GATE Questions

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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 need to find the total cost to send r messsages, r > 1000.

The first 1000 messsages will cost Rs.p each (Or) 

The total cost of first 1000 messsages = Rs.1000p

The remaining (r - 1000) messsages will cost Rs.q each (Or)

The cost of the (r - 1000) = Rs.(r - 1000)y

Therefore, total cost = 1000p + rq - 1000q

= 1000(p - q) + qr

Given the average age of couple and their son = 40

=> Sum of age (H +W +S) = 40×3

Let the age of daughter in law at the time of marriage = D years

Now after 10 years,

(H + S +W) + 3×12 + D +12 + 10 = 38×5

178 + D = 190

D = 190 -178 = 12 years

Let 'x' be the amount he had in the bank.

=> 20/100(25/100(30/100(x))) = 750

x = 750 x 8000/120 = Rs. 50000

Let Reena’s present age be 'K' yrs.
Given:{(K+3) x 4} - {(K-3) x 3)}
=> K = 21 yrs
So her present age is 21 yrs.
Then, her age after 1 year is 22 yrs.

Microwaves are high-frequency signals in the 300 MHz to 300 GHz range. This is in contrast to radio signals, which are typically broadcast in all directions. Radio signals operate in the 3 Hz to 300 MHz range.

Microwave signals are used for both satellite and ground-based communications.

The ratio of X and Y ages at present is 4:5. 

Then, the ratio 20 years ago will not be more than the ratio at present.

So, from the options 9:10 is not satifying => its ratio is 0.9 which is greater than presnt ratio of 0.8.

An Indian boy has won the world’s largest pre-college science competition in the US in the environmental engineering category for his project on biodegradation of pesticides. Prashant Ranganathan, a 12th grader from Jamshedpur, alongwith over 20 high school students from various parts of India, participated in the Intel International Science and Engineering Fair.