18 Questions
What is the sum of a symmetric matrix and a skew-symmetric matrix?
A zero matrix
What is the derivative of $\sin(x)\sin(x)$ with respect to $x$?
$2\cos(x)\sin(x)$
For $x = a(\theta + \sin(\theta))$ and $y = a(1 - \cos(\theta))$, what is $dx$ in terms of trigonometric functions?
$\tan(2\theta)$
In which intervals is the function $f(x) = 10 - 6x - 2x^2$ decreasing?
$(-\infty, -1)$ and $(1, \infty)$
What is the result of evaluating $\int (x-1)(x-2) dx$?
$x^3 - 3x^2 + 4x$
What is the area of the parallelogram formed by vectors $\mathbf{a} = \mathbf{i} + \mathbf{j} - \mathbf{k}$ and $\mathbf{b} = \mathbf{i} - \mathbf{j} + \mathbf{k}$?
$8$
Which of the following correctly represents the inverse of the product of invertible matrices A and B?
(AB)^{-1} = A^{-1}B^{-1}
Given x = a(θ - sinθ) and y = a(1 + cosθ), what is dx?
dx = -a cos(θ)
For the function f(x) = x^2 - 4x + 6, in which interval is f decreasing?
(2, ∞)
What is the integral of (x+1)(x+2) dx?
(x^2 + 3x + 4) + C
Given sec^2(x) tan(y) dx + sec^2(y) tan(x) dy = 0, solve the differential equation.
y = x
If one defective item is randomly chosen from a stockpile containing items from machines A and B, what is the probability it was produced by machine B?
0.40
If the function 𝑓(𝑥) = 𝑎𝑥 + 𝑏$ is continuous for $2 < x < 10$, what are the values of a and b?
a = 1, b = 0
Using the equation 𝐴² - 𝐴 + 2𝐼 = 𝑂, find the inverse of matrix A if 𝐴 = $\begin{bmatrix}4 & -2 \ 4 & -2 \end{bmatrix}$, 𝐼 is 2x2 identity matrix, and 𝑂 is the zero matrix.
$\begin{bmatrix}0.5 & 0.5 \ -1 & 2 \end{bmatrix}$
In the relation 𝑅 = {(1,1), (2,2), (3,3), (1,3)}, which ordered pair should be added to make R the smallest equivalence relation?
(2,1)
Given the function 𝑓: 𝑅 → 𝑅 as 𝑓(𝑥) = |𝑥| for 𝑥 ∈ 𝑅, what type of function is 𝑓?
Neither one-one nor onto function
If a function is both one-one and onto, what type of function is it?
Bijection
What is the result when the determinant of a matrix is zero?
The matrix is non-invertible
This quiz involves finding the values of a and b in a given function and solving a matrix equation. It also requires finding the inverse of a matrix satisfying the equation A^2 - A + 2I = O, where I is the identity matrix and O is the zero matrix. Questions are based on preparatory model question paper for Mathematics.
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