CAT Questions

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Length of largest tile = H.C.F. of 1517 cm and 902 cm = 41 cm.
Area of each tile = (41 x 41) sq.cm

Required number of tiles =1517 x 902/(41 x 41) = 814.

Speed of Man = 4.5 kmph
Speed of stream = 1.5 kmph
Speed in DownStream = 6 kmph
Speed in UpStream = 3 kmph
Average Speed = (2 x 6 x 3)/9 = 4 kmph.

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

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.

A periscope is an optical instrument that uses a system of prisms, lenses, or mirrors to reflect images through a tube.

Light from a distant object strikes the top mirror and is then reflected at an angle of 90 degrees down the periscope tube. At the bottom of the periscope, the light strikes another mirror and is then reflected into the viewer’s eye.

Hence, A periscope works by the principle of Total internal reflection.

The two events mentioned are independent.

The first roll of the die is independent of the second roll. Therefore the probabilities can be directly multiplied.

P(getting first 4) = 1/6

P(no second 6) = 5/6

Therefore P(getting first 4 and no second 6) = 1/6 x 5/6 = 5/36

Let the required number of minutes = M
Total minutes between 3o'clock and 6o' clock = 180 minutes
M + 50 + 4M = 180
5M + 50 = 180
5M = 130
M = 26 minutes.

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%