Let the positive numbers a1,a2,a3,a4 and a5 be in a G.P. Let their mean and variance be 1031 and nm respectively, where m and n are co-prime. If the mean of their reciprocals is 1031 and a3+a4+a5=14, then m+n is equal to ____________.
Held on 12 Apr 2023 · Verified 6 Jul 2026.
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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:
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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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