let p ∈K_n [x] snd A and H two rlements of K[x]
1) prove that p(A(x)+H(x))=Σ_(k=0) ^n ((p^((k)) (A(x)))/(k!)).(H(x))^k
2)find the condition that p(A(x)+H(x))is
divided by H(x)≠0
3) if p(x)≠c prove that p(p(x))−x is divided
by p(x)−x.
please help me solve these two
questions
1. A magician cuts a rope into two
parts at a point selected at
random. what is the probability that
the length of the longer rope is at least
8 times the length of the shorter
rope.
2. find the sum of co−efficient of
thebinomial expansion of
(4x−1)^(16)
A delegation of 4 students is to be
selected from a total of 12 students.
In how many ways can the delegation
be selected if:
1) 2 particular students wish to be
included together only in the delegation?
2) 2 particular students refuse to be
together and 2 other particular students
wish to be together only in the delegation?
Three prizes are awarded each for
getting more than 80%marks,
98% attendance and good
behaviour in the college.In how
many ways the prozes can be
awarded if 15 student of the college
are eligible for the three prizes?