The rank of m x n matrix whose elements are unity is ________.

(a)

0

(b)

1

(c)

m

(d)

n

For the system of equations x + 2y + 3z = 1, 2x + y + 3z = 2, 5x + 5y + 9z = 4 _______.

(a)

there is only one solution

(b)

there exists infinitely many solutions

(c)

there is no solution

(d)

None of these

If \(\left| \begin{matrix} 2x & 5 \\ 8 & x \end{matrix} \right| =\left| \begin{matrix} 6 & -2 \\ 7 & 3 \end{matrix} \right| \) then x =

(a)

3

(b)

± 3

(c)

± 6

(d)

6

\(\Gamma (n)\) is _______.

(a)

(n −1)!

(b)

n!

(c)

\(n\Gamma (n)\)

(d)

(n −1)\(\Gamma \)(n)

If ∫ x sin x dx = - x cos x + α then α = __________ +c

(a)

sin x

(b)

cos x

(c)

C

(d)

none of these

\(\int _{ 1 }^{ e }{ log } x\) dx = __________ +c

(a)

1

(b)

e-1

(c)

e+1

(d)

0

∫ (1-x) \(\sqrt { x } \) dx = ______________+c 

(a)

\(\frac { 2 }{ 3 } { x }^{ \frac { 3 }{ 2 } }-\frac { 5 }{ 2 } \)

(b)

\({ x }^{ \frac { 3 }{ 2 } }-\frac { 2 }{ 5 } { x }^{ \frac { 5 }{ 2 } }\)

(c)

\(\frac { 3 }{ 2 } { x }^{ \frac { 2 }{ 3 } }-\frac { 5 }{ 2 } { x }^{ \frac { 2 }{ 5 } }\)

(d)

\(\frac { 2 }{ 3 } { x }^{ \frac { 3 }{ 2 } }-\frac { 2 }{ 5 } { x }^{ \frac { 5 }{ 2 } }\)

∫ 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

For a demand function p, if \(\int \frac{d p}{p}=k \int \frac{d x}{x}\) then k is equal to ________.

(a)

\(\eta \)_d

(b)

-\(\eta \)_d

(c)

\(\frac{-1}{\eta_{d}}\)

(d)

\(\frac{1}{\eta_{d}}\)

The area enclosed by the curve y = cos²x in [0,\(\pi\)] the lines x=0, x = \(\pi\) and the X-axis is ________sq.units.

(a)

2\(\pi\)

(b)

2\(\pi\)

(c)

\(\frac{2}{\pi}\)

(d)

\(\frac{\pi}{2}\)

The Producer's surplus for the supply function P = g(x) for the quantity X_o and price P_o is_________

(a)

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

(b)

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

(c)

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

(d)

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

The differential equation of y = mx + c is ______.(m and c are arbitrary constants) 

(a)

\(\frac { { d }^{ 2 }y }{ d{ x }^{ 2 } } \) = 0

(b)

y = x \(\frac { dy }{ dx } \) + c

(c)

xdy + ydx = 0

(d)

ydx − xdy = 0

A homogeneous differential equation of the form  \(\frac { dx }{ dy } \) = f\(\left( \frac { y }{ x } \right) \) can be solved by making substitution,______.

(a)

x = v y

(b)

y = v x

(c)

y = v

(d)

x = v

The differential equation of all circles with centre at the origin is _____________

(a)

xdy +ydx = 0

(b)

xdy - ydx = 0

(c)

xdx + ydy = 0

(d)

xdx - ydy = 0

In (x²-y²)dy = 2xy dx, if we put y = vx, then the equation is transformed into _____________

(a)

\(\frac { 1+{ v }^{ 2 } }{ v+{ v }^{ 3 } } dv=\frac { dx }{ x } \)

(b)

\(\frac { 1{ -v }^{ 2 } }{ v(1+{ v }^{ 2 }) } dv=\frac { dx }{ x } \)

(c)

\(\frac { dv }{ { v }^{ 2 }-1 } =\frac { dx }{ x } \)

(d)

\(\frac { dv }{ 1+{ v }^{ 2 } } =\frac { dx }{ x } \)

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

∇ ≡ _______.

