CAT 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

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

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

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.

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

The boring of India’s first underwater rail tunnel under the Hooghly River for establishing metro link between Howrah and Kolkata has completed before its scheduled deadline of July 2017. The tunnel is 16.6 km long, out of which 10.8 km runs under the ground. Of this 10.8 km, 502 metres is under the water and the whole thing connects Howrah to the west and Salt lake to the east. It will have 12 stations and six will be underground. Estimated cost of the entire project is $750 million or about Rs 5,000 crores. The final commissioning of the project is expected by December 2019, following which it will be operational. The project is built by Afcons Transtonnelstroy and implemented by Kolkata Metro Railway Corporation Ltd (KMRCL).

Paytm Payments Bank becoming the first bank to offer cash backs on deposits. Customers will also be offered zero charges on all online transactions and no minimum balance requirement. The Payments Bank plans to roll out 31 branches and 3,000 customer service points in the first year. For savings accounts, it will offer an interest of 4 percent per annum. It will also offer current accounts to its millions of merchants.

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.