GATE Questions

Q:

There are three rooms in a Hotel: one single, one double and one for four persons. How many ways are there to house seven persons in these rooms ?

A) 105 B) 7! x 6!
C) 7!/5! D) 420
 
Answer & Explanation Answer: A) 105

Explanation:

Choose 1 person for the single room & from the remaining choose 2 for the double room & from the remaining choose 4 people for the four person room, 

 Then, 7C1 x 6C2 x 4C

= 7 x 15 x 1 = 105

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Filed Under: Permutations and Combinations
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14 15624
Q:

Which of the following is an Autotroph?

A) Fish B) Algae
C) Butterfly D) Mushroom
 
Answer & Explanation Answer: B) Algae

Explanation:

Here from the above options, Algae is an Autotroph.

Autotrophs : 

An Autotroph is also called as Producer, is an organism that produces complex organic compounds from simple substances present in its surroundings, generally using energy from light or inorganic chemical reactions.

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Filed Under: Biology
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78 15577
Q:

A milkman claims to sell milk at its cost price, still, he is making a profit of 30% since he has mixed some amount of water in the milk. What is the % of milk in the mixture?

A) 71.02% B) 76.92%
C) 63.22% D) 86.42%
 
Answer & Explanation Answer: B) 76.92%

Explanation:

Let the milk he bought is 1000 ml

Let C.P of 1000 ml is Rs. 100

Here let he is mixing K ml of water

He is getting 30% profit

=> Now, the selling price is also Rs. 100 for 1000 ml

=> 100 : K%

= 100 : 30

10 : 3 is ratio of milk to water

=> Percentage of milk = 10 x 100/13 = 1000/13 = 76.92%

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Filed Under: Alligation or Mixture
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26 15548
Q:

If the positions of the first and the third digit within each number are interchanged, which of the following will be the third digit of the second lowest number ?

987, 514, 658, 487, 404, 269

A) 8 B) 9
C) 2 D) 4
 
Answer & Explanation Answer: D) 4

Explanation:

According to the question, after the position of the first and third digit interchanged new numbers are
789, 415, 856, 784, 404, 962

962, 856, 789, 784, 404, 415
Here the second lowest number is 404 and the last digit of it is '4'.

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55 15531
Q:

A group consists of 4 men, 6 women and 5 children. In how many ways can 2 men , 3 women and 1 child selected from the given group ?

A) 600 B) 610
C) 609 D) 599
 
Answer & Explanation Answer: A) 600

Explanation:

Two men, three women and one child can be selected in ⁴C₂ x ⁶C₃ x ⁵C₁ ways = 600 ways.

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Filed Under: Permutations and Combinations
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6 15524
Q:

What will come in place of question mark (?) in the following question?

34 of 35 of 23 of ? = 3174

A) 10550 B) 10540
C) 10580 D) 10500
 
Answer & Explanation Answer: C) 10580

Explanation:

23x35x34x?=31743174x10/3= 10580

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0 15513
Q:

In a party there are 5 couples. Out of them 5 people are chosen at random. Find the probability that there are at the least two couples ?

A) 6/7 B) 19/21
C) 7/31 D) 5/21
 
Answer & Explanation Answer: D) 5/21

Explanation:

Number of ways of (selecting at least two couples among five people selected) = (⁵C₂ x ⁶C₁)

As remaining person can be any one among three couples left.

Required probability = (⁵C₂ x ⁶C₁)/¹⁰C₅
= (10 x 6)/252 = 5/21

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Filed Under: Probability
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12 15494
Q:

Second & fourth Saturdays and every Sunday is a holiday. How many working days will be there in a month of 31 days beginning on a Friday ?

A) 24 B) 23
C) 22 D) 25
 
Answer & Explanation Answer: A) 24

Explanation:

Given that the month begins on a Friday and has 31 days

 

Sundays = 3rd, 10th, 17th, 24th, 31st
=> Total Sundays = 5

 

Every second & fourth Saturday is holiday.
2nd & 4th Saturday in every month = 2

 

Total days in the month = 31

 

Total working days = 31 - (5 + 2) = 24 days.

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Filed Under: Calendar
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68 15434