Daily Math · 2026-05-14

Question 1

The matrix $A = \begin{pmatrix} 2 & 4 \ 1 & 2 \end{pmatrix}$ is:

Accepted Answer

$\det A = 0$, so $A$ is singular (not invertible).

Answer

invertible

Answer

not invertible

Answer

diagonal

Answer

the identity

Question 2

$\displaystyle\lim_{x 	o 0} \dfrac{\sin 3x}{	an 5x}$ equals:

Accepted Answer

$\dfrac{\sin 3x}{	an 5x} = \dfrac{\sin 3x}{3x} \cdot \dfrac{5x}{	an 5x} \cdot \dfrac{3}{5} 	o 1 \cdot 1 \cdot \dfrac{3}{5} = \dfrac{3}{5}$.

Answer

$	frac{3}{5}$

Answer

$	frac{5}{3}$

Answer

$1$

Answer

$0$

Question 3

For $n \ge 2$, the sum of all $n$th roots of unity equals:

Accepted Answer

The polynomial $z^n - 1$ has zero coefficient for $z^{n-1}$, so by Viète's formula the sum of its roots is $0$. Equivalently, the geometric sum $\sum_{k=0}^{n-1} e^{2\pi i k / n} = \dfrac{1 - 1}{1 - e^{2\pi i / n}} = 0$ (for $n \ge 2$).

Answer

$0$

Answer

$1$

Answer

$n$

Answer

$\dfrac{1}{n}$

Problems & worked solutions

Problem 1 — Matrix Equations

Problem 2 — Calculus

Problem 3 — Complex Numbers