(a)

1+E

(b)

1 - E

(c)

1− E⁻¹

(d)

1+ E⁻¹

∆f(x + 3h) ______________

(a)

f(x + 3h) - f(x + 4h)

(b)

f(x + 4h) - f(x + 3h)

(c)

f(x + h) - f(x)

(d)

f(x + 2h) - f(x + 3h)

If the values of x are not at equi-distant then we can use ______________

(a)

Newton's forward interpolation

(b)

Newton's backward interpolation

(c)

Lagrange's formula

(d)

graphical method.

If y is to be estimated for the value of x between two extreme points in a set of values, it is called ___________

(a)

Interpolation

(b)

extrapolation

(c)

Forward interpolation

(d)

backward interpolation

A formula or equation used to represent the probability distribution of a continuous random variable is called ________.

(a)

probability distribution

(b)

distribution function

(c)

probability density function

(d)

mathematical expectation

Which one is not an example of random experiment?

(a)

A coin is tossed and the outcome is either a head or a tail

(b)

A six-sided die is rolled

(c)

Some number of persons will be admitted to a hospital emergency room during any hour

(d)

All medical insurance claims received by a company in a given year

Variance of the random variable. X is 4, Its mean is 2. Then E(X²) is _________

(a)

2

(b)

4

(c)

6

(d)

8

If F(x) is the probability distribution function, then F(∞) is ________.

(a)

1

(b)

2

(c)

∞

(d)

0

If F(x) is the probability distribution function, then F(- ∞) is_______.

(a)

1

(b)

2

(c)

∞

(d)

0

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

If X ~ N(9,81) the standard normal variate Z will be ________.

(a)

\(Z=\frac { X- 81 }{ 9 } \)

(b)

\(Z=\frac { X-9 }{ 81 } \)

(c)

\(Z=\frac { X-9 }{ 9 } \)

(d)

\(Z=\frac { 9-X }{ 9 } \)

The starting annual salaries of newly qualified chartered accountants (CA’s) in South Africa follow a normal distribution with a mean of  Rs.180,000 and a standard deviation of Rs. 10,000. What is the probability that a randomly selected newly qualified CA will earn between Rs. 165,000 and Rs. 175,000 per annum?

(a)

0.819

(b)

0.242

(c)

0.286

(d)

0.533

If the area to the left of a value of z (z has a standard normal distribution) is 0.0793, what is the value of z?

(a)

-1.41

(b)

1.41

(c)

-2.25

(d)

2.25

The probability that a normal variate X lies in the interval (μ-σ, μ+σ) is ___________

(a)

0.0027

(b)

0.9973

(c)

0.6826

(d)

0.9544

A coin is tossed 3 times. The probability of getting exactly 2 heads is _________

(a)

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

(b)

\(\frac{1}{8}\)

(c)

\(\frac{3}{8}\)

(d)

\(\frac{1}{4}\)

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 number of ways in which one can select 2 customers out of 10 customers is __________

(a)

90

(b)

60

(c)

45

(d)

50

The point estimate variance of 6.33, 6.37, 6.36, 6.32, 6.37 is

(a)

0.0022

(b)

0.00055

(c)

0.0055

(d)

0.055

The additive model of the time series with the components T, S, C and I is ________.

(a)

y = T + S + C × I

(b)

y = T + S × C × I

(c)

y = T + S + C + I

(d)

y = T + S × C + I

While computing a weighted index, the current period quantities are used in the: ________.

(a)

Laspeyre’s method

(b)

Paasche’s method

(c)

Marshall Edgeworth method

(d)

Fisher’s ideal method

The component of a time series which is attached to short term fluctuations is __________

(a)

Seasonal variations

(b)

Cyclic variation

(c)

Irregular variation

(d)

all the above

Fine data relating to x and yare to be fit in a straight line. It is found that Σx = 0 and Σy = 15. Then the y- intercept of the line is_____

(a)

1

(b)

2

(c)

3

(d)

42

Seasonal variations can be measured when the data are available in season wise __________

(a)

weeks

(b)

days

(c)

months

(d)

Quarters

North-West Corner refers to ________.

(a)

top left corner

(b)

top right corner

(c)

bottom right corner

(d)

bottom left corner

Decision theory is concerned with _______.

(a)

analysis of information that is available

(b)

decision making under certainty

(c)

selecting optimal decisions in sequential problem

(d)

All of the above

_____determines the highest out come for each alternative.

(a)

Maximum cost

(b)

Minimax criteria

(c)

Maximin criteria

(d)

Payoff