NEB Class 12 Science Applied Mathematics Question Paper 2082

Group 'A'

Rewrite the correct option of each question in your answer sheet.

11 questions·1 marks each

1mcq1 marks

What is the formula for Karl Pearson's coefficient of Skewness depending upon mean, median and standard deviation?

A
$\dfrac{\text{mean} - \text{median}}{\text{standard deviation}}$
B
$\dfrac{3(\text{mean} - \text{median})}{\text{standard deviation}}$
C
$\dfrac{\text{median} - \text{mean}}{\text{standard deviation}}$
D
$\dfrac{3(\text{median} - \text{mean})}{\text{standard deviation}}$

skewnessstatistics

2mcq1 marks

What is the volume of a hemisphere whose radius is 'y' cm?

A
$\dfrac{2}{3}\pi y^3\ \text{cm}^3$
B
$2\pi y^3\ \text{cm}^3$
C
$\dfrac{4}{3}\pi y^3\ \text{cm}^3$
D
$4\pi y^3\ \text{cm}^3$

mensurationhemispherevolume

3mcq1 marks

Which one of the following is formula for calculating Value Added Tax?

A
rate of VAT × Marked price
B
rate of VAT × Cost price
C
rate of VAT × Selling price
D
rate of VAT × Purchasing price

vatfinancial-mathematics

4mcq1 marks

Unit cost of a pen is Rs. x and unit cost of a book is Rs. y. The maximum cost of 20 pen and 30 books is Rs. 7,000. Which one is the correct mathematical representation of the context?

A
$20y + 30x \le 7000$
B
$20x + 30y \le 7000$
C
$20x + 30y \ge 7000$
D
$20y + 30x \ge 7000$

linear-inequalitylinear-programming

5mcq1 marks

The extreme Nepal oil corporation decision is "to drill" with the outcomes of finding oil is or not finding oil with chances of occurrence of 0.340 and not finding is 0.660. The respective contribution are Rs. 3900 and Rs. 3500. The expected Monetary Value (EMV) of decision to drill is .....

A
$0.34 \times 3500 + 0.66 \times 3500$
B
$0.34 \times 3900 + 0.66 \times 3500$
C
$0.34 \times 3500 + 0.66 \times 3900$
D
$0.34 \times 3900 + 0.34 \times 3500$

expected-monetary-valuedecision-theory

6mcq1 marks

What is the probability of selecting a letter card from the word "RAPATI" containing A.

A
$\dfrac{1}{6}$
B
$\dfrac{1}{3}$
C
$\dfrac{1}{2}$
D
$1$

probability

7mcq1 marks

Which one of the following is equal to $\dfrac{(n-1)!}{(n+1)!}$ ?

A
$(n-1)$
B
$n$
C
$(n+1)$
D
$\dfrac{1}{n(n+1)}$

factorialpermutations

8mcq1 marks

If A and B are two independent events such that $P(A) = 2P(B) = \dfrac{1}{4}$ . Which one of the following is $P(A \cap B)$ ?

A
$\dfrac{1}{32}$
B
$\dfrac{1}{12}$
C
$\dfrac{1}{8}$
D
$\dfrac{1}{4}$

probabilityindependent-events

9mcq1 marks

It is given that demand (x) is greater than or equal to stock, then the formula of pay off is ........

A
MP × sells stock
B
MP × units in stock
C
SP × units stock
D
MP × sells in stock

payoffinventory

10mcq1 marks

Line AB meets X-axis and Y-axis at A and B respectively. The equation of AB is $4x + 3y - 24 = 0$ . Which one of the following is area of triangles AOB, where O is the origin?

A
48 sq. unit
B
24 sq. unit
C
8 sq. unit
D
6 sq. unit

coordinate-geometryarea-of-triangle

11mcq1 marks

A boy is running equally inclined with the axes. Which one of the following is equation of the path made by the boy?

