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?

Consider the function $f: \mathbb{R} \rightarrow \mathbb{R}$ defined as follows:

$$ f(x)=\left\{\begin{array}{cc} c_1 e^x-c_2 \log _e\left(\frac{1}{x}\right), & \text { if } x>0 \\ 3, & \text { otherwise } \end{array}\right. $$

where $c_1, c_2 \in \mathbb{R}$.

If $f$ is continuous at $x=0$, then $c_1+c_2=$ $\_\_\_\_$ . (answer in integer)