Mathematics Quiz

Differential Equations

• The standard form of a linear differential equation is $\frac{dy}{dx} + Py = Q$, where $P$ and $Q$ are functions of $x$.
• The integral of $Pdx$ is required to solve this type of equation.
• The integrating factor is $e^{-\int Pdx}$.

Second-Order Linear Homogeneous Differential Equations

• The general form of a second-order linear homogeneous differential equation is $y" + py = 0$.
• The differential equation of $sinpx + bcospx$ is $y" + p²y = 0$.

Vectors

• The resultant of vectors $60i + 3j$, $40i - 8j$, and $xí - 52j$ is $40$.

Direction Cosines

• The direction cosines of the vector $-3i - 6j - 2k$ are $\frac{3}{7},\frac{6}{7},\frac{2}{7}$.

Probability

• If $P(B) = \frac{5}{7}$ and $P(AUB) = \frac{3}{4}$, then $P(A) = \frac{1}{3}$.
• The formula for probability of union of two events is $P(AUB) = P(A) + P(B) - P(A ∩ B)$.

Matrices

• The inverse of the matrix $|2,3,1|$ is not given in the options.
• The determinant of a matrix is a scalar value that can be used to find the inverse of the matrix.