The mean of 12 observations is 75. If two observation are discarded, then the mean of the remaining observations is 65. What is the mean of the discarded observations?

If k is one of the roots of the equation x(x + 1) + 1 = 0, then what is its other root?

The geometric mean of a set of observations is computed as 10. The geometric mean obtained when each observations x_i is replaced by $\rm 3x_i^4$ is

If $\rm P(A\cup B)=\dfrac{5}{6}, P(A\cap B)=\dfrac{1}{3}\:and\:P(\bar A)=\dfrac{1}{2}$, then which of the following is/are correct?

1. A and B are independent events.

2. A and B are mutually exclusive events.

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