NEB Class 12 Management Business Mathematics Question Paper 2080 (Set B)

If $A = \begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix}$ and $B = \begin{bmatrix} 3 & 2 \\ 1 & 2 \end{bmatrix}$, then $AB$ is

If $AB$ is identity matrix such that the leading diagonal elements of $A$ are the roots of $x^2 - 2x + 1 = 0$ and order of $A$ is $2\times2$ then $B$ is

If $\begin{bmatrix} 0 & x+2 \\ 5 & 0 \end{bmatrix}$ is a skew-symmetric matrix for positive $x+2$ then $x$ is

The point of inflection of the function $y = x^4$ is

The solution of differential equation $y\,dx + x\,dy = 0$ is

The product of three numbers in G.P. is 64, which one of the following is second term of the G.P.

If net return after 1 year is Rs. 5000 and initial investment is Rs. 40,000, then Internal Rate Return (IRR) is

The present value of an immediate annuity of Rs. 1200 payable for 5 years compound interest at the rate of 10% p.a. is

Every linear programming problem (LPP) is associated with another linear programming problem (LPP) is

Which of the following is condition for negative skewness in a data?

$(p+q)^n$ is a binomial distribution with parameters $n$ and $p$. What is the variance of distribution?

The cost of 3 chairs, 2 tables and 1 desk is Rs. 97000. The cost of 2 chairs, 1 table and 3 desks is Rs. 86000 and the cost of 1 chair, 3 tables and 2 desks is Rs. 99000. Find the cost of a chair, a desk and a table by using matrix method.

a) Solve the following system of equations by using Gauss elimination method: $3x+y+z=5,\ x-4y+z=-2,\ x+y-3z=-1$ (3)

b) Prove that without expanding, $\begin{vmatrix} bc & a & a^2 \\ ca & b & b^2 \\ ab & c & c^2 \end{vmatrix} = \begin{vmatrix} 1 & a^2 & a^3 \\ 1 & b^2 & b^3 \\ 1 & c^2 & c^3 \end{vmatrix}$ (2)

The total cost function and demand function of a commodity are $2Q - Q^2$ and $Q - 3$ respectively.

a) Write the revenue function in terms of Q. (1)

b) Write the related profit function. (1)

c) Name the marginal revenue function. (1)

d) What is profit at Q = 2? (2)

a) Find the area bounded by curves $y = x^2 + 2$ and $y = x$. (3)

b) Solve the differential equation $\dfrac{dy}{dx} + y = e^x$. (2)

The demand and supply function of a commodity are given by $P_d = 113 - x^2$ and $P_s = (x+1)^2$ in a perfect competition. Find the consumer surplus and producer surplus at the market equilibrium prices. (5)

Solve the following linear programming problem by Simplex method to maximize $P = 12x + 5y$ subject to the constraints $4x + y \le 3,\ 3x + y \le 1,\ x \ge 0,\ y \ge 0$.

In a data, $\bar{x}$, $M_d$, $M_o$ and $\sigma$ represent the mean, median, mode and standard deviation respectively.

a) Write two different formula of Karl Pearson's skewness. (2)

b) Write the relation between mean, median and mode of the data. (1)

c) Write the coefficient of variation in terms of $\sigma$ and $\bar{x}$. (1)

d) State the condition of positive skewness in terms of above symbols. (1)

A box has total 15 golf gloves of same size and shape. The ratio of left hand gloves and right hand gloves is 2:1. If two gloves are randomly selected from the box without replacement, what is the probability that

a) both gloves are left handed?

b) one right handed and one left handed?

c) What would be the probability of getting both gloves are right handed if the process of drawing is different than that in cases (a) and (b)?

A company manufactures different types of electrical appliances. It has been using radio for advertising its products. The following table shows amount of radio time (x in minutes) and the number of electrical appliances sold (y) over the last six days.

a) Calculate the Karl Pearson's coefficient of correlation. (4)

b) Estimate the sales of the number of electrical appliances when the amount of radio time (x) is 50. (4)

The compound interest on certain sum at certain rate is Rs. 204 in 2 years and simple interest at the same rate is Rs. 300 in 3 years.

a) Find the sum and rate of the interest.

b) If the rate of interest is double and principal is same, how many years later amount to Rs. 3149.28.

The demand and supply functions in a competitive market are $Q_d = 500 - 5p$ and $Q_s = 20p - 40$ respectively. The initial price $P_0$ is Rs. 100. Derive a function for the time path P and use it to predict price in time periods 5 given that the price adjust is proportion to excess demand at the rate $\dfrac{dp}{dt} = 0.02(Q_d - Q_s)$. How many time periods would you have to wait for the price to drop by Rs. 60? Comment on the stability of this market?