33 If there are $74$ heads and $196$ legs, how many horses and humans are there? 17 Proof that square of an $\sqrt{2 - 4q}$ is not an integer 16 Prove that $n$ is also a power of $2$. 16 Is there a perfect square in the sequence $6, 96, 996, 9996, … , 99999…996, …$? 15 Subtracting empty set from another

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 +10 $\lim_{n \to \infty} (\frac{(n+1)(n+2)\dots(3n)}{n^{2n}})^{\frac{1}{n}}$ is equal to : +20 Evaluation of $\int_{\frac{1}{2014}}^{2014} \frac{\tan^{-1}x}{x} dx$ +20 What is the expected length of the hypotenuse formed by bending a unit length randomly at a right angle? +10 If $\sin C=\frac{\sin A}{2\cos B}$, then prove that the triangle is isosceles

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### Tags (150)

 137 calculus × 68 54 sequences-and-series × 20 130 algebra-precalculus × 47 50 limits × 20 85 integration × 40 44 elementary-set-theory × 7 64 elementary-number-theory × 14 42 definite-integrals × 13 58 combinatorics × 19 41 derivatives × 14