A
$x = 0$
B
$y = 0$
C
$x + y = 1$
D
$x - y = 0$

coordinate-geometryequation-of-line

Group 'B'

Short answer questions.

9 questions·5 marks each

12short5 marks

Calculate the coefficient of correlation at the following data.

Marks in science	30	40	50	60	70	80
Marks in math	30	40	60	40	80	90

correlationstatistics

13short5 marks

Represent the following data in a pie-chart.

Items	Expenditure in Rs.
food	14000
education	7000
clothing	6000
medicine	5000
fuel	4000

pie-chartstatistics

14ashort2 marks

A tent is in the form of cone and cylinder with common base. The total height of the solid is 21 feet, height of the cone is 6 feet and slant height of the cone is 10 feet.

Tent in the form of a cone over a cylinder with a common circular base

a) Find the area of the base.

mensurationconecylinder

14bshort3 marks

A tent is in the form of cone and cylinder with common base. The total height of the solid is 21 feet, height of the cone is 6 feet and slant height of the cone is 10 feet.

b) Find the total canvas required for the tent.

mensurationconecylindersurface-area

15short5 marks

A machine depreciates at the rate of 10% in first 2 years and then 15% in next 3 years. The original price of the machine is Rs. 80,000. Find the price of the machine at the end of five years and compare its original price and final price.

depreciationfinancial-mathematics

16short5 marks

Ram can do $\dfrac{1}{3}$ of a work in 6 days and Geeta can do $\dfrac{1}{4}$ of the same work in 5 days.

a) Find the efficiency of Ram and Geeta. [2]

b) Divide Rs. 18000 among Ram and Geeta if they work together to finish the work from beginning. [3]

time-and-workratio-and-proportion

17short5 marks

There are 12 male and 10 female candidates for a committee of 8 people.

a) Find the number of combinations if equal number of male and female are selected. [2]

b) Find the number of combinations if 75% of them are male and 25% are female. [3]

combinationspermutations-and-combinations

18short5 marks

Make an objective function, and related constraints for maximum profit. Represent it graphically.

linear-programming

19short5 marks

There are 2 red balls and 8 white balls of same size and shape in box A. There are 6 red and 6 white balls of same size and shape in box B. It two red and 3 white coloured balls are selected from either of the box, find all possible cases and their probabilities.

probability

Group 'C'

Long answer questions.

8 questions·8 marks each

20along5 marks

The marks of Maths and Nepali of 6 students are given below.

Maths	50	45	65	30	60	80
Nepali	40	60	55	45	70	75

Find the marks in Nepali when the marks of Maths is 55.

regressionstatistics

20blong3 marks

If $a:b = 2:3$ , $b:c = 5:4$ , $c:d = 9:7$ , find $a:d$ , where a, b, c, d are variables related cost from different articles.

ratio-and-proportion

21along2 marks

The diameter of a wheel of cement is 44cm and height is 21cm. The cost of each wheel is Rs. 1200 and 15 wheels are required to make a well, then

a) What is the total cost of wheels? Find it.

mensurationcylindercost

21blong3 marks

The diameter of a wheel of cement is 44cm and height is 21cm.

b) If the water level is up to 12 wheels then find the volume of water in litre.

mensurationcylindervolume

21clong3 marks

c) If the water machine pull water from well at the rate of 100 litres per 5 minutes, at what time the water machine fill 900 litres?

rateunitary-method

22along3 marks

The difference between compound interest and simple interest of certain sum of money is Rs. 250 at the rate of 8% per annum for 2 years. Find the sum of money.

compound-interestsimple-interestfinancial-mathematics

22blong3 marks

A bag contain 20 bulbs in which 8 are defective. A bulb is selected at random, what is the probability that more than 6 bulbs are defective?

probability

22clong2 marks

A and B are two partners invested Rs. 40,000 and Rs. 50,000 respectively. They earn total profit of Rs. 10,000 at the end of a year. Find their share of profit.

profit-sharingratio-and-proportion