CDS 2009 (II) Mathematics Q5, Q9

08:42 , 1 Comments

Q5.  If a + b= 2m2 , b + c = 6m, a + c = 2, where m is a real number and a <= b <= c, then which one of the following is correct?

A) 0 <= m <= 1/2 
B) -1<= m <= 0 
C) 1/3 <= m <=1
D) 1 < m <= 2

Soln:     Adding all the given equations we get, 2a + 2b + 2c = 2m2 + 6m + 2   >>>  a + b + c = m2 + 3m + 1.

Therefore, a =  m2 - 3m + 1, c = - m2 + 3m + 1 and b = m2 + 3m - 1.

Given, a<=b  >>>   m2 - 3m + 1 <= m2 + 3m - 1  >>>  2 <= 6m  >>>  m >= 1/3.  

Given, b<=c  >>>   m2 + 3m - 1 <= - m2 + 3m + 1  >>>  m2 <= 1  >>>  m <= 1.  


So, 1/3 <= m <= 1. 


Q9.  If x:y=1:3, y:z=5:k, z:t=2:5 and t:x=3:4, then what is the value of k?

Soln:    Adding all the ratios, (x*y*z*t)/(x*y*z*t)=(1*5*3*2)/(3*k*5*4).
            >>>  1=30/(60k)  >>>  K=1/2.


Itachi443

Itachi443

Some say he’s half man half fish, others say he’s more of a seventy/thirty split. Either way he’s a fishy bastard.

1 comment:

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