Find the Truth - April Fool's Edition

Algebra Level 5

This is a part of set Find the Truth

So April Fool's Day has arrived and it's time for the ultimate test.

"True or False is not easy as 1-2-3"- Anonymous

Note: This is not a troll question.

(1) If the first term of a GP is 2, product of first five terms is 32, product of first 9 terms is 512, then the sum of first 3 terms is 6.

(2) When velocity and acceleration due to gravity are given, area under projectile is maximum when angle of projection is \({ 45 }^{ o }\). Neglect all other values like air resistance

(3) In any series with only positive terms, following the rule \({ t }_{ n }={ t }_{ n-1 }+{ t }_{ n-2 }\), where \({ t }_{ n }\) is the nth term, the ratio of a term to its previous term tends to \(\frac { 1+\sqrt { 5 } }{ 2 } \), as n approaches infinite.

(4) If f(x) is an even function, then f'(x) is always an even function.

(5) If f(x) is an even function, then f'(x) is never an even function.

(6) If f'(x) is an even function, then f(x) is always an odd function.

Add the serial numbers of all true statements in the list. If all are false, then answer is 0.


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