q1. The directors of Motive, a corporation, mailed a notice of the annual shareholders' meeting specifying

the order of business as "(1) Election of directors, and (2) such further business as may come before the

meeting" together with proxy materials soliciting authorization for Scripps, the corporation's Secretary, to

act as proxy at the meeting.

Motive manufactures combustion engines for power equipment. Its stock is not listed on any stock

exchange. Its 2 million outstanding shares are held by about 300 shareholders. A quorum of shareholders

consists of a majority of the outstanding shares, present by proxy or in person.

Only Char, the chairperson of the board of directors, owning 10,000 shares, Scripps owning 5,000

shares, Mr. Gad owning 1,000 shares and Mrs. Gad owning 1 share, were present in person at the meeting.

Scripps held sufficient proxies, however, to establish a quorum. Gad had signed and mailed a proxy to

Scripps covering his 1,000 shares; however, he announced at the meeting that he intended to vote his 1,000

shares in person.

At the meeting, after the election of directors was completed, Char, the duly elected chairperson of the

meeting, asked if there was any further business to come before the meeting. Gad then made the following

motion, duly seconded by Mrs. Gad:

"Resolved, that one-half of the firm's profits for the next year be devoted to research and development

of pollution-free engines."

After the motion was made and seconded, and before any vote upon it, Scripps left the meeting.

Immediately after Scripps left, Char unilaterally adjourned the meeting and left. Nevertheless, Mr. and

Mrs. Gad remained, and both voted in favor of the motion.

Applicable state statutes allow the voting shares by proxy and provide that at annual meetings

directors may be elected and "any other business may be transacted which is within the powers of the

shareholders." There are no other relevant statutory, charter or bylaw provisions.

Is the board of directors required to follow the Gad resolution. What result? Discus

QUESTION 2

The following actions were taken pursuant to the unanimous vote of the directors of Ajax, a

corporation:

1. In an effort to prevent a minority shareholder from acquiring control, Ajax purchased shares

from three shareholders at their asking price of $80 per share. At the time, Ajax's shares had a book value

of $92 and a market value of $75 per share.

2. After it was announced that Bob, the long-time treasurer for Ajax, was retiring, Ajax agreed to

pay Bob $5,000 annually during his life-time.

3. Ajax agreed to pay the legal fees and costs of Curt, a vice-president, who was being sued in a

shareholders' derivative action for making political contributions from corporate funds to foreign

corporations with whom Ajax did business.

4. Ajax adopted a stock option plan for all officers and directors, and issued the first set of

options.

Pat owns 100 Ajax shares which he acquired before the above events took place. He purchased 50

additional shares two months ago, but has been unable to have the shares transferred to his name because,

according to the corporate secretary, the shares are subject to a restrictive shareholders' agreement

preventing the transfer. No such restriction appears upon the Ajax stock certificates, including those in

Pat's name representing his earlier shareholdings.

Pat feels that all the above described actions by Ajax and its directors have violated his rights as a

shareholder and damaged him. He also wants to know if he is entitled to have the additional 50 shares of

Ajax stock registered in his name.

A. Does Pat have any claim for relief with respect to each of the above described actions taken by

Ajax? Discuss.

B. Does Pat have a right to have the 50 shares of Ajax stock registered in his name? Discuss

Question 3

prove that n

k=0

sin k =

cos 1

2

cos(n +

1

2

)

2 sin 1

2

. ()

(i) Deduce that, for n 1 , n

k=0

sin (

k

n

)

= cot (

2n

)

.

(ii) By differentiating () with respect to , or otherwise, show that, for n 1 ,

n

k=0

k sin2

(

k

2n

)

=

(n + 1)2

4

+

1

4

cot2

(

2n

)

Q4.. What are the Administrative Problems of State Enterprises?