One degree of freedom goes to the total

Consider a six faced die whose i-th face is marked with i dots, i = 1, 2, …, 6. In a single random throw of the die, let $p_i$ denote the probability that the obtained upper face has i dots, i = 1, 2, …, 6. The die is rolled 240 times independently and the following result is obtained — face observed 1, 2, 3, 4, 5, 6 with frequencies 40, 55, 40, 25, 35, 45 respectively. Suppose we want to test $H_0:p_i=1/6$ for i = 1, 2, …, 6; against $H_1:p_i\ne 1/6$ for at least one i. It is given that ${\chi }_5^2{;}_0{.}_{05}=11.07,{\chi }_6^2{;}_0{.}_{05}=12.59,{\chi }_5^2{;}_0{.}_{01}=15.09,{\chi }_6^2{;}_0{.}_{01}=16.81$. Based on the asymptotic goodness of fit ${\chi }^2$ test for testing $H_0$ against $H_1$, which of the following statements are true?