Statement-1 : The variance of first n even natural numbers is 4n2−1 Statement-2 : The sum of first n natural numbers is 2n(n+1) and the sum of squares of first n natural numbers is 6n(n+1)(2n+1)
Held on 30 Apr 2009 · Verified 6 Jul 2026.
Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1
Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1
Statement-1 is true, Statement-2 is false
Statement-1 is false, Statement-2 is true
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A bag contains 10 balls out of which $k$ are red and ($10-k$) are black, where $0 \leq k \leq 10$. If three balls are drawn at random without replacement and all of them are found to be black, then the probability that the bag contains 1 red and 9 black balls is:
If X follows a Poisson distribution with P(X=1) = P(X=2) then the mean of the distribution is:
If the mean and the variance of the data \(\begin{array}{|c|c|c|c|c|} \hline \text{Class} & 4\text{-}8 & 8\text{-}12 & 12\text{-}16 & 16\text{-}20 \\ \hline \text{Frequency} & 3 & \lambda & 4 & 7 \\ \hline \end{array}\) are $\mu$ and 19 respectively, then the value of $\lambda+\mu$ is
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Let the mean and the variance of seven observations $2, 4, \alpha, 8, \beta, 12, 14$, $\alpha < \beta$, be $8$ and $16$ respectively. Then the quadratic equation whose roots are $3\alpha + 2$ and $2\beta + 1$ is :
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