If \(\left| A \right| \neq 0,\) then A is _______.

(a)

non-singular matrix

(b)

singular matrix

(c)

zero matrix

(d)

none of these

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 _______.

(a)

\(\int_{a}^{b} f(x) d x-\int_{a}^{c} f(x) d x\)

(b)

\(\int_{a}^{c} f(x) d x-\int_{a}^{b} f(x) d x\)

(c)

\(\int_{a}^{b} f(x) d x\)

(d)

0

\(\int _{ 0 }^{ 1 }{ \frac { 1 }{ 2x-3 } } \) dx = ____________

(a)

\(\frac { 1 }{ 2 } log3\)

(b)

\(-\frac { 1 }{ 2 } log3\)

(c)

\(\frac { 1 }{ 2 } log1\)

(d)

0

When x₀ = 5 and p₀ = 3 the consumer’s surplus for the demand function p_d = 28 − x² is ________.

(a)

250 units

(b)

\(\frac{250}{3}\)units

(c)

\(\frac{251}{2}\) units

(d)

\(\frac{251}{3}\) units

The are bounded by the demand curve xy = 1, the X-axis, x = 1 and x = 2 is ________

(a)

log 2

(b)

log \(\frac{1}{2}\)

(c)

2 log 2

(d)

\(\frac{1}{2}\)log 2

Which of the following is the homogeneous differential equation?

(a)

(3x−5)dx = (4y−1)dy

(b)

xy dx−(x³+y³)dy = 0

(c)

y²dx+(x² − xy  − y²)dy = 0

(d)

(x²+y)dx = (y²+x)dy

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)

A discrete probability function p(x) is always non-negative and always lies between ________.

(a)

0 and \(\infty \)

(b)

0 and 1

(c)

–1 and +1

(d)

–∞ and +∞

If f(x) = kx(1-x), 0< x < 1 is a p.d.f. then the value of k is ________.

(a)

\(\frac{1}{5}\)

(b)

\(\frac{2}{5}\)

(c)

\(\frac{3}{5}\)

(d)

6

If P(Z > z) = 0.5832 what is the value of z (z has a standard normal distribution)?

(a)

-0.48

(b)

0.48

(c)

1.04

(d)

-0.21