E f (x)= _______.

A type of decision –making environment is _______.

In a degenerate solution number of allocations is _______.

Which of the following is the homogeneous differential equation?

The solution of the differential equation \(\frac { dy }{ dx } \) + Py = Q where P and Q are the function of x is ______.

The integrating factor of the differential equation \(\frac{dx}{dy}+Px=Q\) is ______.

The LCL for R chart is given by ________.

Which of the following Index number satisfy the time reversal test?

The components of a time series which is attached to short term fluctuation is ________.

Errors in sampling are of  ______.

\(\int _{ 0 }^{ \infty }{ { x }^{ 4 }{ e }^{ -x } } \)dx is _______.

If f (x) is a continuous function and a < c < b, then \(\int_{a}^{c} f(x) d x+\int_{c}^{b} f(x) d x\) is _______.

ഽ\(\sqrt { { e }^{ x } } \) dx is _______.

Let z be a standard normal variable. If the area to the right of z is 0.8413, then the value of z must be: ________.

The starting annual salaries of newly qualified chartered accountants (CA’s) in South Africa follow a normal distribution with a mean of  Rs.180,000 and a standard deviation of Rs. 10,000. What is the probability that a randomly selected newly qualified CA will earn between Rs. 165,000 and Rs. 175,000 per annum?

The parameters of the normal distribution \(f(x)=\left(\frac{1}{\sqrt{72 \pi}}\right)\)\(\frac{e^{-(x-10)^{2}}}{72}\) –∞ <  x  <  ∞ ________.

The height of persons in a country is a random variable of the type ________.

A variable which can assume finite or countably infinite number of values is known as ________.

A probability density function may be represented by ________.

Demand of products per day for three days are 21, 19, 22 units and their respective probabilities are 0.29, 0.40, 0.35. Profit per unit is 0.50 paisa then expected profits for three days are ________.

The area bounded by the parabola y² = 4x bounded by its latus rectum is ________.

The producer’s surplus when the supply function for a commodity is P = 3 + x and x₀ = 3 is ________.

The marginal revenue and marginal cost functions of a company are MR = 30 − 6x and MC = −24 + 3x where x is the product, then the profit function is ________.

If \(\frac { { a }_{ 1 } }{ x } +\frac { { b }_{ 1 } }{ y } ={ c }_{ 1 },\frac { { a }_{ 2 } }{ x } +\frac { { b }_{ 2 } }{ y } ={ c }_{ 2 },\) \({ \triangle }_{ 1= }\begin{vmatrix} { a }_{ 1 } & { b }_{ 1 } \\ { a }_{ 2 } & { b }_{ 2 } \end{vmatrix}, \ { \triangle }_{ 2 }=\begin{vmatrix} { b }_{ 1 } & { c }_{ 1 } \\ { b }_{ 2 } & { c }_{ 2 } \end{vmatrix}{ \triangle }_{ 3 }=\begin{vmatrix} { c }_{ 1 } & { a }_{ 1 } \\ { c }_{ 2 } & a_{ 2 } \end{vmatrix}\) then (x, y) is _______.

If the rank of the matrix  \(\left( \begin{matrix} \lambda & -1 & 0 \\ 0 & \lambda & -1 \\ -1 & 0 & \lambda \end{matrix} \right) \)  is 2. Then \(\lambda \) is ________.