6 Questions
What is the integrating factor for the differential equation $\frac{dy}{dx} + Py = Q$?
$e^{-\int Pdx}$
What is the differential equation for $sinpx + b cospx$?
$y'' + p^2y = 0$
Given the position vectors $60i +3j$, $40i-8j$, $xi-52j$, what is the value of $x$ for them to be collinear?
$40$
What are the direction cosines of the perpendicular to $-39-62-3=0$?
$\frac{2}{3}, \frac{3}{6}, \frac{6}{7}$
If $2P(B)=\frac{5}{7}$ and $P(A \cup B) = \frac{3}{4}$, what is $P(A)$?
$\frac{1}{2}$
What is the inverse of $2|24|$?
None of these
Study Notes
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.
This quiz covers various topics in mathematics, including differential equations, trigonometry, and vectors.
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