The rank of the unit matrix of order n is ________.

(a)

n −1

(b)

n

(c)

n +1

(d)

n²

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 \(\int _{ -\frac{\pi}{2}}^{ \frac{\pi}{2}}\) cos x dx is _______.

(a)

0

(b)

2

(c)

1

(d)

4

The marginal revenue and marginal cost functions of a company are MR = 30 − 6x and MC = −24 + 3x where x is the product, then the profit function is ________.

(a)

9x² + 54x

(b)

9x² − 54x

(c)

54x - \(\frac { { 9x }^{ 2 } }{ 2 } \)

(d)

54x - \(\frac { { 9x }^{ 2 } }{ 2 } \) + k

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

If c is a constant then Δc = _______.

(a)

c

(b)

Δ

(c)

Δ²

(d)

0

E f (x)= _______.

(a)

f(x− h)

(b)

f (x)

(c)

f(x+ h)

(d)

f(x+ 2h)

If c is a constant, then E(c) is ________.

(a)

0

(b)

1

(c)

c f (c)

(d)

c

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

(a)

zero

(b)

one

(c)

mean

(d)

infinity

In a parametric distribution the mean is equal to variance is ________.

(a)

binomial

(b)

normal

(c)

poisson

(d)

all the above

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

A _______is one where each item in the universe has an equal chance of known opportunity of being selected.

(a)

Parameter

(b)

random sample

(c)

statistic

(d)

entire data

An estimator is said to be ________ if it contains all the information in the data about the parameter it estimates.

(a)

efficient

(b)

sufficient

(c)

unbiased

(d)

consistent

The standard error of sample mean is  ______.

(a)

\(\frac { \sigma }{ \sqrt { 2n } } \)

(b)

\(\frac { \sigma }{ { n } } \)

(c)

\(\frac { \sigma }{ \sqrt { n } } \)

(d)

\(\frac { { \sigma }^{ 2 } }{ \sqrt { n } } \)

The value of ‘b’ in the trend line y = a + bx is ________.

(a)

Always positive

(b)

Always negative

(c)

Either positive or negative

(d)

Zero

Consumer price index are obtained by: ________.

(a)

Paasche’s formula

(b)

Fisher’s ideal formula

(c)

Marshall Edgeworth formula

(d)

Family budget method formula

\(\overset {-}{X}\) chart is a ________.

(a)

attribute control chart

(b)

variable control chart

(c)

neither Attribute nor variable control chart

(d)

both Attribute and variable control chart

The Penalty in VAM represents difference between the first ________.

(a)

Two largest costs

(b)

Largest and Smallest costs

(c)

Smallest two costs

(d)

None of these

If number of sources is not equal to number of destinations, the assignment problem is called______.

(a)

balanced

(b)

unsymmetric

(c)

symmetric

(d)

unbalanced

A type of decision –making environment is _______.

(a)

certainty

(b)

uncertainty

(c)

risk

(d)

all of the above

Find the rank of each of the following matrices.
\(\left( \begin{matrix} 5 & 6 \\ 7 & 8 \end{matrix} \right) \)

If f'(x) = x + b, f(1)= 5 and f(2) = 13, then find f(x)

Integrate the following with respect to x
\(\sqrt { { 1+x+x }^{ 2 } } \)

If the marginal cost function of x units of output is \(\frac { a }{ \sqrt { ax+b } } \) and if the cost of output is zero. Find the total cost as a function of x.

Find the area of the region bounded by the curve y² = 27x³ and the lines x = 0, y = 1 and y = 2.

Solve: \(\frac { dy }{ dx } \) = y sin 2x

Solve yx²dx + e ^{− x}dy = 0

Find the rank of the matrix \(\begin{pmatrix} -5 & -7 \\ 5 & 7 \end{pmatrix}\)

Evaluate \(\int \sqrt{2 x+1} \ d x\)

The demand function of a commodity is y = 36 − x². Find the consumer’s surplus for y₀ = 11

Solve the differential equation \(\frac { dy }{ dx } =\frac { x-y }{ x+y } \)

From the following table find the missing value

x	2	3	4	5	6
f(x)	45.0	49.2	54.1	-	67.4

A pair of dice is thrown 4 times. If getting a doublet is considered a success, find the probability of 2 successes.

Fit a trend line by the method of semi-averages for the given data.

Year	1990	1991	1992	1993	1994	1995	1996	1997
Sales	15	11	20	10	15	25	35	30

Solve the equations 2x + 3y = 7, 3x + 5y = 9 by Cramer’s rule.

Evaluate \(\int _{ \frac { \pi }{ 6 } }^{ \frac { \pi }{ 3 } }{ \sin x } \) dx

From the following table find the number of students who obtained marks less than 45.

Marks	30-40	40-50	50-60	60-70	70-80
No. of Students	31	42	51	35	31

One fifth percent of the the blades produced by a blade manufacturing factory turn out to be defective. The blades are supplied in packets of 10. Use Poisson distribution to calculate the approximate number of packets containing no defective, one defective and two defective blades respectively in a consignment of 1,00,000 packets (e^–0.2 =.9802)

The mean weekly sales of soap bars in departmental stores were 146.3 bars per store. After an advertising campaign the mean weekly sales in 400 stores for a typical week increased to 153.7 and showed a standard deviation of 17.2. Was the advertising campaign successful at 95% confidence limit?

Construct the cost of living index number for 2011 on the basis of 2007 from the given data using family budget method.

Commodities	Price		Weights
	2007	2011
A	350	400	40
B	175	250	35
C	100	115	15
D	75	105	20
E	60	80	25

Solve the following assignment problem.