# JEE AITS probs,need help!

1]If median AD of a triangle ABC makes angle 30 degrees with side BC then $(\cot B-\cot C)^2$ is equal to?Options:6,9,12,15.  2]$T_n=\sum_{r={2n}}^{3n-1}\dfrac{rn}{r^2+n^2},S_n=\sum_{r={2n+1}}^{3n}\dfrac{rn}{r^2+n^2}$.Then,$T_n,S_n >\ or\ < \dfrac{\ln 2}{2}$.

3 years, 6 months ago

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For number 1, this is what I thought of:

The way the question is worded implies that the result of $(\cot{B}-\cot{C})^2$ is always the same regardless of what the values of $m\angle{B}$ and $m\angle{C}$ are. You can use this to your advantage.

Let $m\angle{ADC}=30^\circ$, and let $m\angle{C}=90^\circ$. Now $\cot{C}=0$, and you can use 30/60/90 triangle relationships to find $\cot{B}$. I hope this helps!

- 3 years, 6 months ago

The second one is based on a Jee 2008 question . I'll post the solution next week if you want me to. :)

- 3 years, 6 months ago

Yep... Its a JEE problem based on Riemann Sums....

- 3 years, 6 months ago

Best of luck for tmmrw!

- 3 years, 6 months ago

Thanks..... :-)

- 3 years, 6 months ago

But how can we use that bcoz we don't know that n tends to infinity?  And yes,best of luck!

- 3 years, 6 months ago

A definite integral is bounded between 2 summations

- 1 year, 2 months ago

- 3 years, 6 months ago

Is the ans. Tn> ln2/2 and Sn<ln2/2 ?. You should see this video https://www.khanacademy.org/math/integral-calculus/indefinite-definite-integrals/riemann-sums/v/simple-riemann-approximation-using-rectangles

- 3 years, 6 months ago