Cramer’s rule is applicable only to get an unique solution when _______.

(a)

\({ \triangle }_{ z }\neq 0\)

(b)

\({ \triangle }_{ x }\neq 0\)

(c)

\({ \triangle } \neq 0\)

(d)

\({ \triangle }_{ y }\neq 0\)

The value of \(\int _{ 2 }^{ 3 }{ f(5-x) } dx-\int _{ 2 }^{ 3 }{ f(x) } dx\) is _______.

(a)

1

(b)

0

(c)

-1

(d)

5

\(\int { \frac { { x }^{ 5 }-{ x }^{ 4 } }{ { x }^{ 3 }-{ x }^{ 2 } } } \)dx = __________ +c

(a)

1

(b)

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

(c)

\(\frac { { x }^{ 3 } }{ 2 } \)

(d)

\(\frac { { x }^{ 2 } }{ 2 } \)

The demand function for the marginal function MR = 100 − 9x² is ________.

(a)

100 − 3x²

(b)

100x − 3x²

(c)

100x − 9x²

(d)

100 + 9x²

Integrating factor of \(\frac { dy }{ dx } +\frac { 1 }{ xlogx } y=\frac { 2 }{ x^{ 2 } } \) is ______

(a)

e^x

(b)

log x

(c)

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

(d)

e^-x

E^-nf(x) is ______________

(a)

F(x + nh)

(b)

F(x - nh)

(c)

F(-nh)

(d)

f(x - n)

Which of the following are correct?
(i) E(aX+b) = a E(X) + b
(ii) μ₂ = μ₂¹ - (μ₁¹)²
(iii) μ² = variance
(iv) V (a X + b) = a² V(x)

(a)

all

(b)

i, ii and iii

(c)

ii and iii

(d)

i and iv

A manufacturer produces switches and experiences that 2 per cent switches are defective. The probability that in a box of 50 switches, there are atmost two defective is ________.

(a)

2.5 e^-1

(b)

e^-1

(c)

2e^-1

(d)

none of the above

A random sample of 500 apples was taken from large consignment and 45 of them were found to be bad. Then the standard error is __________

(a)

0.033

(b)

0.0128

(c)

0.0128

(d)

0.00128

_____determines the lowest out comes for each alternative.

(a)

Least cost

(b)

Minimax criteria

(c)

Maximin criteria

(d)

Payoff matrix