NEB Class 11 Science Applied Mathematics Question Paper 2078

If a shoe manufacturing company wants to know the most demanding number of shoes, which one of the following measures represents the best central value?

How much 'Aana' consists in one 'Kathha'?

If the area and the breadth of a rectangular table are $24x^2y-18xy^2$ and $4x-3y$ respectively, then the length of this table is:

If the cost of 2 kg tea is the same as the cost of 3.3 kg sugar, and the cost of 2.2 kg sugar is the same as the cost of 0.5 kg coffee, then how much quantity of tea is the same as 2 kg of coffee in terms of cost?

If a person has two children and there are 5 colleges in his/her town, in how many different ways can the person admit his/her children among those 5 colleges if both children do not want to admit to the same college?

A shopkeeper wants to buy stationery items costing Rs. 50 per unit and playing items costing Rs. 200 per unit, but has only Rs. 20,000. Let $x$ and $y$ be the number of stationery and playing items respectively. Which mathematical model best describes the condition to decide the maximum number of items to buy?

A student has a probability of getting grade A in mathematics of 0.55 and getting grade B of 0.40. What is the probability that the person will get both grades?

What is the probability of getting 5 Saturdays in a month of 30 days?

How many numbers of three different digits less than 500 are formed?

Observe the following table carefully and select the best value in the missing place.

If $x=y$ at every point $(x,y)$ on a straight line, then which of the following statements is true?

If consistency in the scores is the criteria for awarding the students, who should get the award based on the following performance of two students X and Y in six tests of 100 full marks? $[5]$

If the height of a square-shaped room is 10 feet and the volume of the same room is 1440 cubic feet, with a door of height 7 feet and breadth half the height, and two windows covering an area double that of the door, how much should a person pay for plastering the 6 faces of the room at the rate of Rs. 20 per square foot? $[5]$

If the distance between two cities A and B is 40 km and between B and C is 50 km, how much time does a person need to travel from A to C through B if the person maintains 30 km/h in the beginning and then increases speed by 10 km more for each next 20 km? $[5]$

Look at the following tariff rates of electricity consumption shared by the Nepal Electricity Authority.

If A has a meter box of 15-ampere capacity and consumes 188 units in a month, and B has a meter box of 30-ampere capacity and consumes 175 units in a month, decide which will pay more electricity bill. $[5]$

To prepare a team for the volleyball game, 6 persons are to be selected including 2 girls. In how many different ways can such groups be formed from 10 boys and 4 girls? $[5]$

Define independent events with an example. A person wins the game if she/he obtains a head on the coin and an even number on the dice while tossing a coin and rolling a dice simultaneously. What is the probability of winning the game? $[2+3]$

A farmer can buy two types of fertilizers. A bag of fertilizer M costs Rs. 50 and contains 6 kg of nitrogen and 3 kg of potassium. A bag of fertilizer N costs Rs. 40 and contains 3 kg of nitrogen and 3 kg of potassium. If the farmer wants to add at least 30 kg of nitrogen and at least 18 kg of potassium to each plot, formulate a mathematical model for minimizing the cost of fertilizing a plot. Also, solve it. $[5]$

In a book, there are 825 pages and each page contains 45 lines.

a. How many lines should be there on one page if the entire book is to be completed in 700 pages? $[2]$

b. If a page with 50 or more lines costs Rs. 25 to type, and a page with fewer than 50 lines costs Rs. 20, in which form (825 pages or 700 pages) will the cost be minimum? $[3]$

The following box plots describe the scores of students in the test of mathematics taken in the evening and in the morning.

Compare and explain the scores of the students based on the following parameters:

a. Median values $[3]$

b. Deviation on the scores $[3]$

c. Taking math tests in the morning results in better grades than taking the test in the evening. Do the data support this argument? $[2]$

a. What do you mean by decision alternatives? Describe with an example. $[2]$

b. Define decision-making under certainty with examples. $[2]$

c. Mr. Indramani has Rs. 1,00,000 to invest in one of the three options A, B, C. The return depends on whether the economy experiences inflation, recession or no change. The possible returns are:

Suggest the best option to invest using minimax and maximin criteria. $[4]$

a. What is the difference between simple and compound partnerships? $[2]$

b. Two persons A and B started a business in partnership. A contributed Rs. 30,000 and B contributed Rs. 75,000. At the end of 6 months, C joined as a passive partner, contributing Rs. 45,000. They arranged that A and B shall share equally 20% of the profits and all three will share the remaining. The profit for the first 6 months is Rs. 21,000 and for the second six months is Rs. 27,000. How much do A, B and C get from the business at the end of the year? $[6]$