Q.  The average age of 30 students of a class is 14 years 4 months. After admission of 5 new students in the class the average becomes 13 years 9 months. The youngest one of the five new students is 9 years 11 months old. The average age of the remaining 4 new students is
(A) 11 years 2 months 
(B) 13 years 6 months 
(C) 10 years 4 months
(D) 12 years 4 months
(E) None of these 42.

Q. If  x=a1 /2+ a-1/2 ,  y =  al/2— a-1/2, then value of (x‚Äč4 - x2 y2 — 1) + (y4 — x2y2 + 1)
(A) 9
(B) 25
(C) 14
(D)16
(E)None of these

Q.A man purchases some oranges at the rate of 3 oranges for Rs. 40. and  the same quantity at 5 oranges for Rs. 60. If he sells all the oranges at the rate of 3 oranges for Rs. 50, find his gain or loss percent (to the nearest integer).
(A) 34 % loss
(B) 32 % profit 
(C) 31 % profit 
(D) 31 % loss 
(E) None of theses.  
 

Dear student
We have x=a12+a-12,y=a12-a-12To find : x4-x2y2-1+y4-x2y2+1Consider,x+y=a12+a-12+a12-a-12x+y=2a  ...1Now consider, x-y=a12+a-12-a12-a-12=a12+a-12-a12+a-12=2a  ...2Consider, x4-x2y2-1+y4-x2y2+1= x4-x2y2+y4-x2y2=x4+y4-2x2y2=x2-y22    using a-b2=a2+b2-2ab=x-yx+y2    using a2-b2=a+ba-b=2a×2a2    using 1 and 2=42=16
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