New user? Sign up

Existing user? Sign in

Let \(n \ge 3\) be an integer. For an ordered n-tuple of permutation \(\sigma\) of \((1,2, \cdots ,n)\), where \(\sigma = \left(a_1, a_2,\cdots, a_n \right)\) let a function ...

Let \(A_n = \max \left\{ \dbinom{n}{k} : 0 \le k \le n \right\}\) where \(n\) is a positive integer between 1 and 20 (both inclusive). Find the number of such ...

Two spherical objects each of radii \(R\) and masses \(m\) and \(M\) are suspended using two strings of equal length \(\ell\) as shown below (assume \(\ell >> R\)). What is ...

\[\large \int \frac{x^2+20}{(x \sin x+ 5 \cos x)^{2}} dx = \frac{-Ax}{\cos x (x \sin x + B \cos x)} +\tan x + C\]

Find ...

\[ \large \displaystyle \sum_{i\ne j, j\ne k, k\ne i } \frac{1}{2^i 2^j 2^k} = \frac{a}{b}, \] where \(i,j,k\) are distinct whole ...

Problem Loading...

Note Loading...

Set Loading...