GATE Questions

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The total number of ways of forming the group of ten representatives is ²²C₁₀.
The total number of ways of forming the group that consists of no seniors is ¹⁰C₁₀ = 1 way
The required number of ways = ²²C₁₀ - 1

5 L from A are V --- 5 Letters from Alphabets are Vowels.

Cost of each cake P1 & P2 = Rs. 12

Offer decrease in % = 20%

Increase in sale per day (Q2) = 250 - 18%

Total quantity per day (Q1) = 250

Hence, required change total revenue

TR = P2Q2 - P1Q1 = (12 x 0.8 x 250 x 1.18) -  (12 x 250) = - Rs.168.

1) Man's wife. = 1
2) Man's 4 son's wives. = 4
3) Man's daughter. = 1
4) 4 son's has each one daughter. = 4
Therefore, total number of female members in the family = 1+4+1+4 = 10.

Probability of occurrence of an event, 

P(E) = Number of favorable outcomes/Numeber of possible outcomes = n(E)/n(S)

⇒ Probability of getting head in one coin = ½, 

⇒ Probability of not getting head in one coin = 1- ½ = ½, 

Hence, 

All the 11 tosses are independent of each other.

∴ Required probability of getting only 2 times heads =122×129=1211

We can select atleast one item from 6 different items = 26-1  

Similarly we can select atleast one item from other set of 6 different items in 26-1 ways. 

Required number of ways = (26-1)26-1 = 26-12 = 3969

The length of the longest pole which can be kept in a room 12 m long, 4 m broad and 3 m high is

=>  d2 = 122 + 42 + 32 = 13mts.

Let the speed of the stream = x kmph

From the given data,

 129+x+129-x=3 hrs

3x2 = 27

=> x = 3 kmph

Therefore, the speed of the stream = 3 kmph