# IMBA 线上笔试

/15 MSc in IMBA - Admission Examination

IMBA Admission Exam  2022

Instructions
- You will have 60 minutes to complete this exam.
- Questions in this exam will be presented one at a time.

- During this exam you won’t be permitted to review previous questions.

- Partial credit will be given when steps or thinking flow are shown.
- The answers in the Math part within 2 decimal places whenever necessary.

- Answer mathematics term or equation in scientific method,

e^2, sin(x), ln(x), a/b, …

- You must only attempt this exam once. Any additional attempts should only be used in the event where a serious technical issue has occurred and supporting evidence supporting this will be required.

1 / 15

If a matrix has eight elements, find the possible orders of the matrix. (5pts)

2 / 15

A mathematics book containing 20 pages. One sheet is missing among them. Sum of the page numbers of the remaining pages of the mathematics book is 195. The numbers written on both the sides of the missing sheet of the mathematics book must be?   (10pts)

Show steps

3 / 15

A, B and C entered into a partnership. A invested $2560 and B invested$ 2000. At the end of the year, they gained $1105, out of which A got$ 320.C’s capital was –  (10pts)

4 / 15

In an election between two candidates, the candidates who gets 30% of the vote pulled is defeated by 15000 votes. The number of votes polled by the winning candidate is :(5pt)

5 / 15

A man spends 1/5 of his salary on food, 1/10 of his salary on house rent, and 3/5  of his salary on clothes. He still has \$18000 left with him. Find his salary. (10pts)

6 / 15

The average of x₁, x₂, x₃, x₄ is 16. Half the sum x₂, x₃, x₄ is 23. What is the value of x₁? (10pts)

7 / 15

729 ml of mixture contains milk and water in the ratio 7:2. How much more water is to be added to get a new mixture containing milk and water in the ratio 7:3? (10pts)

8 / 15

If n(A - B) = 18, n(A ∪ B) = 70 and n(A ∩ B) = 25, then find n(B).  (10pts)

9 / 15

Find the domain of the given function.  (10 pt)

f(x,y)=ln(2x3y+1)

10 / 15

Tony is our CUHKSZ soccer player. He makes a goal 65% of the time he shoots. Tony is going to attempt two goals in a row in the next game.

A = the event Tony is successful on his first attempt. P(A) = 0.65.

B = the event Tony is successful on his second attempt.

P(B) = 0.65.

Tony tends to shoot in streaks. The probability that he makes the second goal GIVEN that he made the first goal is 0.90. (15 pts)

a. What is the probability that he makes both goals?

b. What is the probability that Tony makes either the first goal or the second goal?

11 / 15

How many ways can the letters of the word "CUHKSZ" can be arranged?

12 / 15

Determine the area of the region bounded by   and .   (10 pt)

13 / 15

Let A and B be two finite sets such that n(A) = 20, n(B) = 28 and n(A ∪ B) = 36, find n(A ∩ B). (10 pts)

14 / 15

If the average of three consecutive even numbers is 34, find the largest of these numbers.(5 Pt)

15 / 15

General Code

sum(range(1,5))=？    (5 pts)

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