The rank of m x n matrix whose elements are unity is ________.

If the number of variables in a non-homogeneous system AX = B is n, then the system possesses a unique solution only when _______.

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

The given demand and supply function are given by D(x) = 20 − 5x and S(x) = 4x + 8 if they are under perfect competition then the equilibrium demand is ________.

If MR = 15 - 8x, then the revenue function is _________

Solve the following system of equations by rank method
x + y + z = 9, 2x + 5y + 7z = 52, 2x − y − z = 0

Find the rank of the matrix A =\(\left( \begin{matrix} 1 & -3 \\ 9 & 1 \end{matrix}\begin{matrix} 4 & 7 \\ 2 & 0 \end{matrix} \right) \)

Integrate the following with respect to x.
\(\frac { { x }^{ 3 } }{ x+2 } \)

Evaluate \(\int { \frac { 2+3cosx }{ { sin }^{ 2 }x } } dx\)

Find the revenue function and the demand function if the marginal revenue for x units is MR = 10 + 3x − x².

Find the rank of the matrix \(\left( \begin{matrix} 0 & -1 & 5 \\ 2 & 4 & -6 \\ 1 & 1 & 5 \end{matrix} \right) \)

Solve: 2x + 3y = 5, 6x + 5y = 11

Evaluate ഽ\(\frac { dx }{ { 4x }^{ 2 }-1 } \)

Using integration find the area of the region bounded between the line x = 4 and the parabola y² = 16x.

Determine the cost of producing 3000 units of commodity if the marginal cost in rupees per unit is C'(x) = \(\frac{x}{3000}+2.50\)

Solve by Cramer’s rule x + y + z = 4, 2x − y + 3z = 1, 3x + 2y − z = 1

The marginal revenue function (in thousand of rupees ) of a commodity is 10 + e^−0.05x Where x is the number of units sold. Find the total revenue from the sale of 100 units (e⁻⁵ = 0.0067)

Find the area of the region bounded by the parabola y² = 4x and the line 2x - y = 4.