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

(a)

\(\rho (A)=\rho (A,B)>n\)

(b)

\(\rho(A)=\rho(A, B)=n\)

(c)

\(\rho (A)=\rho (A,B) < n\)

(d)

none of these

\(\int _{ 0 }^{ 1 }{ (2x+1) } dx\) is _______.

(a)

1

(b)

2

(c)

3

(d)

4

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 ________.

(a)

40

(b)

\(\frac{41}{2}\)

(c)

\(\frac{40}{3}\)

(d)

\(\frac{41}{5}\)

If the marginal cost function MC = 2 - 4x, then the cost function is _________

(a)

2x- 2X²+ k

(b)

2-4x²

(c)

\(\frac{2}{x}-4\)

(d)

2x-4x²

The complementary function of (D²+ 4)y = e^2x is ______.

(a)

(Ax +B)e^2x

(b)

(Ax +B)e^−2x

(c)

A cos 2x + B sin 2x

(d)

Ae^−2x+ Be^2x

The variable separable form of \(\frac { dy }{ dx } =\frac { y(x-y) }{ x(x+y) } \) by taking y = vx and \(\frac { dy }{ dx } =v+x\frac { dv }{ dx } \) is ______.

(a)

\(\frac { 2{ v }^{ 2 } }{ 1+v } dv=\frac { dx }{ x } \)

(b)

\(\frac { 2{ v }^{ 2 } }{ 1+v } dv=-\frac { dx }{ x } \)

(c)

\(\frac { 2{ v }^{ 2 } }{ 1-v } dv=\frac { dx }{ x } \)

(d)

\(\frac { 1+v }{ 2{ v }^{ 2 } } dv=-\frac { dx }{ x } \)

The integrating factor of x\(\frac { dy }{ dx } \)-y = e^x is _____________

(a)

log x

(b)

e^-yx

(c)

\(\frac { 1 }{ x } \)

(d)

\(\frac { -1 }{ x } \)

For the given points (x₀, y₀) and (x₁, y₁) the Lagrange’s formula is _______.

(a)

\(y(x)=\frac{x-x_{1}}{x_{0}-x_{1}} y_{0}+\frac{x-x_{0}}{x_{1}-x_{0}} y_{1}\)

(b)

\(y(x)=\frac{x_{1}-x}{x_{0}-x_{1}} y_{0}+\frac{x-x_{0}}{x_{1}-x_{0}} y_{1}\)

(c)

\(y(x)=\frac{x-x_{1}}{x_{0}-x_{1}} y_{1}+\frac{x-x_{0}}{x_{1}-x_{0}} y_{0}\)

(d)

\(y(x)=\frac{x_{1}-x}{x_{0}-x_{1}} y_{1}+\frac{x-x_{0}}{x_{1}-x_{0}} y_{0}\)

E [c.f(x)] = ___________ where c is a constant

(a)

E (f(c)

(b)

c. Ef(x)

(c)

E\(\left( \frac { f}{c } \right) \)

(d)

E(-fc)

The probability density function p(x) cannot exceed ________.

(a)

zero

(b)

one

(c)

mean

(d)

infinity