Concours ENSPY Practice Questions - Concours ENSPY - École Nationale Supérieure Polytechnique de Yaoundé (Cameroon) Exam - Concours ENSPY Practice Questions - Concours ENSPY - École Nationale Supérieure Polytechnique de Yaoundé (Cameroon) Exam

Question 1

Let $z_1 = 1 + i\sqrt{3}$ and $z_2 = 1 - i$. What is the trigonometric/polar form of the quotient $Z = \frac{z_1}{z_2}$?

Z = \sqrt{2} \left(\cos\left(\frac{7\pi}{12}\right) + i \sin\left(\frac{7\pi}{12}\right)\right) Z = \sqrt{2} \left(\cos\left(\frac{\pi}{12}\right) + i \sin\left(\frac{\pi}{12}\right)\right) Z = 2 \left(\cos\left(\frac{7\pi}{12}\right) + i \sin\left(\frac{7\pi}{12}\right)\right) Z = 1 \left(\cos\left(\frac{5\pi}{12}\right) + i \sin\left(\frac{5\pi}{12}\right)\right)

Correct Answer:

Z = \sqrt{2} \left(\cos\left(\frac{7\pi}{12}\right) + i \sin\left(\frac{7\pi}{12}\right)\right)

Question 2

What is the determinant of the $3 \times 3$ real matrix $A = \begin{pmatrix} 2 & 1 & 3 \\ 0 & 4 & -1 \\ 0 & 0 & 5 \end{pmatrix}$?

40 0 20 11

Correct Answer:

Question 3

A geometric sequence $(u_n)$ of positive terms satisfies $u_2 = 12$ and $u_5 = 96$. What is its common ratio $q$ and its first term $u_0$?

q = 2 and u_0 = 3 q = 2 and u_0 = 6 q = 4 and u_0 = 3 q = 8 and u_0 = 1.5

Correct Answer:

q = 2 and u_0 = 3

Question 4

Find the eigenvalues $\lambda$ of the matrix $M = \begin{pmatrix} 3 & 1 \\ 2 & 2 \end{pmatrix}$.

λ₁ = 4 and λ₂ = 1 λ₁ = 3 and λ₂ = 2 λ₁ = 5 and λ₂ = 0 λ₁ = 2 and λ₂ = -1

Correct Answer:

λ₁ = 4 and λ₂ = 1

Question 5

What is the cross product $\vec{u} \times \vec{v}$ of vectors $\vec{u} = (1, 2, 3)$ and $\vec{v} = (4, 5, 6)$ in $\mathbb{R}^3$?

(-3, 6, -3) (3, -6, 3) (32, 32, 32) (0, 0, 0)

Correct Answer:

(-3, 6, -3)

Question 1

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Prepare with the Concours ENSPY Practice Questions - Concours ENSPY - École Nationale Supérieure Polytechnique de Yaoundé (Cameroon) Exam practice quiz. This question bank includes 100 questions covering text, frac, mass, pmatrix, and velocity. Use it to review important concepts, identify knowledge gaps, and build confidence for the related exam, course, or assessment.

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Concours ENSPY Practice Questions - Concours ENSPY - École Nationale Supérieure Polytechnique de Yaoundé (Cameroon) Exam

This practice set contains 100 questions from the matching question bank and focuses on text, frac, mass, pmatrix, and velocity. Work through each question carefully, review the provided solutions, and revisit topics that need more study before your next attempt.

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Concours ENSPY Practice Questions - Concours ENSPY - École Nationale Supérieure Polytechnique de Yaoundé (Cameroon) Exam

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