NEB Class 12 Management Business Mathematics Question Paper 2082 (Set A)

If A is a non-singular matrix, then $A^{-1}$ equal to

What is the value of $\begin{vmatrix} 4 & 3 & 5 \\ 0 & 0 & 7 \\ 8 & 6 & -1 \end{vmatrix}$ ?

Which of the following matrix is satisfied Hawkin's-Simon condition ?

If $f(x) = x^2 - 4x$, the function $f(x)$ is increasing at

Which one of the following is the degree of differential equation $\dfrac{d^4y}{dx^4} = \sqrt{\dfrac{d^3y}{dx^3}}$ ?

Three numbers are in the ratio of $1:4:12$. If one is added to the first number, the resulting number together with other two numbers form a G.P. The three original numbers are :

Which one of the following represents net present value ?

The initial cost of a bicycle is Rs. $50{,}000$ and the rate of compound depreciation is $10\%$ p.a. diminishing balance, then scrap value at the end of third year is

In a simplex method a constraint $x+2y \le 6$ is written as $x+2y+v=0$. What is the 'v' known as ?

For a distribution, the distance of the median from first quartile is equal to the distance of the third quartile from the median. The coefficient of skewness is

X and Y are two dependent events. Which one of the following is $P(X \cap Y)$ ?

Write the associative property of matrix addition.

Define symmetric matrix.

If A is a square matrix then what is the value of $A \times (\text{adj. } A)$ ?

Write the condition in Cramer's rule that the system of linear equations cannot be solved.

What is the Leontief's technology matrix if $X$ = output vector, $A$ = input coefficient matrix and $I$ the unit matrix.

Given the input-output table for the two sector economy

Calculate the input-output coefficient matrix.

Calculate the Leontief matrix $(I - A)$, where I being unit matrix of order 2.

Test Hawkins-Simon condition for the viability of the system.

Write the average revenue (AR) in terms of total revenue (R) and output (Q).

Write the formula of elasticity of supply ($\varepsilon_s$).

Write the condition of maximization of a function.

If C be the total cost and R be the total revenue, write the break-even condition in terms of cost and revenue.

What is the condition for finding stationary point for the function $g(x)$ ?

If the revenue function is $R = Q - 3Q^2$ and the cost function is $C = Q^2 - 2Q$, find the value of the maximum profit.

It is given that the demand function $P = 3Q + 6$. Find the elasticity of demand at $Q = 3$.

It is given that $R(x) = 2x^2 + 6x + 5$; where $R(x)$ is the revenue function. Find the marginal revenue at $x = 10$.

Find the area under the curve $y^2 = 4x$ between $x = 2$ to $x = 5$ using fundamental theorem of calculus.

Using Simplex method, maximize $W = 5x + 2y$ subject to the constraints, $3x + 5y \le 15,\; 5x + 2y \le 10,\; x \ge 0,\; y \ge 0$.

Calculate the Karl Pearson's coefficient of correlation between the height (X) and weight (Y) for the following data. Also interpret the result.

In a cap factory, machine A, B and C manufacture respectively $30\%$, $35\%$ and $45\%$ out of their output $2\%$, $3\%$ and $4\%$ defectives respectively are found. A cap is drawn at random to be defective, what is the probability that it is manufactured by the machine A ?

Give an example of first order linear differential equation with constant coefficient and constant term. Solve it.

A function $f(x) = \dfrac{1}{x}$ defined in $(-8, 0)$. $f'(x)$ is decreasing in the interval $(-8, 0)$. Justify it.

Derivative and anti derivative are inverse of each other. Justify with example.

Find two geometric mean between 9 and 243.

A sum doubles itself in 5 years by compound interest. How long does it take to be four times the sum ?

A loan of Rs. $2{,}00{,}000$ is to be paid in 10 yearly instalment. Find the amount of each installment if the rate of interest is $15\%$ p.a.

Using the line of regression, estimate the weight of a baby at the age of 4 months and age of the baby when weight is 6 kg, from the following table.

A fair coin is tossed 4 times. What is the probability of getting at least 2 heads.