An examinee is required to answer the eight questions out of 16 questions which are divided into two groups each containing eight questions each and he is not permitted to answer more than six questions from any group. In how many ways can he answer the eight questions?
Required number of ways = (⁸C6 × ⁸C₂ + ⁸C5 × ⁸C₃ + ⁸C4 × ⁸C4 + ⁸C₃ × ⁸C5 + ⁸C₂ × ⁸C6) = (28 × 28 + 56 × 56 + 70 × 70 + 56 × 56 + 28 × 28) = 12,740
In a Glass there is 520 ml of a mixture composed of juice and water in a ratio of 17:9. If 'y' ml of juice and 'y + 60' ml of water are added to this mi...
A container contains Alcohol and water in ratio of 3:1 and Capacity of Container is 40 lit. If half of the Container is replaced with 15 lit of water th...
A mixture contains wine and water in the ratio 5:1. On adding 5 litre of water, the ratio of wine to water becomes 5:2. The quantity of wine in the mix...
A jar contains a mixture of milk and water in the ratio 6:5, respectively. If 10-litres of the mixture is taken out, then the quantity of water left in ...
Two vessels A and B contain mixture of milk and water. Ratio of milk and water in vessel A and B are in the ratio 1:2 and 3:2 respectively. In what rati...
In a mixture, the initial quantity of milk and water is 11:12 respectively. If (z-14) and ‘z’ litres of milk and water are added respectively in the...
Quantity of water in a 320 litres mixture (alcohol + water) is 20 litres less than the quantity of alcohol in it. Find the quantity of water to be mixed...
55% of the original 'a' liters of pure petrol is taken out from a container and replaced with 66 liters of Methanol, ensuring the total quantity of the ...
In a mixture of milk & water, 80 litres water is mixed due to which ratio changes from 3 : 4 to 1 : 3. Find initial quantity of mixture. (in litres)
Tap P can fill a water tank in 15 minutes, Tap Q can fill it in 20 minutes, and Tap R can empty half of the tank in 15 minutes. Now, if all the taps, P,...