + 3 = 0

for real z,

(5-x)^2 - 4(z^2 -5z +3) >=0

3x^2 - 10x -13 <= 0
(3x-13)(z+1)<=0
hence the largest and the smalles values are (13/3, -1). Answer option b.

[raj_bhatia]

Thx a lot gaurav...nice thread indeed

[kingnitin]

try this one--
Find the value of 1.1! + 2.2! + 3.3! + ......+n.n!

[kingnitin]

another one..pls post the solution

Train A traveling at 60 km/hr leaves Mumbai for Delhi at 6 P.M. Train B traveling at 90 km/hr also leaves Mumbai for Delhi at 9 P.M. Train C leaves Delhi for Mumbai at 9 P.M. If all three trains meet at the same time between Mumbai and Delhi, what is the speed of Train C if the distance between Delhi and Mumbai is 1260 kms?

[prade]

Originally Posted by kingnitin

another one..pls post the solution

Train A traveling at 60 km/hr leaves Mumbai for Delhi at 6 P.M. Train B traveling at 90 km/hr also leaves Mumbai for Delhi at 9 P.M. Train C leaves Delhi for Mumbai at 9 P.M. If all three trains meet at the same time between Mumbai and Delhi, what is the speed of Train C if the distance between Delhi and Mumbai is 1260 kms?

In 3 hrs A travels = 180km
time to meet (A and B) = 180/30 = 6hr

Distance travelled for AB meet = 540km

Distance travelled by C = 1260-540 = 720km/hr

hence speed of C = 720/3 = 120km

[nagi_nov3]

Originally Posted by kingnitin

try this one--
Find the value of 1.1! + 2.2! + 3.3! + ......+n.n!

we can write this as (2-1)1!+(3-1)2!+(4-1)3!+........+(n+1 - 1)n!

so this is
2!-1! +3!- 2!+4!-3!+.........+(n+1)!-n!

all will gets cancelled except first and last but one

so (n+1)!-1

[kingnitin]

thanks

here goes another
How many times 0 appears between 1 and 10,000?

have done using the longer one
in 2 digit nos. 0 appears 9 times...and so on
need a short method..