CAT Questions

Q:

There is an empty reservoir whose capacity is 30 litres. There is an inlet pipe which fills at 5 L/min and there is an outlet pipe which empties at 4 L/min. Both the pipes function alternately for 1 minute. Assuming that the inlet pipe is the first one to function, how much time will it take for the reservoir to be filled up to its capacity?

A) 49.5 min B) 50 min
C) 51 min D) 52 min
 
Answer & Explanation Answer: C) 51 min

Explanation:

The work to be done = Capacity of reservoir  = 30 litres.

 1st Minute ---> inlet pipe opened ---> 5 lit filled

 2nd minute ---> inlet pipe closed; outlet pipe opened ---> 4 lit emptied

 

In 2 minutes (5 litres - 4 litres = 1lit) is filled into the reservoir.

It takes 2 minutes to fill 1lit ---> it takes 50 minutes to fill 25 litres into the reservoir.  

 

In the 51st minute inlet pipe is opened and the reservoir is filled.

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Filed Under: Pipes and Cistern
Exam Prep: CAT
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24 9043
Q:

A person of good understanding knowledge and Reasoning power

A) Snob B) Expert
C) Literate D) Intellectual
 
Answer & Explanation Answer: D) Intellectual

Explanation:

The one word substitute for A person of good understanding knowledge and Reasoning power is Intellectual.

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9 9042
Q:

Buying and selling goods over the internet is called

A) Digital Marketing B) E - Commerce
C) Net Banking D) Onine Shopping
 
Answer & Explanation Answer: B) E - Commerce

Explanation:

Buying and selling goods over the internet is called E - Commerce.

 

buying_and_selling_goods_over_the_internet_is_called1553690676.png image

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Filed Under: General Awareness
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6 9039
Q:

Anu's present age is 9 years more than that of what Raj's age will be after five years. Raj's present age is seven years more than that of what Renu's age was 4 years ago. Renu's present age is 19 years. What will be Anu's age after 5 years ?

A) 39 yrs B) 36 yrs
C) 46 yrs D) 41 yrs
 
Answer & Explanation Answer: D) 41 yrs

Explanation:

Anu = (Raj + 5) + 9

= Raj + 14 -------- (I)

Raj = (Renu - 4) + 7

= Renu + 3 ------- (II)

Raj's age = 19 + 3 = 22 years

After 5 years Anu's age = 22 + 14 + 5 = 41 years

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Filed Under: Problems on Ages
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9 9038
Q:

Cyanide is historically found in the following except

A) Teflon B) Cherries
C) Apricots D) All of the above
 
Answer & Explanation Answer: A) Teflon

Explanation:

Cyanide is historically found in the following except Teflon. Cyanide is found in the stones of cherries, apricots,...

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Filed Under: General Science
Exam Prep: AIEEE , Bank Exams , CAT
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5 9036
Q:

There are 44 students in a hostel, due to the administration,  15 new students has joined. The expense of the mess increase by Rs. 33 per day. While the average expenditure per head diminished by Rs. 3, what was the original expenditure of the mess ?

A) Rs. 404 B) Rs. 514
C) Rs. 340 D) Rs. 616
 
Answer & Explanation Answer: D) Rs. 616

Explanation:

Let the average expenditure per head be Rs. p
Now, the expenditure of the mess for old students is Rs. 44p
After joining of 15 more students, the average expenditure per head is decreased by Rs. 3 => p-3
Here, given the expenditure of the mess for (44+15 = 59) students is increased by Rs. 33
Therefore, 59(p-3) = 44p + 33
59p - 177 = 44p + 33
15p = 210
=> p = 14
Thus, the expenditure of the mess for old students is Rs. 44p = 44 x 14 = Rs. 616.

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Filed Under: Average
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11 9018
Q:

Calculate the number of bricks, each measuring 25 cm x 15 cm x 8 cm required to construct a wall of dimensions 10 m x 4 cm x 6 m when 10% of its volume is occupied by mortar  ?

A) 720 B) 600
C) 660 D) 6000
 
Answer & Explanation Answer: A) 720

Explanation:

Let the number of bricks be 'N'

10 x 4/100 x 6 x 90/100 = 25/100 x 15/100 x 8/100 x N

10 x 4 x 6 x 90 = 15 x 2 x N => N = 720.

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Filed Under: Area
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6 9017
Q:

A box contains 4 different black balls, 3 different red balls and 5 different blue balls. In how many ways can the balls be selected if every selection must have at least 1 black ball and one red ball ?

A) 24 - 1  

B) 2425-1   

C) (24-1)(23-1)25   

D) None 

A) A B) B
C) C D) D
 
Answer & Explanation Answer: C) C

Explanation:

It is explicitly given that all the 4 black balls are different, all the 3 red balls are different and all the 5 blue balls are different. Hence this is a case where all are distinct objects.

 

Initially let's find out the number of ways in which we can select the black balls. Note that at least 1 black ball must be included in each selection.

 

Hence, we can select 1 black ball from 4 black balls
or 2 black balls from 4 black balls.
or 3 black balls from 4 black balls.
or 4 black balls from 4 black balls.

 

Hence, number of ways in which we can select the black balls

 

= 4C1 + 4C2 + 4C3 + 4C4
= 24-1 ........(A)

 

Now let's find out the number of ways in which we can select the red balls. Note that at least 1 red ball must be included in each selection.

 

Hence, we can select 1 red ball from 3 red balls
or 2 red balls from 3 red balls
or 3 red balls from 3 red balls

 

Hence, number of ways in which we can select the red balls
= 3C1 + 3C2 + 3C3
=23-1........(B)

 

Hence, we can select 0 blue ball from 5 blue balls (i.e, do not select any blue ball. In this case, only black and red balls will be there)
or 1 blue ball from 5 blue balls
or 2 blue balls from 5 blue balls
or 3 blue balls from 5 blue balls
or 4 blue balls from 5 blue balls
or 5 blue balls from 5 blue balls.

 

Hence, number of ways in which we can select the blue balls
= 5C0 + 5C1 + 5C2 + … + 5C5
= 25..............(C)

 

From (A), (B) and (C), required number of ways
=  2524-123-1

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Filed Under: Permutations and Combinations
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3 9013