Let xk be real numbers such that x_k ≥ k^4 + k^2 + 1 \for 1 ≤ k ≤ 2018. Denote N = ∑↖{2018 }↙{k=1} k . Consider the following inequalities :- I. (∑↖{2018 }↙{k=1}kx_k )^2≤N (∑↖{2018 }↙{k= 1}kx_k^2 )II. (∑↖{2018 }↙{k=1}kx_k )^2≤N(∑↖{2018 }↙{k=1}k^2x_k^2 ) Then

Question

Let xk be real numbers such that x_k ≥ k^4 + k^2 + 1 \for 1 ≤ k ≤ 2018. Denote N =  ∑↖{2018 }↙{k=1} k  . Consider the following inequalities :- I. (∑↖{2018 }↙{k=1}kx_k )^2≤N (∑↖{2018 }↙{k=  1}kx_k^2 )II. (∑↖{2018 }↙{k=1}kx_k )^2≤N(∑↖{2018 }↙{k=1}k^2x_k^2 ) Then

Examsnet · Accepted Answer

Correct Answer is :  both I and II are true

KVPY SX SB Exam 2018 Question Paper