ISRO CSE 2023

Given P is a 4x4 matrix $\begin{bmatrix} 3 & 2 & 1 & 4 \\ 4 & 0 & 3 & 1 \\ 6 & 4 & 2 & 8 \\ 2 & 5 & 1 & 3 \end{bmatrix}$. If det|P| denotes the determinant of P, which statement is true?

Which of the following is true for a graph G with n vertices and e edges?

A box contains 5 red balls and 10 white balls. Two balls are drawn at random one after another without replacement. What is the probability that both balls are red?

Which of the following is a necessary condition for a square matrix A to be invertible?

The complexity of matrix multiplication of two matrices A and B whose orders are m x n and n x p respectively is