GATE Data Science & AI

Consider two distinct positive real numbers m, n, with m > n. Let x = nlog10(m) and y = mlog10(n). The relation between x and y is _________.

Five integers are picked from 0 to 20, with possible repetitions, such that their mean is 12, median is 18, and they have a single mode of 20. Ignoring permutations, the number of...

In the given figure, P, Q, and R are three points on a circle of radius 10 cm with O as its center, PQ = RQ, and ∠PQR = 45°. The figure is representative. The area of the shaded re...

Let f(x) = x^3 - 3x^2 + 2 be a function defined on (-1, 3]. Which of the following statements is/are correct?

Let L = lim_{n→∞} Σ_{k=0}^{n} (e^{-n} n^k / k!) Which of the following is the value of L?

Let $\gamma_1, \gamma_2, \gamma_3$ be the eigenvalues of the matrix $\begin{bmatrix} 1 & 0 & 0 \\ 0 & \cos t & \sin t \\ 0 & -\sin t & \cos t \end{bmatrix}$, where $t \in [-\pi, \p...

For a given data set {x1, x2, ..., xn}, where n = 100, it is known that $\frac{1}{2000} \sum_{i=1}^{n} \sum_{j=1}^{n} (x_i - x_j)^2 = 99$ Let us denote $\bar{x} = \frac{1}{n} \sum_...

Let X be a random variable that follows Uniform(-1,1) distribution. The conditional distribution of the random variable Y given X = x is the Uniform($x^2 - 0.1, x^2 + 0.1$) distrib...

Let A$_{5 \times 5}$ be a matrix such that each of its elements follows Bernoulli(p = 0.50) distribution independently. The probability that the row-sum of the second row and the c...

Let A = $(I_n - \frac{1}{n} \mathbf{1} \mathbf{1}^T)$ be a matrix, where $\mathbf{1} = (1,1,1, ...,1)^T \in \mathbb{R}^n$ and $I_n$ is the identity matrix of order n. The value of...