Read the passage given below:
People tend to amass possessions, sometimes without being aware of doing so. They can have a delightful surprise when they find something useful which they did not know they owned. Those who never have to change house become indiscriminate collectors of what can only be described as clutter. They leave unwanted objects in drawers, cupboards and attics for years in the belief that they may one day need them. Old people also accumulate belongings for two other reasons, lack of physical and mental energy, and sentiment. Things owned for a long time are full of associations with the past, perhaps with the relatives who are dead, and so they gradually acquire a sentimental value.
Some things are collected deliberately in an attempt to avoid wastage. Among these are string and brown paper, kept by thrifty people when a parcel has been opened. collecting small items can be a mania. A lady cuts out from newspapers sketches of model clothes that she would like to buy if she had money. As she is not rich, the chances are that she will never be able to afford such purchases. It is a harmless habit, but it litters up her desk.
Collecting as a serious hobby is quite different and has many advantages. It provides relaxation for leisure hours, as just looking at one’s treasure is always a joy. One doesn’t have to go out for amusement as the collection is housed at home. Whatever it consists of - stamps, records, first editions of books, china- there is always something to do in connection with it, from finding the right place for the latest addition to verifying facts in reference books. This hobby educates one not only in the chosen subject, but also in general matters which have some bearing on it.
There are other benefits also. One gets to meet like-minded collectors to get advice, compare notes, exchange articles, to show off one’s latest find etc. So one’s circle of friends grows. Soon the hobby leads to travelling, perhaps a meeting in another town, possibly a trip abroad in search of a rare specimen, for collectors are not confined to one country. Over the years one may well become an authority on one’s hobby and will probably be asked to give informal talks to little gatherings and then, if successful, to larger audiences.
(a) On the basis of your understanding of the above passage make notes on it, using headings and subheadings. Use recognisable abbreviations (wherever necessary - minimum four) and a format you consider suitable. Also supply an appropriate title to it.
(b) Write a summary of the passage in about 80 words.
and 
respectively, externally in the ratio 1 : 2. Also, show that P is the mid-point of the line segment RQ.
where a, b, c are the magnitudes of the sides opposite to the vertices A, B, C, respectively
and 
where 
and 
and 
and
and 
then find the value of λ, so that 
and 
are perpendicular vectors.
and 
in the ratio
and 
