An urn contains one red ball and one blue ball. At each step, a ball is picked uniformly at random from the urn, and this ball together with another ball of the same color is put back in the urn. The probability that there are equal number of red and blue balls after two steps is

Consider $4 \times 4$ matrices with their elements from $\{0,1\}$. The number of such matrices with even number of 1 s in every row and every column is

For $n>1$, the maximum multiplicity of any eigenvalue of an $n \times n$ matrix with elements from $\mathbb{R}$ is

Let $n>1$. Consider an $n \times n$ matrix $M$ with its elements from $\mathbb{R}$. Let the vector ( 0,1 , $0,0, \ldots, 0) \in \mathbb{R}^n$ be in the null space of $M$.

Which of the following options is/are always correct?