26. From a pack of 52 playing cards, three cards are drawn random. Find the probability of drawing a king, a queen and a jack.

A king can be drawn in 4C1 ways
Similarly, a queen and a Jack can be drawn in 4C1, 4C1.
Hence,
(4c1*4c1*4c1)/(52c3)=16/5525

27. Find the total numbers in the range 100 to 1000, where in the product of individual digits of the number gives 24 (For instance: 234 gives 2*3*4 = 24)

A product of 24 can be achieved by (1,3,8), (1,4,6), (2,2,6), (2,3,4)
Now these numbers can be arranged in 3! ways respectively
However 2,2,6 can be arranged in 3!/2! ways
Hence, the answer is 3*3! + 1*3!/2! = 18+3 = 21

28. There is cask full of milk. E litres are drawn from the cask, it is then filled with water. This process is repeated. Now the ratio of milk to water is 16:9.What is the capacity of the cask in litres?

if x is capacity of cask, then
initially
x ltr milk .. 0 ltr water
after first draw and water filling by E ltrs,
x-E ltr milk and E ltr water
after 2nd draw and water filling by E ltrs,
x- [2E-(E^2/x)] and 2E -( E^2)/x ltr water
As per condition
x- [2E-(E^2/x)] /[ 2E -( E^2)/x] = 16/9

solving, we get
x=5E

29. What should come in the place of (?) in the given series?

ACE, FGH, ?, PON

A) KKK

B) JKI

C) HJH

D) IKL

A +5==>F +5==>K +5==>P
C +4==>G +4==>K +4==>O
E +3==>H +3==>K +3==>N

30. If (9+9^2+9^3+.......9^n) is divided by 6, remainder will be? (n is a multiples of 11)

now since n is a multiple of 11 then
3(11)=33 i.e. rem =3
again 3(22)==66 rem =0
3(33)=99 rem=3
if n is odd then remainder is 3
if n is even the remainder is 0
ans remainder is 3,0

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