AIEEE Questions

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Proof of Sum of cubes of first n even natural numbers ::

Hence, in other words, the sum of the first n cubes is the square of the sum of the first n natural numbers.

Urea is a by product of amino acid catabolism, Which occurs in the liver. The nitrogen in the  amino acid becomes converted to ammonia and this is further converted by the liver into urea

Ans. Let radius of the base and height of the cone be ‘r’ & ‘h’ respectively.

Then volume of cone = πr2h/3 For cylinder, radius is reduced by 4 times = r/4 And,  height is increased by 8 folds = 8h Volume of cylinder = πR2H = π(r/4)2 (8h) = (16/8)πr2h = πr2h/2 Ratio of volume of cone to volume of cylinder = (πr2h/3) : (πr2h/2) Or, Ratio = 2 : 3.

Venus planet is known as the Morning Star or the Evening Star.

Exercise frequency refers to number of times you exercise per week.