If \(\rho (A)\) = r  then which of the following is correct?

(a)

all the minors of order r which does not vanish

(b)

A has at least one minor of order r which does not vanish

(c)

A has at least one (r+1) order minor which vanishes

(d)

all (r+1) and higher order minors should not vanish

ഽ\(\frac { { e }^{ x } }{ \sqrt { { 1+e }^{ x } } } \) dx is _______.

(a)

\(\frac { { e }^{ x } }{ \sqrt { { 1+e }^{ x } } } +c\)

(b)

\(2\sqrt { 1+{ e }^{ x } } +c\)

(c)

\(\sqrt { 1+{ e }^{ x } } +c\)

(d)

\({ e }^{ x }\sqrt { 1+{ e }^{ x } } +c\)

If the marginal revenue MR = 35 + 7x − 3x², then the average revenue AR is ________.

(a)

35x + \(\frac { 7{ x }^{ 2 } }{ 2 } -{ x }^{ 3 }\)

(b)

35x + \(\frac { 7{ x }^{ 2 } }{ 2 } -{ x }^{ 2 }\)

(c)

35 +\(\frac { 7{ x }^{ 2 } }{ 2 } +{ x }^{ 2 }\)

(d)

35 + 7x + x²

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

E f (x)= _______.

(a)

f(x− h)

(b)

f (x)

(c)

f(x+ h)

(d)

f(x+ 2h)

E[X-E(X)]² is ________.

(a)

E(X)

(b)

E(X²)

(c)

V(X)

(d)

S.D(X)

A statistical analysis of long-distance telephone calls indicates that the length of these calls is normally distributed with a mean of 240 seconds and a standard deviation of 40 seconds. What proportion of calls lasts less than 180 seconds?

(a)

0.214

(b)

0.094

(c)

0933

(d)

0.067

A ________ is a statement or an assertion about the population parameter.

(a)

hypothesis

(b)

statistic

(c)

sample

(d)

census

The quantities that can be numerically measured can be plotted on a ________.

(a)

p - chart

(b)

c – chart

(c)

x bar chart

(d)

np – chart

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

(a)

4

(b)

3

(c)

7

(d)

12