Mathematics Quiz
6 Questions
1 Views

Choose a study mode

Play Quiz
Study Flashcards
Spaced Repetition
Chat to lesson

Podcast

Play an AI-generated podcast conversation about this lesson

Questions and Answers

What is the integrating factor for the differential equation $\frac{dy}{dx} + Py = Q$?

  • $\int Pdx$
  • None of these
  • $e^{-\int Pdx}$ (correct)
  • $Pdx$

    • What is the differential equation for $sinpx + b cospx$?

  • $y'' + p^2y = 0$ (correct)
  • $y'' - py = 0$
  • $y''=0$
  • $y - p^2y = 0$

    • Given the position vectors $60i +3j$, $40i-8j$, $xi-52j$, what is the value of $x$ for them to be collinear?

  • $-20$
  • $-40$
  • $40$ (correct)
  • $30$

    • What are the direction cosines of the perpendicular to $-39-62-3=0$?

    <p>$\frac{2}{3}, \frac{3}{6}, \frac{6}{7}$</p> Signup and view all the answers

    If $2P(B)=\frac{5}{7}$ and $P(A \cup B) = \frac{3}{4}$, what is $P(A)$?

    <p>$\frac{1}{2}$</p> Signup and view all the answers

    What is the inverse of $2|24|$?

    <p>None of these</p> Signup and view all the answers

    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.

    Studying That Suits You

    Use AI to generate personalized quizzes and flashcards to suit your learning preferences.

    Quiz Team

    Description

    This quiz covers various topics in mathematics, including differential equations, trigonometry, and vectors.

    More Like This

    Use Quizgecko on...
    Browser
    Open
    Browser
    Browser