CUET Mathematics Mock Test - 3

Let $R$ be a relation on the set of natural numbers defined by $xRy⟺x\le y$. Which one of the following is correct?

If a function is defined as $f:\mathbb{N}\to \mathbb{N},f(x)=\frac{x-1}{2}$, then which of the following is true regarding this function?

For a Linear Programming Problem, $Z=2x+4y$. Feasible corner points are $O(0,0),A(0,2.5),B(3,1),C(4,0)$. What is the optimal maximized value of $Z$?

$M$ is a square matrix of order $n$ and $|M|=5$. If all elements of $M$ are multiplied by $2$, the determinant becomes $40$. The value of $n$ is:

Evaluate: ${\tan }^{-1}(1)+{\cos }^{-1}(-1/2)+{\sin }^{-1}(-1/2)$