@pankaj1988 forget abt circle. take values for isosceles right angled triangle.
@nick_baba said:The set M consists of p consecutive integers with sum 2p. The set N consists of 2p consecutive integers with sum p. The difference between the largest elements of M and N is 9. Then p is(a) 17 (b) 36 (c) 9 (d) 27 (e) 21
M = {k+1,k+2,k+3,......k+p}
N = {s+1,s+2,s+3..............s+2p}
sum(M) = pk + p(p+1)/2 = 2p => 2k+p = 3......................(i)
sum(N) = 2ps + 2p(2p+1)/2 = p => s+p = 0.....................(ii)
largest element M = k+p
largest element N = s+2p
=>difference = |k-s-p| = 9
=> |k - (s+p)| = 9
=>k=9 or k = -9...........(using ii)
for k =9 we get p = -15 (not possible)
for k =-9 we get p = 21.
ATDH.
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@pankaj1988 said:PQ is a diameter of circle and R is any point on the circumference of the circle. If "S" and "A" are the perimeter and area of the triangle, respectively then which of the following is true.1) A and S is maximum if triangle PQR is isosceles.2) A and S is minimum if triangle PQR is isosceles.3) A is maximum and S is minimum if triangle PQR is isosceles.4) A is minimum and S is maximum if triangle PQR is isosceles.
1 ??
@anytomdickandhary said:M = {k+1,k+2,k+3,......k+p}N = {s+1,s+2,s+3..............s+2p}sum(M) = pk + p(p+1)/2 = 2p => 2k+p = 3......................(i)sum(N) = 2ps + 2p(2p+1)/2 = p => s+p = 0.....................(ii)largest element M = k+plargest element N = s+2p=>difference = |k-s-p| = 9 => |k - (s+p)| = 9 =>k=9 or k = -9...........(using ii)for k =9 we get p = -15 (not possible)for k =-9 we get p = 21.ATDH.
sir _/\_ !!!
@audiq7 said:what is the highest power of x to yield an integral ans for 167!/(24!)^x?
7, highest power of 23
@Brooklyn said:7, highest power of 23
@krum said:i just checked for 23, 167/23=7.xx
didnt get u. why 23?
@audiq7 said:a man is stranded on an island. all he has to drink is 20cc bottle of vodka. to conserve his drink, he decides that on 1st day he will drink 1cc and replace it with water. on second day, he will drink 2cc and refill the botle. by the time all the vodka is gone, how much water has he drunk?
on 20th day man will drink the whole bottle. (on this day he does not add any water)
=> on 20th day man will have drunk all the water he had added and all the vodka the bottle initially had.
Now, man kept on adding water till 19th day.
total water added was 1+2+3+4+...19 = 190 cc.
hence he drank 190 cc of water.
ATDH.
@pankaj1988 said:PQ is a diameter of circle and R is any point on the circumference of the circle. If "S" and "A" are the perimeter and area of the triangle, respectively then which of the following is true.1) A and S is maximum if triangle PQR is isosceles.2) A and S is minimum if triangle PQR is isosceles.3) A is maximum and S is minimum if triangle PQR is isosceles.4) A is minimum and S is maximum if triangle PQR is isosceles.
A and S max if PQR isosceles?
@audiq7 said:what is the highest power of x to yield an integral ans for 167!/(24!)^x?
7
In 24 factorial consider largest prime 23... Highest power of 23 in 167! is 7... So is the answer...
In 24 factorial consider largest prime 23... Highest power of 23 in 167! is 7... So is the answer...
@audiq7 said:didnt get u. why 23?
Coz 23 is the highest prime..there can be many 2,3,7,17etc. but 23 highest prime hain aur uska hi power min. hoga so 23
@audiq7 said:didnt get u. why 23?
24!=2^22*3^10*5^2*7^2*11^2*13*17*19*23
here 23 will be the limiting value so 7
here 23 will be the limiting value so 7