Consider two distinct positive numbers \( m, n \) with \( m > n \). Let \[ x = n^{\log_n m}, \quad y = m^{\log_m n}. \] The relation between \( x \) and \( y \) is -
Let \( M = \left(I_n - \frac{1}{n} 11^T \right) \) be a matrix where \( 1 = (1,1,\dots,1)^T \in \mathbb{R}^n \) and \( I_n \) is the identity matrix of order \( n \). The value of \[ \max_{x \in S} x^T M x \] where \[ S = \{ x \in \mathbb{R}^n \mid x^T x = 1 \} \] is ________.
R(A B C D E) F = A$\rightarrow$ BC, CD$\rightarrow$ E, E$\rightarrow$AWhich of the following is correct?
For a given data set \({X$_1$, X$_2$, ..., X$_n$}\) where n = 100 $\frac{1}{2000} \sum_{i=1}^{n} \sum_{j=1}^{n} (x_i - x_j)^2 = 99$ Let us denote $\bar{x} = \frac{1}{n}\sum_{i=1}^{n} x_i$ The value of $\frac{1}{99} \sum_{i=1}^{n} (x_i - \bar{x})^2$ is __________.
A recursive function is given: def mystery(n): if n $<=$ 0: return 1 else: return mystery(n-1) + mystery(n-2) Find the value of mystery(4).
def fun(L, i=0): if i $>=$ len(L) - 1: return 0 if L[i]> L[i+1]: L[i+1], L[i] = L[i], L[i+1] return 1 + fun(L, i+1) else: return fun(L, i+1) data = [5, 3, 4, 1, 2] count = 0 for _ in range(len(data)): count += fun(data) print(count)