GATE Questions

Q:

Rushi and Arun are two business partners. They invest their capital in the ratio 7 : 9. After 6 months, a third person Ram joins them with a capital of two third of that of Arun. After a year, profit share of Rushi was Rs. 5600, then find total profit?

A) 26,250 B) 19,200
C) 18,650, D) 15,200
 
Answer & Explanation Answer: D) 15,200

Explanation:

Ratio of investment of all the three members = (7 x 12) : (9 x 12) : (2/3 x 9 x 6)

= 7 : 9 : 3

Given Rushi's one year profit = Rs. 5600

=> Let the total profit = Rs. P

Then,

P x 7/19 = 5600

Total profit P = 19 x 5600/7 = Rs. 15,200.

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Filed Under: Partnership
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8 7268
Q:

What is the total no of ways of selecting atleast one item from each of the two sets containing 6 different items each?

A) 2856 B) 3969
C) 480 D) None of these
 
Answer & Explanation Answer: B) 3969

Explanation:

We can select atleast one item from 6 different items = 26-1  

 

Similarly we can select atleast one item from other set of 6 different items in 26-1 ways. 

 

Required number of ways = (26-1)26-1 = 26-12 = 3969

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Filed Under: Permutations and Combinations
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1 7254
Q:

A group of 10 representatives is to be selected out of 12 seniors and 10 juniors. In how many different ways can the group be selected if it should have at least one senior ?

A) ²²C₁₀ + 1 B) ²²C₉ + ¹⁰C₁
C) ²²C₁₀ D) ²²C₁₀ - 1
 
Answer & Explanation Answer: D) ²²C₁₀ - 1

Explanation:

The total number of ways of forming the group of ten representatives is ²²C₁₀.
The total number of ways of forming the group that consists of no seniors is ¹⁰C₁₀ = 1 way
The required number of ways = ²²C₁₀ - 1

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Filed Under: Permutations and Combinations
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2 7252
Q:

5 L from A are V?

Answer

5 L from A are V --- 5 Letters from Alphabets are Vowels.


 

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13 7251
Q:

A restaurant offers a new promotion of 20% off the original price of cakes, which is Rs. 12. Before the promotion 250 cakes were sold each day. After the promotion, the sale of cakes increases an average of 18% more per day. How much more or less does the restaurant make each day in cakes sales after the promotion?

A) Rs. 185 less B) Rs. 202 more
C) Rs. 175 more D) Rs. 168 less
 
Answer & Explanation Answer: D) Rs. 168 less

Explanation:

Cost of each cake P1 & P2 = Rs. 12

Offer decrease in % = 20%

Increase in sale per day (Q2) = 250 - 18%

Total quantity per day (Q1) = 250

Hence, required change total revenue

TR = P2Q2 - P1Q1 = (12 x 0.8 x 250 x 1.18) -  (12 x 250) = - Rs.168.

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Filed Under: Percentage
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15 7242
Q:

What is the length of the longest pole which can be kept in a room 12 m long, 4 m broad and 3 m high  ?

A) 13 m B) 14 m
C) 15 m D) 16 m
 
Answer & Explanation Answer: A) 13 m

Explanation:

The length of the longest pole which can be kept in a room 12 m long, 4 m broad and 3 m high is

 

=>  d2 = 122 + 42 + 32 = 13mts.

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Filed Under: Area
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13 7240
Q:

Which of the following has the highest entropy?

A) Hydrogen B) Diamond
C) Liquid nitrogen D) Mercury
 
Answer & Explanation Answer: A) Hydrogen

Explanation:

Entropy is a measure of disorder . It will be maximum in gases followed by liquids and least in solids.

 

Hence, here the gas is only hydrogen and it has the highest entropy.

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Filed Under: Physics
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8 7236
Q:

A boat whose speed in still water is 9 kmph, goes 12 km downstream and comes back in 3 hrs. Find the speed of the stream?

A) 1 kmph B) 3 kmph
C) 5 kmph D) 4 kmph
 
Answer & Explanation Answer: B) 3 kmph

Explanation:

Let the speed of the stream = x kmph

 

From the given data,

 

 129+x+129-x=3 hrs

3x2 = 27

 

=> x = 3 kmph

 

Therefore, the speed of the stream = 3 kmph

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Filed Under: Boats and Streams
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