Quadratic Equations
If α, β, γ, δ are the four positive roots of the equation x4 -12x3+ax2+bx +81=0, then find “a” and “b”.
2
Permutations and Combinations
Find all possible arrangements of the word "COMBINATORICS" such that all the vowels are in alphabetical order and consonants are also in alphabetical order.
Note: Consonants and vowels to be considered separately.
Note: These are not puzzles but JEE-level questions
8 comments:
Is the Answer to d P & C question 1162 ? If it is wrong do tell me if i am near d answer or not.
COMBINATORICS - 1287
ananth is right
The answer is 13 C 5
the first question involves observation..observe the given details carefully
i think th first ans is :
a = 54 and b = -108
and 2nd ques. : my logic: COMBINATORICS
2 GPS: [O I A O A]
& [C M B N T R C S]
BOTH to be arranged in alpha order - 1 way each. but 2 gps : 2 arrangements: so my ans. : 2
but i may have understood ques wrongly
if 13 C 5 is right tell me logic as well please
your 1st answer is correct.please give the explanation
i hope you enjoyed the question
2nd
just chose 5 places for vowels
man i misunderstood the 1st quest
i thoought u were saying treat vowels and conson. as diff gps even in arrangmnt
otherwise its just chose any 5 spots : 13 C 5 and arrange in alpha order.... so ananth is correct
for 1st one : eqn with real co-eff.:
so sum of roots : 12
prod : 81
root : 3
a = -6(3.3)
b = 4(3.3.3) ...(as per theory of eqns.)
assuming the first question to be subjective, please give ample reason(s) to prove that the root is 3.
(though it can be found through observation)
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