Job Roles

A person can be chosen out of 18 people in 18 ways to be seated between Musharraf and Manmohan. Now consider Musharraf, Manmohan, and the third person, sitting between them, as a single personality, we can arrange them in 17! ways but Musharraf and Manmohan can also be arranged in 2 ways. 

Required number of permutations = 18 x (17!) x 2 = 2 x 18!

There are 7 digits 1, 2, 0, 2, 4, 2, 4 in which 2 occurs 3 times, 4 occurs 2 times.

 Number of 7 digit numbers = 7!3!×2! = 420

But out of these 420 numbers, there are some numbers which begin with '0' and they are not 7-digit numbers. The number of such numbers beginning with '0'.

=6!3!×2! = 60

Hence the required number of 7 digits numbers = 420 - 60 = 360

There are total 9 places out of which 4 are even and rest 5 places are odd.

4 women can be arranged at 4 even places in 4! ways.

and 5 men can be placed in remaining 5 places in 5! ways.

Hence, the required number of permutations  = 4! x 5! = 24 x 120 = 2880

If all the A's are dropped from the above arrangement, we get

C U B E D E D B E B U C D B C D B D U B C C B E D. 

Here the eleventh from the left end of the above arrangement is U

The whole of India, south of the Himalayas can be climatically treated as a tropical country as the Himalayas provide the barrier effect. 

Indian subcontinent is separated from the rest of Asia by the lofty Himalayan ranges which block the cold air masses moving southwards from Central Asia.

 As a result, during winters, the northern half of India is warmer by 3°C to 8°C than other areas located on same latitudes.

During summer, due to over the head position of the sun, the climate in the southern parts resemble equatorial dry climate.

The seasonal reversal of winds in Arabian Sea and Bay of Bengal give India a typical tropical monsoon climate.

So Indian climate, to be precise, is Tropical monsoon type (a distinct wet and dry climate) rather than just a tropical or half temperate climate.

wine(left)wine(added) = 343169

It means  wine(left)wine(initial amount) = 343512    (since 343 + 169 = 512)

Thus,  343x = 512x1 - 15k3

 343512 = 783 = 1 - 15k3

 1-15k=78=1-18

Thus the initial amount of wine was 120 liters.

Let the initial amount of honey in the jar was k, then

 512 = k1 - 154 or 512 = k454 

 => k = 512 × 625256 

=> k = 1250

 Hence initially the honey in the jar = 1.25 kg

The amount of petrol left after 4 operations  

= 200 × 1-402004  

= 200 × 454  

= 200 × 256625  

= 81.92 litres

Hence the amount of kerosene = 200 - 81.92 = 118. 08 litres