In a certain city there are 30 colleges. Each college has 15 peons, 6 clerks, 1 typist and 1 section officer. Express the given information as a column matrix. Using scalar multiplication, find the total number of posts of each kind in all the colleges.

A finance company has offices located in every division, every district and every taluka in a certain state in India. Assume that there are five divisions, thirty districts and 200 talukas in the state. Each office has one head clerk, one cashier, one clerk and one peon. A divisional office has, in addition, one office superintendent, two clerks, one typist and one peon. A district office, has in addition, one clerk and one peon. The basic monthly salaries are as follows : Office superintendent Rs 500, Head clerk Rs 200, cashier Rs 175, clerks and typist Rs 150 and peon Rs 100. Using matrix notation find The total number of posts of each kind in all the offices taken together,

A finance company has offices located in ewery division, every didtrict and every taluka in a certain state in India. Assume that there are five divisions, thirty districts and 200 talukas in the state. Each office has one head clerk, one cashier, one clerk and one peon. A divisional office has, in addition, one office superntendent, two clerks, one typist and one poen. A district office, has in addition, one clerk and one peon. The basic monthly salaries are as follows : Office superintendernt Rs 500, Head clerk Rs 200, cashier Rs 175, clerks and typist Rs 150 and peon Rs 100. Using matrix motation find the total basic monthly salary bill of each kind of office

A finance company has offices located in ewery division, every didtrict and every taluka in a certain state in India. Assume that there are five divisions, thirty districts and 200 talukas in the state. Each office has one head clerk, one cashier, one clerk and one peon. A divisional office has, in addition, one office superntendent, two clerks, one typist and one poen. A district office, has in addition, one clerk and one peon. The basic monthly salaries are as follows : Office superintendernt Rs 500, Head clerk Rs 200, cashier Rs 175, clerks and typist Rs 150 and peon Rs 100. Using matrix motation find the total basic monthly salary bill of all the offices taken together.

A particular resistance wire has a resistance of 3.0 ohm per metre. Find : The total resistance of three lengths of this wire each 1.5 m long, joined in parallel.

An examination consists of 10 multiple choice questions, where each question has 4 options, only one of which is correct. In every question, a candidate earns 3 marks for choosing the correct opion, and -1 for choosing a wrong option. Assume that a candidate answers all questions by choosing exactly one option for each. Then find the number of distinct combinations of anwers which can earn the candidate a score from the set {15, 16,17,18, 19, 20}.

An object O (real ) is placed at focus of an equi-biconvex lens as shown in. figure-I . The refractive index of lens is mu = 1.5 and the radius of curvature of either suface of lens is R . The lens is surronded by air . In each statement of column-I some changes are made to situation given above and information regarding final image formed as a result is given in column-II . The distance between lens and object is unchanged in all statements of column-I. match the statements in column-I with resulting image in column-II.

Two mirros are inclinded by an angle 30^(@) . An object is placed 10^(@) with the mirror M_(1) . Find the positons of first two images formed by each mirror. Find the total number of images using (i) direct formula and (ii) counting the images.