Joint Entrance Test

Joint Entrance Test 

 Once upon a time there was a quiz question "what happens if Pakistan has 

 institutes equivalent to our IITs?" The answer was .....  those institutes would than 

be called "Pakistan Institute of Technology"s or PITs for short.  

Looks Pakistan has taken the first step towards achieving this goal. A friend of mine had 

sent me an interesting mail. As usual I have not been able to resist the temptation of 

tampering with what he forwarded to me, but I hope the concoction is tastier.

The following is the Question Paper for the Joint Entrance Test (JET) to PITs to be held

on  the 1st of April 2017, followed by Communal Re-orientation Appraisal in Science & 

Humanities  (CRASH). All those who survive JET - CRASH will be absorbed into what 

is known as CRAP (Composite Research & Analytical Program) of PITs. 

JET - PITs

Instructions

i) Students found copying will be shot on the spot.

ii) Any student coming late after 10 minutes after the examination starts will be forced 

to join Al Qaida Group.

iii) AK47s and grenades are not allowed in the exam hall.

iv) Students may keep their daggers, revolvers and pack of anthrax bombs only for 

self-defence.

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Time: 3 hours                                    Math Exam                                Full Marks: 100

   All questions are compulsory.

1. Abdul was sent to jail for murder. He has 4 wives & 28 children in his house. 

Before going    to jail, Abdul distributed all the money he had to his wives in such a 

proportion that the youngest and most recent wife receives maximum and oldest 

wife gets minimum and each wife gets double of her immediate former competitor. 

Abdul distributed Rupaye 1700 that day. 

            Abdul's oldest wife needs at least Rupaye 25 per month. Find out the time when

            Abdul will have to break out of jail to come out and earn money so that his wives 

do not starve.

As an alternative, you can also design a plan of action which Abdul can initiate from 

within the jail and continue earning so that he need not break out of the jail. 

(Note : Abdul is not a political leader of the ruling party or  member of the local 

mafia which would have enabled him to live happily in the jail with some higher 

authority taking care of his family. Nor is he likely to get bail for coming out and 

carrying out his activities). 

2. Karim is a drug seller. Prices per gram of marijuana, hasish, heroin and  LSD  

    are Rupaye 50, 60, 70, and 80 respectively. Karim offers a discount of Rupaye 5,

   10, 15 and 20 per gram to his buyers who buy more than 50 grams of any single 

   drug. If Rahim, a buyer, gets Rupaye 120 as discount, find out how many grams

   of LSD he bought assuming that he purchases a minimum of 200 gms distributed

   among the four drugs on sale.

3. Aamir tampers the ball thrice per over. He deforms the ball .05% of its original shape 

    each time. Find the percentage deformation of the ball due to tampering in an ODI 

    against India in which Aamir bowled 9.3 overs. (Assume that the other bowlers

    DO NOT tamper with the ball in order to simplify the problem). 

 As a follow-up state how much fine should Match Referee Clive Lloyd impose on 

 Indian captain Virat Kohli. 

4. D runs a flourishing company conducting kidnappings for ransom and murder 

among   other ‘normal’ activities like peddling arms diverted from US supplies to

 Pakistan army, drug trafficking etc. The company has fixed expenses to run the 

company HQ and variable expenses for conducting the operations. 

In order to break even, he has to threaten 10 people per day over the telephone. 

40% of the people he threatens are movie stars in Mumbai, 30% are businessmen

 in Delhi, 20% are cricket players in Chennai and 10% are shopkeepers in Kolkata. 

If ISD charges are Rupaye 15, 25, 40, 50 per minute or part thereof from D’s city 

Islamabad to Mumbai, Delhi, Kolkata and Chennai respectively, and the average 

duration of telephone calls to the above categories is 3.5 mins, 4.29 mins, 7.12 mins 

and 2.8 mins respectively and he gets a telephone bill of Rupaye 10,230 in a month,

find out the number of movie stars in Mumbai threatened in that particular month. 

 (Disclaimer : The businessman in question does not reside in Pakistan and nor does 

 any Government official in Pakistan know about his whereabouts).

5. A terrorist group has to provide one AK 47, one AK 49, one Rocket Launcher, 

   50 Grenades and one pack of RDX to each of its recruits for training. One AK 47 

  costs $100; One AK56 costs $150, a Bazooka Rocket Launcher costs $250, 

  a grenade is $3 each, a pack of RDX bomb attached with remote control is $500. 

The terrorist group admits 2,000 new recruits every year out of which 29.84 % are 

court-martialled and another 44.91% get blown up during the practicals for the 

course Suicide Bombing 101. In addition, an estimated 62.39% of graduates will

be neutralized in surgical strikes from across the border. 

Calculate how many such terrorist camps need to be run if at least 2,500 infiltrators 

are required to be sent across the LOC in Kashmir every year. Assume the success 

ratio of infiltration is 9.75%. 

Find out how much money Pakistan Govt has to seek as humanitarian aid from 

US, G7, WHO and UNESCO (jointly and severally) to run this educational program. 

6. If X denotes the stability of democratic Govt. in Pakistan and is given by the following 

   equation : 

                         X exp3 + X exp2 - 16 = i;           Find out X.

As a corollary carry out LaPlace transform of the above function and prove that 

X à0 as t à infinity where t measures the time from current date.

7. Probability of a Pakistani Prime Minister would be shot while holding office is 78%. 

   Probability of a serving army General coming to a violent end is 43%. 

   Find out the probability that a Prime minister who is also an army General will get 

   shot while holding office. Conversely prove that there exists a non-zero probability

   of an army General shooting a Prime Minister. 

8. Find out geometrically the area of Balochistan using Pythagoras Theorem with

   Osama Bin Laden’s correction (That is taking the value of Pi = 7.86 instead of 3.14....), 

   if  Balochistan is taken as a regular heptagon.

9. If Al Qaida is planning to attack some US installations during the midnight Christmas          mass Eastern Time, when should President Sharif phone President of USA  conveying his   deepest sympathies for the losses suffered:

a.  2359 hrs Pakistan local time on 24^th Dec

b.  0001 hrs Pakistan local time on 25^th Dec

c.  0800 hrs Pakistan local time on 25^th Dec

10. If the current budgetary deficit of Pakistan is US $ 10.5 billion and the annual rate of      growth of revenues and expenditure are (-) 3.2% and + 5.9% respectively, find out how   many squadrons of F16s should Pakistan buy from US every year. The current price of a   single F16 can be assumed to be US$ 125 million per plane, and will rise @5% p.a. Assume a squadron consists of 50 planes.

 As per the past experience, wars with India were fought when the budgetary  deficit crosses US$ 50 billion. Find out when the next war with India will be fought.