If a card hand that consists of four Queens and an Ace is rearranged, nothing has changed.
The hand still contains four Queens and an Ace. Thus, use the combination formula for problems with cards.
We have 4 eights and 4 sevens.
We want 3 eights and 2 sevens.
C(have 4 eights, want 3 eights) x C(have 4 sevens, want 2 sevens)
C(4,3) x C(4,2) = 24
Therefore there are 24 different ways in which to deal the desired hand.
Let the required number of units of work = k
According to the formula,
W1= m and W2 = k
M1T1D1W2 = M2T2D2W1
? m x m x m x k = n x n x n x m
? x= (m x n3) / m3 = n3/m2
Let the ages of mother, father and boys be M, F, B1 and B2, respectively.
The total age of four member
= 19 x 4
= 76 yr.
Given (B1 + B1)/2 = 11/2
? B1 + B2 = 11
M + F + B1 + B2 = 76 - 11
? M + F = 65 .......(i)
According to the question,
(B1 + B2 + F) / 3 = (B1 + B2 + M) / 3 + 3
? B1 + B2 + F) = B1 + B2 + M + 9
? F = M + 9
? F - M = 9 ............. (ii)
From Eqs (i) and (ii), we get
F = 37 yr and M = 28 yr
Given expression = a2+b2+2ab = (a+b)2
where a = 387 and b = 114
= (387 + 114 )2
= (501)2
=(500 +1 )2
=(500)2 + (1)2+ 2 x 500 x 1
= 250000 + 1 +1000 = 251001.
3 pumps, can empty a tank in 2 days by working 8 hours a day.
1 pumps, can empty a tank in 2 days by working 8 x 3 hours a day.
1 pumps, can empty a tank in 1 days by working 8 x 3 x 2hours a day.
4 pumps, can empty a tank in 1 days by working 8 x 3 x 2 / 4 hours a day.
4 pumps, can empty a tank in 1 days by working 2 x 3 x 2 hours a day.
4 pumps, can empty a tank in 1 days by working 12 hours a day.
Total number of letters = 5
Number of vowels = 2.
If we consider both vowel as a one letter then,
Required number = 4! 2! = 48.
S.I for 1 year = Rs. (925 - 850) = Rs. 75
S.I for 3 year = Rs. (75 x 3) = Rs. 225
? Sum = Rs. (850 - 225) = Rs. 625
Original area = ?(d/2)2
= (?d2) / 4
New area = ?(2d/2)2
= ?d2
Increase in area = (?d2 - ?d2/4)
= 3?d2/4
? Required increase percent
= [(3?d2)/4 x 4/(?d2) x 100]%
= 300%
Interval of changes = (L . C . M of 48, 72, 108) sec. = 432 sec.
So, the lights will simultaneously changes after every 432 seconds i,e 7 min. 12 sec.
So, the next simultaneously changes will take place at 8 : 27 : 12 hrs.
Here n1 = 19, a1 = 74, n2 = 38, a1 = 63
Total average weight = (n1a1 + n2 a2) / (n1 + n2)
= [(19) (74) + (38) (63)] / (19 + 38)
= 3800/57 ? 67 kg
84 = 22 x 3 x 7
∴ H.C.F. = 22 x 3 = 12.
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