GATE Questions

Q:

The number of ways in which six boys and six girls can be seated in a row for a photograph so that no two girls sit together is  ?

A) 2(6!) B) 6! x 7
C) 6! x ⁷P₆ D) None
 
Answer & Explanation Answer: C) 6! x ⁷P₆

Explanation:

We can initially arrange the six boys in 6! ways.
Having done this, now three are seven places and six girls to be arranged. This can be done in ⁷P₆ ways.

Hence required number of ways = 6! x ⁷P₆

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Filed Under: Permutations and Combinations
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Q:

Wild animals are not considered a natural resource.

A) TRUE B) FALSE
Answer & Explanation Answer: B) FALSE

Explanation:

Natural resources are resources taken from nature to satisfy our needs. As wild animals are on the earth naturally, they are considered as natural resources.


 


Hence, the given statement is false.

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Subject: General Science
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Q:

What is the Probability of all cars not clashing each other ?

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A) 1/8 B) 0
C) 1/4 D) 1
 
Answer & Explanation Answer: C) 1/4

Explanation:

Non collision can happen only when all the cars move in same direction.

That is either all cars moving in clockwise direction or all cars moving in anti clockwise direction.
P(all cars not colliding)

= P(all cars moving in the same direction)

= P(all cars moving in clockwise direction)  +  P(all cars moving in anticlockwise direction)

= [p(A --> C) x p(C --> B) x p(B --> A)]  +  [p(A --> B) x p(B --> C) x p(C --> A)]

= [1/2 x 1/2 x 1/2] + [1/2 x 1/2 x 1/2]

= 1/8 + 1/8

= 1/4

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Filed Under: Math Puzzles
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Q:

7 C in the R?

Answer

The given letter equation implies that, 


7 C in the R = 7 Colours in a Rainbow.

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Subject: Logic Puzzles Exam Prep: GATE , CAT , Bank Exams , AIEEE
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Q:

What is the gram formula mass of Li2SO4?

A) 101.2487 B) 109.9446
C) 111.2687 D) 106.5871
 
Answer & Explanation Answer: B) 109.9446

Explanation:

The term gram formula mass is synonymous with molecular mass. So, to get this, we must add molar mass of all the elements in this compound.

 

Given compound is Lithium Sulphate - Li2SO4

Elemental calculation ::

Li  -  Lithium   -   6.941    -     2   -   13.88200 %
S  -  Sulfur     -    32.065   -    1   -   32.065 %
O  -  Oxygen   -   15.9994  -    4   -   63.9976 %

Now, total = 12.6264 + 29.1647 + 58.2090 = 109.9446 

 

Hence, the gram formula mass of Li2SO4 = 109.9446.

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Filed Under: Chemistry
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Q:

The average monthly salary of 24 employees in an organisation is Rs. 1500. If the manager's salary is added, then the average salary increases by Rs. 400. What is the manager's monthly salary ?

A) Rs. 8840 B) Rs. 11,500
C) Rs. 12,800 D) Rs. 9450
 
Answer & Explanation Answer: B) Rs. 11,500

Explanation:

Manager's monthly salary

= Rs. (1900 x 25 - 1500 x 24) = Rs. 11,500

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Q:

A train covers 180 km distance in 5 hours. Another train covers the same distance in 1 hour less. What is the difference in the distances covered by these trains in one hour if they are moving in the same direction?

A) 15 kms B) 9 kms
C) 6 kms D) 18 kms
 
Answer & Explanation Answer: B) 9 kms

Explanation:

The first train covers 180 kms in 5 hrs

=> Speed = 180/5 = 36 kmph

Now the second train covers the same distance in 1 hour less than the first train => 4 hrs

=> Speed of the second train = 180/4 = 45 kmph

Now, required difference in distance in 1 hour = 45 - 36 = 9 kms.

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Filed Under: Time and Distance
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Q:

A person travels from K to L a speed of 50 km/hr and returns by increasing his speed by 50%. What is his average speed for both the trips ?

A) 55 kmph B) 58 kmph
C) 60 kmph D) 66 kmph
 
Answer & Explanation Answer: C) 60 kmph

Explanation:

Speed on return trip = 150% of 50 = 75 km/hr.

Average speed = (2 x 50 x 75)/(50 + 75) = 60 km/hr.

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Filed Under: Time and Distance
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