If \(\rho(A) \neq \rho(A, B)\), then the system is _______.

(a)

Consistent and has infinitely many solutions

(b)

Consistent and has a unique solution

(c)

inconsistent

(d)

consistent

ഽ\(\frac { dx }{ \sqrt { { x }^{ 2 }-{ 36 } } } \) is _______.

(a)

\(\sqrt { { x }^{ 2 }-{ 36 } } +c\)

(b)

log\(\left| x+\sqrt { { x }^{ 2 }-36 } \right| +c\)

(c)

log\(\left| x-\sqrt { { x }^{ 2 }-36 } \right| +c\)

(d)

\(log\left| { x }^{ 2 }+\sqrt { { x }^{ 2 }-36 } \right| +c\)

∫ x cos x dx = ____________ +c.

(a)

x sin x - cos x

(b)

-x sin x + cos x

(c)

-x sin x - cos x

(d)

x sin x + cos x

The demand and supply function of a commodity are P(x) = (x − 5)² and S(x)= x² + x + 3 then the equilibrium quantity x₀ is ________.

(a)

5

(b)

2

(c)

3

(d)

19

The area below the demand curve p = f(x) and above the line p = p_o is________.

(a)

Producer's Surplus

(b)

Consumer's Surplus

(c)

\(\int _{ 0 }^{ p0 }{ g(x)dx } \)

(d)

\(\int _{ 0 }^{ x0 }{ g(x)dx } \)

The differential equation formed by eliminating A and B from y = e^−2x(A cos x + B sin x) is ______.

(a)

y₂ − 4y₁ + 5 = 0

(b)

y₂+ 4y – 5 = 0

(c)

y₂−4y₁−5= 0

(d)

y₂ + 4y₁ + 5 = 0

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

(a)

log x

(b)

e^-yx

(c)

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

(d)

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

E [f(x₀)] is ______________

(a)

f(x_o + h)

(b)

f(x_o - h)

(c)

f(x_o) + h

(d)

f(x_o) - h

Chance variation in the manufactured product is __________

(a)

controllable

(b)

not controllable

(c)

both (a) and (b)

(d)

none of these

In an assignment problem involving four workers and three jobs, total number of assignments possible are _______.

(a)

4

(b)

3

(c)

7

(d)

12