Use the roster method to represent the following sets :-
i) The counting numbers which are multiples of 6 and less than 50.
ii) The fractions whose numerator is 1, and whose denominator is a counting number less
than 10.
iii) (x : x Î N and x is a prime factor of 84).
iv) The set of odd integers lying between -4 and 8.
v) The set of all natural numbers x for which x+6 is less than 10.
vi) The set of all integers x for which x+ 6 is greater than 10.
vii) The set of all integers x for which x+6 is less than 10.
viii) The set of all integers x for which
is a natural number.
ix)
x: x Î 1, -
< x <
.
x) {x : x Î N and 4x-3 £ 15).
xi) {x : x Î N, x² < 40}
xii) {x: x Î Z and x² < 16}.
xiii) The set of all digits in our number system.
xiv) The set of all letters in the word TRIGONOMETRY.
xv) The set of all vowels in the English alphabet which precedes q.
xvi) {x : x is a consonant in the English alphabet which precedes k).
Answers
Answer:
Formation of the Ministry :
The Prime Minister forms the Ministry. With the appointment of the Prime Minister, the essential task of the President is over, for it is left to the Prime Minister to select his Ministers and present a list to the President. The President has no other alternative but to appoint the Ministers as recommended by the Prime Minister.
It is correctly said that the Prime Minister "is central to its (Ministry's) formation, central to its life and central to its death". The Prime Minister has the privilege to select his Cabinet colleagues. If the Prime Minister resigns, it means the resignation of the whole Ministry. When the Prime Minister dies, the Council of Ministers will automatically cease to exist. The Prime Minister may remove the members of Council of Ministers at any time by demanding the Ministers' resignation or getting them dismissed, by the President.
(2) Distribution of Portfolios:
Distribution of portfolios is another important task of the Prime Minister. He has a free hand in assigning various departments to his colleagues. It is for him to determine the size of the Cabinet and the Ministers to be included in it. He may even select ministers outside the rank if he feels that a person is fit for a job. While distributing portfolios he is to look that important members of the party do get important portfolios. In a federal State like India be is to see that Ministers are selected from all parts of the country.
Further, there might be some aspirants for a few important portfolios like Home, Defence or Finance. He has to bring amity and satisfy all in distributing the portfolios. His work is indeed a difficult one. As Lowell points out. "His work is like that of constructing a figure out of blocks which are too numerous for the purpose and which are not of shapes fit perfectly together".
(3) Chairman of the Cabinet Committee:
The Prime Minister is the Chairman of the Cabinet Committee. He convenes and presides over all the meetings of the Cabinet. He is to fix the agenda of such meetings. The Ministers are individually responsible to him for the good administration of their respective departments. The Prime Minister may warn advice or encourage them in discharge of their functions. He is the head of the Council of Ministers. He acts as the Chairman of various standing and ad-hoc Committees of the Cabinet.
(4) Chief Co-ordinator of Policies:
The Prime Minister is the chief co-ordinator of the policies of several Departments. In case of conflicts between two departments, he acts as the mediator. He irons out quarrels among various Ministers and departments. He keeps an eye on the working of all Departments of the Government of India. He can ask for any file from any Ministry for his perusal.
In case of appointment of Governors and other high federal officers, the voice of the Prime Minister counts and not that of the other Ministers. He is always vigilant regarding the working of the important departments like the Finance, the Foreign Affairs and Home. He also keeps close touch with foreign ambassadors and represents the Union Government at the Conferences of Heads of Foreign Governments.
(5) Sole Adviser to the President:
The Prime Minister is the sole adviser to the President. The right to advice for dissolution of the Lok Sabha rests with Prime Minister. The President is expected to accept the advice of the Prime Minister and not that of other Ministers.
The Prime Minister is the only channel of communication between the President and the Cabinet. He informs the President all the decisions taken in the Cabinet. If the President does not accept the advice of the Prime Minister, the Prime Minister may resign. The resignation of the Prime minister will create difficulty for the President to find out an alternative Ministry. As long as the Prime Minister enjoys the confidence of the majority members of the Lok Sabha it is difficult for the President to dismiss him.
(6) Leader of the Nation:
The Prime Minister is the leader of the nation. He is the chief spokesman of the Governmental policies in the Parliament. All important policy
sikringbp and 19 more users found this answer helpful
THANKS
13
Step-by-step explanation: