Question

State the reason why the Relation R = {(a, b) : a ≤ b²} on the set R of real numbers is not reflexive.

If $A_{i j}$ is the cofactor of the element $a_{i j}$ of the determinant $\begin{vmatrix}2 & -3 & 5 \\ 6 & 0 & 4 \\ 1 & 5 & -7\end{vmatrix}$ , then write the value of $a_{32}A_{32}.$

Write the value of λ so that the vectors $\stackrel{\rightarrow}{a}\$ = $2 \stackrel{\wedge}{i}+λ\stackrel{\wedge}{j} +\stackrel{\wedge}{k}$ and $\stackrel{\rightarrow}{b}\$ = $\stackrel{\wedge}{i}-2\stackrel{\wedge}{j} +3\stackrel{\wedge}{k}$ are perpendicular to each other ?

Find the scalar components of the vector $\stackrel{\rightarrow}{A B}$ with initial point A(2,1) and terminal point B (– 5, 7).

If a matrix has 5 elements, then write all possible orders it can have.

Write the order of the differential equation: $\log\,\left(\frac{d^{2}y}{d x^{2}}\right)=\left(\frac{d y}{d x}\right)^{3}+x$

Write the degree of the differential equation $\left({\frac{d^{2}s}{d t^{2}}}\right)^{2}+\left({\frac{d s}{d t}}\right)^{3}+4=0.$