If the rank of the matrix  \(\left( \begin{matrix} \lambda & -1 & 0 \\ 0 & \lambda & -1 \\ -1 & 0 & \lambda \end{matrix} \right) \)  is 2. Then \(\lambda \) is ________.

(a)

1

(b)

2

(c)

3

(d)

only real number

If \(\frac { { a }_{ 1 } }{ x } +\frac { { b }_{ 1 } }{ y } ={ c }_{ 1 },\frac { { a }_{ 2 } }{ x } +\frac { { b }_{ 2 } }{ y } ={ c }_{ 2 },\) \({ \triangle }_{ 1= }\begin{vmatrix} { a }_{ 1 } & { b }_{ 1 } \\ { a }_{ 2 } & { b }_{ 2 } \end{vmatrix}, \ { \triangle }_{ 2 }=\begin{vmatrix} { b }_{ 1 } & { c }_{ 1 } \\ { b }_{ 2 } & { c }_{ 2 } \end{vmatrix}{ \triangle }_{ 3 }=\begin{vmatrix} { c }_{ 1 } & { a }_{ 1 } \\ { c }_{ 2 } & a_{ 2 } \end{vmatrix}\) then (x, y) is _______.

(a)

\(\left( \frac { { \triangle }_{ 2 } }{ { \triangle }_{ 1 } } ,\frac { { \triangle }_{ 3 } }{ { \triangle }_{ 1 } } \right) \)

(b)

\(\left( \frac { { \triangle }_{ 3 } }{ { \triangle }_{ 1 } }, \frac { { \triangle }_{ 2 } }{ { \triangle }_{ 1 } } \right) \)

(c)

\(\left( \frac { { \triangle }_{ 1 } }{ { \triangle }_{ 2 } } ,\frac { { \triangle }_{ 1 } }{ { \triangle }_{ 3 } } \right) \)

(d)

\(\left( \frac { { -\triangle }_{ 1 } }{ { \triangle }_{ 2 } }, \frac { {- \triangle }_{ 1 } }{ { \triangle }_{ 3 } } \right) \)

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

(a)

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

(b)

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

(c)

\(\frac12\sqrt { { e }^{ x } } +c\)

(d)

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

If f (x) is a continuous function and a < c < b, then \(\int_{a}^{c} f(x) d x+\int_{c}^{b} f(x) d x\) is _______.

(a)

\(\int_{a}^{b} f(x) d x-\int_{a}^{c} f(x) d x\)

(b)

\(\int_{a}^{c} f(x) d x-\int_{a}^{b} f(x) d x\)

(c)

\(\int_{a}^{b} f(x) d x\)

(d)

0

\(\int _{ 0 }^{ \infty }{ { x }^{ 4 }{ e }^{ -x } } \)dx is _______.

(a)

12

(b)

4

(c)

4!

(d)

64

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 producer’s surplus when the supply function for a commodity is P = 3 + x and x₀ = 3 is ________.

(a)

\(\frac{5}{2}\)

(b)

\(\frac{9}{2}\)

(c)

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

(d)

\(\frac{7}{2}\)

The area bounded by the parabola y² = 4x bounded by its latus rectum is ________.

(a)

\(\frac { 16 }{ 3 } \) sq.units

(b)

\(\frac { 8 }{ 3 } \) sq.units

(c)

\(\frac { 72 }{ 3 } \) sq.units

(d)

\(\frac { 1 }{ 3 } \) sq.units

The integrating factor of the differential equation \(\frac{dx}{dy}+Px=Q\) is ______.

(a)

e^ഽPdx

(b)

^{\(\int P d x\)}

(c)

ഽPdy

(d)

e^ഽPdy

The solution of the differential equation \(\frac { dy }{ dx } \) + Py = Q where P and Q are the function of x is ______.

(a)

\(y=\int Q e^{\int P d x} d x+c\)

(b)

\(y=\int Q e^{-\int P d x} d x+c\)

(c)

\(y e^{\int P d x}=\int Q e^{\int P d x} d x+c\)

(d)

\(y e^{\int P d x}=\int Q e^{-\int P d x} d x+C\)

Which of the following is the homogeneous differential equation?

(a)

(3x−5)dx = (4y−1)dy

(b)

xy dx−(x³+y³)dy = 0

(c)

y²dx+(x² − xy  − y²)dy = 0

(d)

(x²+y)dx = (y²+x)dy

E f (x)= _______.

(a)

f(x− h)

(b)

f (x)

(c)

f(x+ h)

(d)

f(x+ 2h)

Demand of products per day for three days are 21, 19, 22 units and their respective probabilities are 0.29, 0.40, 0.35. Profit per unit is 0.50 paisa then expected profits for three days are ________.

(a)

21, 19, 22

(b)

21.5, 19.5, 22.5

(c)

0.29, 0.40, 0.35

(d)

3.045, 3.8, 3.85

A probability density function may be represented by ________.

(a)

table

(b)

graph

(c)

mathematical equation

(d)

both (b) and (c)

A variable which can assume finite or countably infinite number of values is known as ________.

(a)

continuous

(b)

discrete

(c)

qualitative

(d)

none of them

The height of persons in a country is a random variable of the type ________.

(a)

discrete random variable

(b)

continuous random variable

(c)

both (a) and (b)

(d)

neither (a) nor (b)

The parameters of the normal distribution \(f(x)=\left(\frac{1}{\sqrt{72 \pi}}\right)\)\(\frac{e^{-(x-10)^{2}}}{72}\) –∞ <  x  <  ∞ ________.

(a)

(10,6)

(b)

(10,36)

(c)

(6,10)

(d)

(36,10)

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

Let z be a standard normal variable. If the area to the right of z is 0.8413, then the value of z must be: ________.

(a)

1.00

(b)

-1.00

(c)

0.00

(d)

-0.41

Errors in sampling are of  ______.

(a)

Two types

(b)

three types

(c)

four types

(d)

five types

The components of a time series which is attached to short term fluctuation is ________.

(a)

Secular trend

(b)

Seasonal variations

(c)

Cyclic variation

(d)

Irregular variation

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

The LCL for R chart is given by ________.

(a)

\({ D }_{ 2 }\bar { R } \)

(b)

\({ D }_{ 2 }\overset { = }{ R } \)

(c)

\({ D }_{ 3 }\overset { = }{ R } \)

(d)

\({ D }_{ 3 }\bar { R } \)

In a degenerate solution number of allocations is _______.

(a)

equal to m+n–1

(b)

not equal to m+n–1

(c)

less than m+n–1

(d)

greather than m+n–1

A type of decision –making environment is _______.

(a)

certainty

(b)

uncertainty

(c)

risk

(d)

all of the above