CAT Questions

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The given word HAPPYHOLI has 9 letters

These 9 letters can e arranged in 9! ways.

But here in the given word letters H & P are repeated twice each

Therefore, Number of ways these 9 letters can be arranged is 

9!2! x 2! = 9 x 8 x 7 x 6 x 5 x 4 x 32 = 90,720 ways.

Accoustics is a subject deals with the Study of sound

Aesthetics is a Philosophy of fine arts

The science or art of flight is called Aeronautics

The science of soil management is called Agronomy.

It is a Postbox or a Mailbox which contains thousands of letters or mails or messages.

The first written story that has come down to us is The Epic of Gilgamesh.

It is a mythologized account of a historical figure, Gilgamesh, a ruler of the Sumerian city-state of Uruk, believed to have ruled sometime between 2700-2500 BC.

The More You Have the Darkness, The Less You See i.e, visible less.

Chennai port is known for its Coastal breakwater, artificial, large seaport type of harbor.

Chennai Port, formerly known as Madras Port, is the second largest container port of India, behind the Nhava Sheva Port, and the largest port in the Bay of Bengal. It is the third oldest port among the 13 major ports of India

Let the required two numbers be a, b

From the given data,

2a + 3b = 36 .....(1)

3a + 2b = 39 .....(2)

Now, by solving 1 and 2 eqnts, we get

5a = 45

a = 9 ....(3)

Put (3) in (1), we get

2(9) + 3b = 36

=> 18 + 3b = 36

3b = 36 - 18

=> b = 18/3 = 6

Required, difference between the numbers = a + b = 9 + 6 = 15.

We know that,  Speed = Distance/time

Let the speed of the train be = x kmph

           NORMAL SPEED                           SPEED 5 KMPH MORE

          Distance = 360 Km                         Distance =360
 
          speed    =  X Kmph                        Speed = (x+5)
 
            Time =360/X                              Time =360/(x+15)
          

For the same journey if the speed increased 10 kmph more it will take 1 hour less

Time with original speed - time with increased speed = 1

 => (360/x) - (360/x+10) =  1                               

 =>  (360(x+5)-360x)/x(x+5) =1

 =>   360X + 1800 -360X  = X(X+5)

  =>   X^2 + 5x - 1800 = 0

  X = 40 or -45

 X cannot be negetive value
                  

 X = 40 kmph.