Ashish Gupta

 13 Find the value of $\sqrt{1+\frac{1}{1^2}+\frac{1}{2^2}}+\sqrt{1+\frac{1}{2^2}+\frac{1}{3^2}}+…+\sqrt{1+\frac{1}{1999^2}+\frac{1}{2000^2}}$ 4 Geometrical interpretation $|z-1| = Re(z+1)$ 4 Conditional Probability (Where did I go wrong?) 3 From a group of $10$ boys and $5$ girls, a committee of $6$ students containing at least $2$ girls in chosen at random. 3 How do you find the sum: $\sum_{r=1}^6 \tan^2\left(\frac{r \pi}{n}\right)$

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### Questions (19)

 11 How do you evaluate $\int_{0}^{\frac{\pi}{2}} \frac{(\sec x)^{\frac{1}{3}}}{(\sec x)^{\frac{1}{3}}+(\tan x)^{\frac{1}{3}}} \, dx ?$ 10 How do you find the value of $\sum_{r=0}^{44} \tan^2(2r+1)$? 8 How do you find the maximum value of $|z^2 - 2iz+1|$ given that $|z|=3$, using triangle inequality? 6 What is the probability of a pen touching a bar given that the length of the pen is $10$ cm and the bars are regularly spaced at $15$ cm? 6 How do you solve this limit involving definite integration?

### Tags (36)

 15 sequences-and-series × 7 3 trigonometric-series × 3 10 complex-numbers × 6 3 geometry × 3 9 probability × 5 3 analytic-geometry × 2 3 contest-math × 14 2 definite-integrals × 4 3 summation × 3 2 combinatorics × 3