Volume (new cube) = (13 + 63 + 83 ) = 729 cm3
a3 = 729
? a = ? 729
? Surface area of the new cube = 6a2
= 6 x 92 = 486 sq cm
Surface area/2 = 486/2 = 243 sq cm
If Mrs. X is selected among the ladies in the committee, then Mr. Y is not selected or if Mrs. X is not selected then Mr. Y can be there in the committee...
So, required number of ways
= 8C3 x 6C4 + 7C3 x 7C4
= [(8 x 7 x 6)/(3 x 2)] x [(6 x 5)/(2 x 1)] + [(7 x 6 x 5)/(3 x 2)] x [(7 x 6 x 5)/(3 x 2)]
= 840 + 1225
= 2065
T.D. ?(P.W. x B.G. )
= ?(576 x 1) = Rs. 24
First, we can select 12 beads out of 18 beads in 18C12 ways.
Now, these 12 beads can make a necklace in 11! / 2 ways as clockwise and anti-clockwise arrangements are same.
So, required number of ways = [ 18C12 .11! ] / 2!
= [18C6.11! ] / 2!
= [18 x 17 x 16 x 15 x 14 x 13 x 11! ] / [6 x 5 x 4 x 3 x 2 x 1 x 2!]
= [17 x 7 x 13! ] / 2!
= 119 x 13 !/ 2
Sd = 15 km/h
Su = 9 km/h
Speed of man= (Sd + Su)/2
? Speed of man = (15 + 9)/ 2 = 12 km/h
Suppose the vessel initially contains 8 litres of liquid.
Let x litres of this liquid be replaced with water.
Quantity of water in new mixture =
litres.
Quantity of syrup in new mixture = litres.
=> 5x + 24 = 40 - 5x
=> 10x = 16 => x = 8/5
So, part of the mixture replaced = = 1/5.
Let speed of the flow of water be x km/h and rate of sailing of sailor be y km/h.
Downstream speed (x + y) = 48/8
? x + y = 6 ....(i)
and upstream speed x - y = 4 ...(ii)
On solving Eqs. (i) and (ii), we get
y = 1 km/h
By the rule of alligation:
Cost of 1 kg rice of 1st kind Cost of 1 kg rice of 2nd kind
Required ratio = 60 : 90 = 2 : 3
Let initial quantity be Q, and final quantity be F
F = Q(1 - 8/Q)
=> Q = 20
Total share given by the person = (1/4) + (1/2) + (1/5)
= (5 + 10 + 4) / 20
=19/20
h = 8 m.
So, r = √l2 - h2 = √(10)2 - 82 = 6 m.
∴ Curved surface area = Πrl = (Π x 6 x 10) m2 = 60Π m2.
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