# mock paper MC

Vehicle hiring company has 4 lorries, 4 vans and 10 drivers. 3 of the drivers can drive vans only and the others can drive

both types of vehicle. An order requiring 2lorries and 1 van (all with drivers) is received. Find the number of ways of

assigning vehicles and drivers for the order.

A. 4P2 4P1 x (10P3 - 3P1 x 3P2)

B. 4P2 4P1 x (10P3 x 3P1 x 3!)

C. 4C2 4C1 x (7P2 - 3P1 x 3!)

D. 4C2 4C1 x (7P2 x 3P1 + 7P3)

(Answer is D)

If p + qi = (4-2i)/(1+i)(q + i), where p and q are real constants, find the values of p and q.

A. p=4,q=-2

B. p = 1/4 ,q = 13/4

C. p = 1/2 ,q = - 1/2

D. Both are not real number

(Answer is B)

The figure shows the graphs of y = log xa , y = log xb , y = log xc , y = log x on the same rectangular coordinate system,

where a, b and c are constants. Which of the following must be true?

https://www.flickr.com/photos/130230543@N06/155620...

A. a < b < 1 < c

B. a < 1< b < c

C. c <a< 1 < b

D. c< b < 1 <a

(Answer is D)

Show log2c, 2log2c, 4log2c is an arithmic sequence

Peter orders either rice or noodles for his lunch every day. The probability that Peter eats in restaurant A is 1/2 and the

probability that he eats in restaurant B is 3/5. The probability that Peter orders rice in restaurant A is 1/2 and the probability

that he orders rice in restaurant B is 2/3. Given that Peter orders rice today, find the probability that he eats in restaurant A.

A. 1/5

B. 1/3

C. 2/5

D. 1/2

(Answer is B)

In the figure, O is the origin and the centre of the circle. The coordinates of A are (6, -8). AOB is a diameter of the circle. If

C is a point in the first quadrant and lies on the circle such that the area of D.ABC is the greatest, then the coordinates of

C are

https://www.flickr.com/photos/130230543@N06/159944...

A. (1, 3√11).

B. (2, 4√6).

C. (6, 8).

D. (8, 6).

(Answer is B)

The frequency polygon below shows the number of students of a tutorial centre in May, June, July and August.

https://www.flickr.com/photos/130230543@N06/159958...

A promoter makes the following claims.

I. The number of students in July is three times the number of students in June.

II. Compared with the previous month, the increase in the number of students in July is twice the increase in June.

III. From May to August, the number of students increases by 75%.

Which of the above claims are false?

A. I and II only

B. I and III only

C. II and III only

D. I, II and III

(Answer is A)

p+qi = [(4-2i)(q+i)] / (1+i)

### 3 個解答

- 邊位都好Lv 55 年 前最佳解答
1. For vehicles :Number of ways to select 2 lorries out of the 4 = 4C2Number of ways to select 1 van out of the 4 = 4C1For drivers, there are 2 possibles ways : (a) choose 1 van driver and 2 others (b) choose 3 othersNumber of ways for (a) = 3P1 * 7P2Number of ways for (b) = 7P3Therefore, number of ways of assigning for the order is :4C2 * 4C1 * (7P2 * 3P1 + 7P3) ⋯⋯⋯⋯ (D)

2. Question not clear.

3. From graph, a > 1 > b > 0 > cSo the answer is D.

4. 2log2c - log2c = log2c, and, 4log2c - 2log2c = 2log2cTheir difference is not the same, it is not an A.S.In the other way, 2log2c / log2c = 2, and, 4log2c / 2log2c = 2They have the same ratio, so, it is a G.S.

5. Wrong question, as eat in A is 1/2, eat in B is 3/5.1/2 + 3/5 = 11/10 > 1, impossible.

6. If the area is the greatest, then OC⊥AB, that is, the coordinates of C is (8, 6) ⋯⋯⋯⋯ (D)

7. Number of students in May, June, July, August are 200, 300, 400, 350 respectively.I. 400/300 = 4/3 ≠ 3 ... FalseII. Increase in July is (400-300)=100, in June is (300-200)=100. same ... FalseIII. Increase % = (350-200)/200 * 100% = 75% ... TrueSo the answer is (A)