AIEEE Questions

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For solving this problem first we would break the whole range in 5 sections

1) From 1 to 9
Total number of zero in this range = 0

2) From 10 to 99
Total possibilities = 9*1 = 9 ( here 9 is used for the possibilities of a non zero integer)

3) From 100 to 999 - three type of numbers are there in this range
a) x00 b) x0x c) xx0 (here x represents a non zero number)
Total possibilities
for x00 = 9*1*1 = 9, hence total zeros = 9*2 = 18
for x0x = 9*1*9 = 81, hence total zeros = 81
similarly for xx0 = 81
total zeros in three digit numbers = 18 + 81 +81 = 180

4) From 1000 to 9999 - seven type of numbers are there in this range
a)x000 b)xx00 c)x0x0 d)x00x e)xxx0 f)xx0x g)x0xx
Total possibilities
for x000 = 9*1*1*1 = 9, hence total zeros = 9*3 = 27
for xx00 = 9*9*1*1 = 81, hence total zeros = 81*2 = 162
for x0x0 = 9*1*9*1 = 81, hence total zeros = 81*2 = 162
for x00x = 9*1*1*9 = 81, hence total zeros = 81*2 = 162
for xxx0 = 9*9*9*1 = 729, hence total zeros = 729*1 = 729
for xx0x = 9*9*1*9 = 729, hence total zeros = 729*1 = 729
for x0xx = 9*1*9*9 = 729, hence total zeros = 729*1 = 729
total zeros in four digit numbers = 27 + 3*162 + 3*729 = 2700
thus total zeros will be 0+9+180+2700+4 (last 4 is for 4 zeros of 10000)
= 2893

As given
200 cats kill 200 mice in 200 days
1 cats kill 1 mouse in 200 days
Then
8 cats kill 8 mice in 200 days.

A compass, which is used to assist in navigation, is an instrument that shows magnetic north. You must apply a correction to determine the direction of true north. The ability to steer a boat by a compass is useful if land is out of sight, visibility is reduced, or the boat operator is disoriented.

Mount a boat compass away from iron, magnets, and electrical wiring and equipment.

Initial wheat per kg cost be Rs. 100

Then, monthly expenditure of the family = 30 x 100 = 3000

After increase in cost,

Let P be new monthly consumption of family.

P x 132 = 110/100 x 3000

=> P = 25 kg.

Alcohol has a freezing point as low as -117oC. So it won't freeze even in very cold countries.

Bad loans in banking terminology are generally known as NPA's. A Non - performing Asset (NPA) is defined as a credit facility in respect of which the interest and installment of principal have remained 'past due' for a specified period of time.

LCM of 4, 6, 8 and 10 = 120
120) 1000 (8
960
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40

The least number of four digits which is divisible by 4, 6, 8 and 10 => 1000 + 120 - 40 = 1080.