GATE Questions

Q:

fifteen persons are sitting around a circular table facing the centre. What is the probability that three particular persons sit together ?

A) 3/91 B) 2/73
C) 1/91 D) 3/73
 
Answer & Explanation Answer: A) 3/91

Explanation:

In a circle of n different persons, the total number of arrangements possible = (n - 1)!
Total number of arrangements = n(S) = (15 – 1)! = 14 !
Taking three persons as a unit, total persons = 13 (in 4 units)
Therefore no. of ways for these 13 persons to around the circular table = (13 - 1)! = 12!
In any given unit, 3 particular person can sit in 3!. Hence total number of ways that any three person can sit =
n(E) = 12! X 3!
Therefore P (E) = probability of three persons sitting together = n(E) / n(S) = 12! X 3 ! / 14!
= 12!x3x2 / 14x13x12! = 6/14x13 = 3/91

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Q:

A man can row 8 kmh in still water. If the river is running at 2 kmh, it takes 4 hrs more upstream than to go downstream for the same distance. Then the distance is given by

A) 54 kms B) 32 kms
C) 45 kms D) 60 kms
 
Answer & Explanation Answer: D) 60 kms

Explanation:

Let the distance be d.

 d8-2-d8+2 = 4

 

=> 2d = 120 

 

=> d = 60 kms.

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23 12097
Q:

Two numbers are respectively 40% and 30% more than a third number. The second number expressed in terms of percentage of the first is ?

A) 92.8% B) 84.23%
C) 87.14% D) 94.1%
 
Answer & Explanation Answer: A) 92.8%

Explanation:

Here, x = 40 and y = 30;
Therefore second number
= [[100+y100+x] x 100 ]% of first number
= [[100+y100+x] x 100 ]% of first number
Second number = 92.8% of the first number.

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12 12092
Q:

A Committee of 5 persons is to be formed from a group of 6 gentlemen and 4 ladies. In how many ways can this be done if the committee is to be included atleast one lady?

A) 123 B) 113
C) 246 D) 945
 
Answer & Explanation Answer: C) 246

Explanation:

A Committee of 5 persons is to be formed from 6 gentlemen and 4 ladies by taking. 

 

(i) 1 lady out of 4 and 4 gentlemen out of 6 

(ii) 2 ladies out of 4 and 3 gentlemen out of 6 

(iii) 3 ladies out of 4 and 2 gentlemen out of 6 

(iv) 4 ladies out of 4 and 1 gentlemen out of 6 

 

In case I the number of ways = C14×C46 = 4 x 15 = 60 

In case II the number of ways = C24×C36 = 6 x 20 = 120 

In case III the number of ways = C34×C26 = 4 x 15 = 60

In case IV the number of ways = C44×C16 = 1 x 6 = 6 

 

Hence, the required number of ways = 60 + 120 + 60 + 6 = 246

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Filed Under: Permutations and Combinations
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10 12091
Q:

How many seconds in 10 years?

A) 31523500 sec B) 315360000 sec
C) 315423000 sec D) 315354000 sec
 
Answer & Explanation Answer: B) 315360000 sec

Explanation:

We know that,

1 year = 365 days

1 day = 24 hours

1 hour = 60 minutes

1 minute = 60 seconds.

 

Then, 1 year = 365 x 24 x 60 x 60 seconds.

= 8760 x 3600

1 year = 31536000 seconds.

 

Hence, 10 years = 31536000 x 10 = 315360000 seconds.

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Q:

An exhibition was conducted for 4 weeks. The number of tickets sold in 2nd workweek was increased by 20% and increased by 16% in the 3rd workweek but decreased by 20% in the 4th workweek. Find the number of tickets sold in the beginning, if 1392 tickets were sold in the last week ?

A) 1124 B) 1420
C) 1345 D) 1250
 
Answer & Explanation Answer: D) 1250

Explanation:

Let initially 'X' ticket has been sold.
So now in 2nd week 20% increases, so
=> X x 120/100
In 3rd week 16% increases, so
=> X x (120/100) x (116/100)
In 4th week 20% decrease, so
=> X x (120/100) x (116/100) x (80/100) = 1392
X = 1250.

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6 12063
Q:

Which of the following is the fastest communication channel?

A) Microwave B) Optical fiber
C) Radio wave D) All are operating at nearly the same propagation speed
 
Answer & Explanation Answer: A) Microwave

Explanation:

A microwave is the fastest communication channel whereas Optical fiber is a way of transferring data not a way of communication.

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Filed Under: Physics
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Q:

The Basic Architecture of Computer was developed by

A) Charles Babbage B) Blaise Pascal
C) Garden Moore D) John Von Neumann
 
Answer & Explanation Answer: D) John Von Neumann

Explanation:

Computer Architecture refers to how a computer system is designed and what technologies it is compatible with. In brief, Computer architecture is a specification detailing how a set of software and hardware technology standards interact to form a computer system or platform.  

                                     comp1518074667.jpg image 

The Von Neumann Architecture, which is also known as the Von Neumann Model and Princeton architecture, is a computer architecture based on the 1945 description of computer by the mathematician and physicist John von Neumann.

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