CAT Questions

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For the first time since Nagaland officially gained recognition as a state, a state Police Officer AtuZumvu has been awarded one of the nations' military honour, ‘Shaurya Chakra’.

From the given information; 

Members   Sex    Profession  

     A         M          Advocate
     Q         F           Doctor
     B         M          Advocate
     R         F           Advocate
     C         M          Doctor
     S         F           Doctor
     D         M          Doctor
     T         F           Teacher
     E         M          Teacher
     U         F           Teacher
     P         F           Doctor

 Answer (D)

 From option (D) A and B are two male advocates, P and S are two female doctors and u is female teacher.

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

The series follows the following pattern

5 X 5 – 5 = 20

20 X 4 – 4 = 76

76 X 3 – 3 = 225

225 X 2 – 2 = 448

Hence, the term 225 denoted by (d) completes the series

A can complete the work in 12 days working 8 hours a day

=> Number of hours A can complete the work = 12×8 = 96 hours 

=> Work done by A in 1 hour = 1/96

B can complete the work in 8 days working 10 hours a day

=> Number of hours B can complete the work = 8×10 = 80 hours 

=> Work done by B in 1 hour = 1/80

Work done by A and B in 1 hour = 1/96 + 1/80 = 11/480

 => A and B can complete the work in 480/11 hours

A and B works 8 hours a day.

Hence total days to complete the work with A and B working together 

= (480/11)/ (8) = 60/11 days

Let the required height of the building be x meter

More shadow length, More height(direct proportion)

Hence we can write as

(shadow length) 40.25 : 28.75 :: 17.5 : x
⇒ 40.25 × x = 28.75 × 17.5
⇒ x = 28.75 × 17.5/40.25
= 2875 × 175/40250
= 2875 × 7/1610
= 2875/230
= 575/46
= 12.5 cm

Glass snake is a lizard.

According to the question, after the position of the first and third digit interchanged new numbers are
789, 415, 856, 784, 404, 962

962, 856, 789, 784, 404, 415
Here the second lowest number is 404 and the last digit of it is '4'.