[简答题]Question 9 (Total: 20 marks) X and Y are in partnership sharing profits and losses in the ratio 3:2. They agree to draw interest on their capital at 8% p.a.; an annual salary to Y of $50,000; and interest on drawings at 10% p.a.; and to allow interest on loans from partners at p.a. The capitals of the partners are to be kept intact. The financial information of the partnership as at 31 january 2001 disclosed the following: $ $ Capital : X 1,000,000 Y 600,000 1600,000 Current Accounts : X 52,600 Cr Y 10,420 Cr 63,020 Loan from X 300,000 Net capital employed 1,963,020 The partners took drawings on 1 July 01: X $60,000; Y $ 30,000 Net trading profit for the year ended 31 December 2001 before interest and salaries to partners was $ 250,000. Required:

[简答题]Question 7 (Total: 20 marks) The book of Delta Ltd as at 31 December 2001 showed the following balances: $ Ordinary share capital ($1 per share) 3,000,000 8% Preferential Share capital ($1 per share) 300,000 Retained earnings at 1 Jan 2001 62,000 Plant and machinery at cost 6,000,000 Provision for depreciation of plant and machinery 2,400,000 Sales 8,000,000 Purchases 4,500,000 Discounts received from suppliers 200,000 Trading stock at 1 Jan 2001 500,000 Trade debtors 600,000 Bad debts written off 40,000 Provision for doubtful debts at 1 Jan 2001 30,000 Trade creditors 200,000 Auditors’ fees 90,000 Salaries and wages 700,000 Rents and rates 1,200,000 General expenses 500,000 Interim Preferential dividend paid 12,000 Cash 50,000 Additional informations Trading stock at 31 December 2001 was $700,000

[简答题]Question 8 (Total: 20 marks) Mr Lee is a sole trader. He does not know accounting and he only keeps records of cash receipts and payments. The following is a statement of a receipts and payments of his business for the year ended 31.12 .01: $ $ Cash in hand 1.1.01 50,400 Payments for goods 1,131,000 Sales receipts 1,569,000 Transport expenses 87,000 Cash put in by Mr Lee 26,000 Rents and rates 38,100 Loan from Mr Wong 200,000 Wages paid to office assistants 60,000 Drawings by Mr Lee 120,000 Purchase of equipment 400,000 ________ Balance at 31.12.01 9,300 1,845,400 1,845,400 Further information: (a) The loan from Mr Wong was received on 1.1.01 . Interest payable is 10% p.a. (b) The equipment was purchased on 1.1.01. Estimated life is 5 years with no residue value. Depreciation should be provided for it on the straight line mrthod. (c) The assets and liabilities of Mr Lee were as follows: 1.1.01 31.12.01 $ $ Stock in trade at cost 150,000 240,000 Trade debtors 138,000 200,000 Trad

[单项选择]设线性无关的函数y₁（x），y₂（x），y₃（x）都是微分方程y"+p（x）y'+q（x）y=f（x）的解，c₁，c₂是任意常数，则此方程的通解为（）。
A. y=c₁y₁(x)+c₂y₂(x)+(1-c₁-c₂)y₃(x)
B. y=c₁y₁(x)+c₂y₂(x)-(1-c₁-c₂)y₃(x)
C. y=c₁y₁(x)+c₂y₂(x)-(c₁+c₂))y₃(x)
D. y=c₁y₁(x)+c₂y₂(x)+y₃(x)

[简答题]设f(x，y)=(x-6)(y+8)，求函数f(x，y)在点(x，y)处的最大的方向导数g(x，y)，并求g(x，y)在区域D=(x，y)|x²+y²≤25)上的最大值与最小值．

[填空题]有以下程序
void f( int y, int *x)
y=y+*x; *X=*X+y;
main（　）
int x=2,y=4;
f(y,&x);
printf("%d %d/n",x,y);

执行后输出结果是______。

[填空题]有以下程序：
void f(int y,int *x)
y=y+*x; *x=*x+y;
main（　）
int x=2,y=4;
f(y,&x);
printf("%d %d/n",x,y);

执行后输出结果是上 【11】 。

[填空题]设x=x(y，z)，y=y(z，x)，z=z(x，y)均为由方程f(x，y，z)=0所确定的具有连续偏导数的函数，则x’_y·y’_z·z’_x=______．

[单项选择]设函数f(x，y)满足f_x(x₀，y₀)=(x₀，y₀)=0，则函数f(x，y)在点(x₀，y₀)处( )
A. 一定连续
B. 一定有极值
C. 一定可微
D. 偏导数一定存在

[单项选择]有以下程序

int f1(int x,int y)

return x＞y x:y;

int f2(int x,int y)

return x＞y y:x;

main( )

int a=4,b=3,c=5,d,e,f;

d=f1(a,b);d=f1(d,c);

e=f2(a,b);e=f2(e,c);

f=a+b+c-d-e;

cout＜＜d＜＜","＜＜f＜＜","＜＜e＜＜endl;



执行后输出结果是
A. 3,4,5
B. 5,3,4
C. 5,4,3
D. 3,5,4

[单项选择]设x和y均为int型变量，则以下语句：“x+=y;y=x-y;x-=y;”的功能是______。
A. 把x和y按从大到小排列
B. 把x和y按从小到大排列
C. 无确定结果
D. 交换x和y中的值

[简答题]已知(X，Y)在直线y=0，y=1，y=x+1，y=x围成的区域D内服从二维均匀分布，
求X，Y的边缘概率密度；

[填空题]若|x|=5，|y|=4，且|x-y|+x-y=0，则x+y的值是（）。

[简答题]已知(X，Y)在直线y=0，y=1，y=x+1，y=x围成的区域D内服从二维均匀分布，
求X+Y的方差。

[简答题]已知(X，Y)在直线y=0，y=1，y=x+1，y=x围成的区域D内服从二维均匀分布，
求X与Y的协方差cov(X，Y)；