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We derive two-sided bounds for moments and tails of random quadratic forms(random chaoses of order $2$), generated by independent symmetric randomvariables such that $\lVert X \rVert_{2p} \leq \alpha \lVert X \rVert_p$ forany $p\geq 1$ and some $\alpha\geq 1$. Estimates are deterministic and exact upto some multiplicative constants which depend only on $\alpha$.

Tail and moment estimates for a class of random chaoses of order two