If $A = \\begin{bmatrix} 1 & 2 \\\\ 3 & 4 \\end{bmatrix}$, then $|A|$ (determinant of $A$) is:

Evaluate: $\\dfrac{d}{dx}\\left[\\tan^{-1}\\left(\\dfrac{x}{1+\\sqrt{1-x^2}}\\right)\\right]$ at $x = \\dfrac{1}{2}$:

The integral $\\int e^x\\left(\\dfrac{1 + \\sin x}{1 + \\cos x}\\right) dx$ equals:

If $f(x) = |\\cos x|$, then $f'(x)$ at $x = \\dfrac{\\pi}{2}$ is:

A die is thrown twice. What is the probability that the sum of the numbers appearing on the dice is 8?

If $P(A) = \\dfrac{3}{5}$, $P(B) = \\dfrac{1}{3}$, and $P(A \\cap B) = \\dfrac{1}{5}$, then $P(A \\cup B)$ is:

A random variable $X$ has the probability distribution: $P(X = 0) = \\dfrac{1}{5}$, $P(X = 1) = \\dfrac{2}{5}$, $P(X = 2) = \\dfrac{2}{5}$. Find $E(X)$:

If $A$ and $B$ are independent events with $P(A) = 0.6$ and $P(B) = 0.4$, then $P(A \\cup B)$ is:

If $\\vec{a} = 2\\hat{i} + 3\\hat{j} - \\hat{k}$ and $\\vec{b} = \\hat{i} - \\hat{j} + 2\\hat{k}$, find the angle between $\\vec{a}$ and $\\vec{b}$:

Find the area of the parallelogram whose adjacent sides are $\\vec{a} = \\hat{i} + \\hat{j} + \\hat{k}$ and $\\vec{b} = \\hat{i} + 2\\hat{j} + 3\\hat{k}$: