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

(a)

0

(b)

1

(c)

m

(d)

n

if T = \(_{ B }^{ A }\left( \begin{matrix} \overset { A }{ 0.4 } & \overset { B }{ 0.6 } \\ 0.2 & 0.8 \end{matrix} \right) \) is a transition probability matrix, then at equilibrium A is equal to ________.

(a)

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

(b)

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

(c)

\(\frac { 1 }{ 6 } \)

(d)

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

The rank of the matrix  \(\left( \begin{matrix} 1 & 1 & 1 \\ 1 & 2 & 3 \\ 1 & 4 & 9 \end{matrix} \right) \) is ________.

(a)

0

(b)

1

(c)

2

(d)

3

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

ഽ2^xdx is _______.

(a)

2^x log 2 + c

(b)

2^x + c

(c)

\(\frac { 2^{ x } }{ log2 } +c\)

(d)

\(\frac { log2 }{ { 2 }^{ x } } +c\)

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

(a)

log\(\left| \frac { { e }^{ x } }{ { e }^{ x }+1 } \right| +c\)

(b)

log\(\left| \frac { { e }^{ x }+1 }{ { e }^{ x } } \right| +c\)

(c)

log\(\left| { e }^{ x } \right| +c\)

(d)

log\(\left| { e }^{ x }+1 \right| +c\)

\(\int _{ 0 }^{ 1 }{ (2x+1) } dx\) is _______.

(a)

1

(b)

2

(c)

3

(d)

4

\(\int _{ 0 }^{ \frac { \pi }{ 3 } }\)tanx dx is _______.

(a)

log 2

(b)

0

(c)

log\(\sqrt { 2 } \)

(d)

2 log 2

Area bounded by the curve y = x (4 − x) between the limits 0 and 4 with x − axis is ________.

(a)

\(\frac{30}{3}\) sq.units

(b)

\(\frac{31}{2}\)sq.units

(c)

\(\frac{32}{3}\) sq.units

(d)

\(\frac{15}{2}\) sq.units

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

(a)

100 − 3x²

(b)

100x − 3x²

(c)

100x − 9x²

(d)

100 + 9x²

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)

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

Area bounded by y = \(\left| x \right| \) between the limits 0 and 2 is ________.

(a)

1sq.units

(b)

3 sq.units

(c)

2 sq.units

(d)

4 sq.units

The order and degree of the differential equation \(\left(\frac{d^{2} y}{d x^{2}}\right)^{\frac{3}{2}}-\sqrt{\left(\frac{d y}{d x}\right)}-4=0\) are respectively ______.

(a)

2 and 6

(b)

3 and 6

(c)

1 and 4

(d)

2 and 4

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

The complementary function of \(\frac { { d }^{ 3 }y }{ d{ x }^{ 3 } } -\frac { dy }{ dx } \) = 0 is ______.

(a)

A + Be^x

(b)

(A + B) e^x

(c)

(Ax + B) e^x

(d)

Ae^x + B

The solution of the differential equation \(\frac { dy }{ dx } =\frac { y }{ x } +\frac { f\left( \frac { y }{ x } \right) }{ f'\left( \frac { y }{ x } \right) } \) is ______.

(a)

\(f\left( \frac { y }{ x } \right) =k.x\)

(b)

\(xf\left( \frac { y }{ x } \right) =k\)

(c)

\(f\left( \frac { y }{ x } \right) =ky\)

(d)

\(yf\left( \frac { y }{ x } \right) =k\)

Δf(x) = _______.

(a)

f(x+ h)

(b)

f(x) − f(x+h)

(c)

f(x + h) − f(x)

(d)

f (x) − f(x−h)

If c is a constant then Δc = _______.

(a)

c

(b)

Δ

(c)

Δ²

(d)

0

For the given points (x₀, y₀) and (x₁, y₁) the Lagrange’s formula is _______.

(a)

\(y(x)=\frac{x-x_{1}}{x_{0}-x_{1}} y_{0}+\frac{x-x_{0}}{x_{1}-x_{0}} y_{1}\)

(b)

\(y(x)=\frac{x_{1}-x}{x_{0}-x_{1}} y_{0}+\frac{x-x_{0}}{x_{1}-x_{0}} y_{1}\)

(c)

\(y(x)=\frac{x-x_{1}}{x_{0}-x_{1}} y_{1}+\frac{x-x_{0}}{x_{1}-x_{0}} y_{0}\)

(d)

\(y(x)=\frac{x_{1}-x}{x_{0}-x_{1}} y_{1}+\frac{x-x_{0}}{x_{1}-x_{0}} y_{0}\)

If f (x)=x²  + 2x + 2 and the interval of differencing is unity then Δf (x) _______.

(a)

2x −3

(b)

2x +3

(c)

x + 3

(d)

x − 3

Value which is obtained by multiplying possible values of random variable with probability of occurrence and is equal to weighted average is called ________.

(a)

Discrete value

(b)

Weighted value

(c)

Expected value

(d)

Cumulative value

Probability which explains x is equal to or less than particular value is classified as ________.

(a)

discrete probability

(b)

cumulative probability

(c)

marginal probability

(d)

continuous probability

If X is a discrete random variable and p(x) is the probability of X, then the expected value of this random variable is equal to ________.

(a)

\(\sum { f(x) } \)

(b)

\(\sum[x+f(x)]\)

(c)

\(\sum { f(x)+x } \)

(d)

\(\sum { xp(x) } \)

If c is a constant in a continuous probability distribution, then p(x = c) is always equal to ________.

(a)

zero

(b)

one

(c)

negative

(d)

does not exist

If Z is a standard normal variate, the proportion of items lying between Z = –0.5 and Z = –3.0 is ________.

(a)

0.4987

(b)

0.1915

(c)

0.3072

(d)

0.3098

 In turning out certain toys in a manufacturing company, the average number of defectives is 1%. The probability that the sample of 100 toys there will be 3 defectives is ________.

(a)

0.0613

(b)

0.613

(c)

0.00613

(d)

0.3913

Forty percent of the passengers who fly on a certain route do not check in any luggage. The planes on this route seat 15 passengers. For a full flight, what is the mean of the number of passengers who do not check in any luggage?

(a)

6.00

(b)

6.45

(c)

7.20

(d)

7.50

The weights of newborn human babies are normally distributed with a mean of 3.2 kg and a standard deviation of 1.1 kg. What is the probability that a randomly selected newborn baby weighs less than 2.0 kg?

(a)

0.138

(b)

0.428

(c)

0.766

(d)

0.262

A __________ of statistical individuals in a population is called a sample.

(a)

Infinite set

(b)

finite subset

(c)

finite set

(d)

entire set

In ________ the heterogeneous groups are divided into homogeneous groups.

(a)

Non-probability sample

(b)

a simple random sample

(c)

a stratified random sample

(d)

systematic random sample

_______ is a relative property, which states that one estimator is efficient relative to another.

(a)

efficiency

(b)

sufficiency

(c)

unbiased

(d)

consistency

Type I error is  ______.

(a)

Accept H₀ when it is true

(b)

Accept H₀ when it is false

(c)

Reject H₀ when it is true

(d)

Reject H₀ when it is false.

Factors responsible for seasonal variations are ________.

(a)

Weather

(b)

Festivals

(c)

Social customs

(d)

All the above

Least square method of fitting a trend is ________.

(a)

Most exact

(b)

Least exact

(c)

Full of subjectivity

(d)

Mathematically unsolved

Which of the following Index number satisfy the time reversal test?

(a)

Laspeyre’s Index number

(b)

Paasche’s Index number

(c)

Fisher Index number

(d)

All of them

R is calculated using ________.

(a)

x_max - x_min

(b)

x_min - x_max

(c)

\(\overset{-}{x}\)_max - \(\overset{-}{x}\)_min

(d)

\(\overset{=}{x}\)_max - \(\overset{=}{x}\)_min

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

Solution for transportation problem using ________method is nearer to an optimal solution.

(a)

NWCM

(b)

LCM

(c)

VAM

(d)

Row Minima

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

(a)

4

(b)

3

(c)

7

(d)

12

A type of decision –making environment is _______.

(a)

certainty

(b)

uncertainty

(c)

risk

(d)

all of the above

If the minor of a₂₃ = the co-factor of a₂₃ in |a_ij| then the minor of a₂₃ is |a_y| then the minor of a₂₃ is ________

(a)

1

(b)

2

(c)

0

(d)

3

\(\int { { 3 }^{ x+2 } } \) dx = ______________ +c

(a)

\(\frac { { 3 }^{ x } }{ log3 } \)

(b)

\(\frac { 9\left( { 3 }^{ x } \right) }{ log3 } \)

(c)

\(\frac { 3.{ 3 }^{ x } }{ log3 } \)

(d)

\(\frac { { 3 }^{ x } }{ 9log3 } \)

The area lying above the X-axis and under the parabola y = 4x - x² is ______ sq. units

(a)

\(\frac{16}{3}\)

(b)

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

(c)

\(\frac{32}{3}\)

(d)

\(\frac{64}{3}\)

The solution of \(\frac { dp }{ dt } \) = ke^-t (k is a constant) is _____________

(a)

c-\(\frac { k }{ { e }^{ t } } \) = p

(b)

p = ke^t+c

(c)

t = log\(\left( \frac { c-p }{ k } \right) \)

(d)

t = log_c p

The backward difference operator ∇ is ______________

(a)

Nepla

(b)

Alpha

(c)

Gamma

(d)

Delta

A probability distribution function is defined by \(F(x)\begin{cases} 0,\ x<0 \\ 1-{ e }^{ -x },\ x\ge 0 \end{cases}\) The probability density function is __________

(a)

\(f(x)\begin{cases} { 3e }^{ -3x },\quad x\ge 0 \\ 0,\quad x<0 \end{cases}\)

(b)

\(\\ f(x)\begin{cases} { 1-e }^{ -3x },\quad x\ge 0 \\ 0,\quad x<0 \end{cases}\)

(c)

\(f(X)=0\forall x\)

(d)

f(x) = 3e - 3x\(\infty\)\(\infty\)

The marks second by 400 students in mathematics test were nolmally distributed, with mean 65. If 120 students got more marks above 85, the number of students securing between 45 and 65 is ____________

(a)

120

(b)

20

(c)

80

(d)

160

If α is the level of significance. then the confidence Co-efficient is

(a)

α

(b)

1

(c)

1-α

(d)

1+α

The multiplicative model bf the time series with the components T, S, C and I is __________

(a)

y = T + S x C x I

(b)

y = T x S x C x I

(c)

y = T + S x C + I

(d)

y = T + S + C + I

lf abasic feasible solution to a transportation problem contains less' than m + n - 1 allocations, it is called a_________basic feasible solution

(a)

Optimum

(b)

Degenerate

(c)

Non-degenerate

(d)

Balanced