GATE Questions

Q:

A rectangular block has the dimensions 5x6x7 cm it is dropped into a cylindrical vessel of radius 6cm and height 10 cm. If the level of the fluid in the cylinder rises by 4 cm, What portion of the block is immersed in the fluid ?

A) 22/7 x 24/35 B) 22/7 x 36 x 4
C) 22/7 x 36/5 D) 22/7 x 37/21
 
Answer & Explanation Answer: A) 22/7 x 24/35

Explanation:

Since level of water increased in cylinder by height 4. 

This is because of the rectangular block .

 

Therefore , area of rectangular block immersed in water is 

= 227×6×6×4  

Thats why portion of block immersed in water is 

= (22/7 * 36 * 4) / total vol. of rectangle 

= (22/7 * 36 * 4)/ (7*5*6) 

= (22/7 * 24)/ 35.

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Filed Under: Volume and Surface Area
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7 7633
Q:

The market price of an article was 40% more than its cost price. Rana was going to sell it at market price to a customer, but he showed Rana some defects in the article, due to which Rana gave him a discount of 28.57%. Next day he came again and showed Rana some more defects, hence he gave him another discount that was equal to 12.5% of the cost price. What was the approximate profit/loss to Rana ?

A) Loss of 12.5% B) Profit of 12.5%
C) Loss of 24.5% D) Profit of 22.5%
 
Answer & Explanation Answer: A) Loss of 12.5%

Explanation:

Let the cost price be Rs. 100
Then, market price is Rs. 140
Now, the first discount is of 28.57% Rs.140 =~ Rs. 40
Hence, its selling price = 140 - 40 = Rs. 100
Now since Rana is selling at cost price, any further discount will be equal to loss percentage.
The next dicount of 12.5% will be the loss percentage to Rana.

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Filed Under: Profit and Loss
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11 7627
Q:

Two pipes A and B can separately fill a cistern in 60 min and 75 min respectively. There is a third pipe in the bottom of the cistern to empty it. If all the three pipes are simultaneously opened, then the cistern is full in 50 min. In how much time, the third pipe alone can empty the cistern ?

A) 85 min B) 95 min
C) 105 min D) 100 min
 
Answer & Explanation Answer: D) 100 min

Explanation:

Work done by the third pipe in 1 min = 1/50 - (1/60 + 1/75) = - 1/100.
[-ve sign means emptying]

The third pipe alone can empty the cistern in 100 min.

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Filed Under: Pipes and Cistern
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7 7624
Q:

A man pointing to a lady says, "Her brother is the father of my only son's sister."  How is that lady related to the man ?

A) sister of father-in-law B) daughter-in-law
C) Sister D) daughter
 
Answer & Explanation Answer: C) Sister

Explanation:
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Filed Under: Blood Relations
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14 7611
Q:

In the series given below , how many 8's are there each of which is exactly divisible by its immediate preceeding as well as succeeding numbers ?
2 8 3 8 2 4 8 2 4 8 6 8 2 8 2 4 8 3 8 2 8 6

A) five B) four
C) two D) one
 
Answer & Explanation Answer: C) two

Explanation:

Clearly, we may mark such sets of 3 numbers, in which the middle number is 8 and each of the two numbers on both sides of it is a factor of 8, as shown below :


2 8 3 8 2 4 8 2 4 8 6 8 2 8 2 4 8 3 8 2 8 6

So, there are two such 8's. Hence the answer is C.

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14 7608
Q:

14 persons are seated around a circular table. Find the probability that 3 particular persons always seated together.

A) 11/379 B) 21/628
C) 24/625 D) 26/247
 
Answer & Explanation Answer: C) 24/625

Explanation:

Total no of ways = (14 – 1)! = 13!

Number of favorable ways = (12 – 1)! = 11!

 

So, required probability = 11!×3!13! = 39916800×66227020800 = 24625

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Filed Under: Probability
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22 7607
Q:

Where should a boat compass be mounted?

A) near magnet B) near iron
C) away from electrical wiring D) All the above
 
Answer & Explanation Answer: C) away from electrical wiring

Explanation:

A compass, which is used to assist in navigation, is an instrument that shows magnetic north. You must apply a correction to determine the direction of true north. The ability to steer a boat by a compass is useful if land is out of sight, visibility is reduced, or the boat operator is disoriented.

 

Mount a boat compass away from iron, magnets, and electrical wiring and equipment.

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Filed Under: Physics
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15 7599
Q:

Dronacharya Award Is Given To

A) Sports Editors B) Umpires
C) Sportsmen D) Coaches
 
Answer & Explanation Answer: D) Coaches

Explanation:

The Dronacharya Award, formally known as Dronacharya Award for Outstanding Coaches in Sports and Games, is sports training honour of the Republic of India. The award is named after Drona, often referred as "Dronacharya" or "Guru Drona", a character from the Sanskrit epic Mahabharata of ancient India.

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Filed Under: Honours and Awards
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15 7584