AIEEE Questions

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We know that perimeter of rectangle = 2(l+b) = 2(8+7)= 30cm
Given perimeter of square is twice the perimeter of rectangle = 2(30) = 60cm
Therefore, side of the square is = 1/4 x 60 = 15cm
Circumference of the required semicircle = πr + 2r = 227× 152 + 2×152 = 23.57 + 15 = 38.57cm.

The Upanishads are commonly referred to as Vedanta. 

The Upanishads alone are widely known and among the most important literature in the history of Indian religions and culture and their central ideas are at the spiritual core of Hindus.

The upanishads are a part of the Vedas and are ancient Sanskrit texts that contain some of the central philosophical concepts and ideas of Hinduism, some of which are shared with Buddhism, and Jainism.

We are having with digits 2, 3, 4, 5 & 6 and numbers greater than 4000 are to be formed, no digit is repeated.

The number can be 4 digited but greater than 4000 or 5 digited.

Number of 4 digited numbers greater than 4000 are
4 or 5 or 6 can occupy thousand place => 3 x P34 = 3 x 24 = 72. 

5 digited numbers = P55 = 5! = 120 

So the total numbers greater than 4000 = 72 + 120 = 192

Let total population = p
number of females = 5p/9
number of males =(p-5p/9) = 4p/9
married females = 30% of 5p/9 = 30x5p/100x9 = p/6
married males = p/6
unmarried males =(4p/9-p/6) = 5p/18
Percentage of unmarried males in the total males = {(5p/18)/4p/9}x100 = (5p/18)x(9/4p) = 125/2 % = 62.5%

P( selecting atleast one couple) = 1 - P(selecting none of the couples for the prize) 

 = 1-16C1× 14C1×12C1×10C116C4=1539

Total ages of 80 boys = 15 x 80 = 1200 yrs.
Total age of 16 boys = 15 x 16 = 240 yrs
Total age of 25 boys = 14 x 25 = 350 yrs.
Average age of remaining boys = 1200 - (240+350) / 80 - (25+15) = 610/41 = 15.25 yrs.

Better is compared with worst and slower must be compared with quickest since fast is the extreme of it.

Hence, Better is to worst as slower is to quickest.

To find the greatest number which divides the numbers 964, 1238 and 1400 leaving the remainders 41, 31 and 51 is nothing but the HCF of (964 - 41), (1238 - 31), (1400 - 51).

Therefore, HCF of 923, 1207 and 1349 is 71.