If A is square matrix of order 3, then |kA| is________.

(a)

k|A|

(b)

-k|A|

(c)

k³|A|

(d)

-k³|A|

The number of Hawkins-Simon conditions for the viability of an input - output analysis is ________.

(a)

1

(b)

3

(c)

4

(d)

2

The value of \(\begin{vmatrix} x & x^2 & -yz & 1 \\ y & y^2 & -zx & 1 \\ z & z^2 & -xy &1 \end{vmatrix}\) is ________.

(a)

1

(b)

0

(c)

-1

(d)

-xyz

If \(\begin{vmatrix} x & 2 \\ 8 &5 \end{vmatrix}=0\) then the value of x is ________.

(a)

\({{-5}\over{6}}\)

(b)

\({{5}\over{6}}\)

(c)

\({{-16}\over{5}}\)

(d)

\({{16}\over{5}}\)

If any three rows or columns of a determinant are identical then the value of the determinant is ________.

(a)

0

(b)

2

(c)

1

(d)

3

If nC₃ = nC₂, then the value of nC₄ is _______.

(a)

2

(b)

3

(c)

4

(d)

5

If nP_r = 720 (nC_r), then r is equal to ______.

(a)

4

(b)

5

(c)

6

(d)

7

The last term in the expansion of (3 +\(\sqrt{2}\) )⁸ is ________

(a)

81

(b)

16

(c)

8\(\sqrt{2}\)

(d)

27\(\sqrt{3}\)

If \(\frac { kx }{ (x+4)(2x-1) } =\frac { 4 }{ x+4 } +\frac { 1 }{ 2x-1 } \) then k is equal to _______.

(a)

9

(b)

11

(c)

5

(d)

7

The total number of 9 digit number which have all different digit is ________.

(a)

10!

(b)

9!

(c)

9\(\times\)9!

(d)

10\(\times\)10!

If the lines 2x - 3y - 5 = 0 and 3x - 4y - 7 = 0 are the diameters of a circle, then its centre is _______.

(a)

(-1, 1)

(b)

(1,1)

(c)

(1, -1 )

(d)

(-1, -1)

The x-intercept of the straight line 3x + 2y - 1 = 0 is _______.

(a)

3

(b)

2

(c)

1/3

(d)

1/2

The length of the tangent from (4,5) to the  circle x² + y² = 16 is _______.

(a)

4

(b)

5

(c)

16

(d)

25

The centre of the circle x² + y - 2x + 2y - 9 = 0 is _______.

(a)

(1,1)

(b)

(-1,-1)

(c)

(-1,1)

(d)

(1, -1)

The double ordinate passing through the focus is _______.

(a)

focal chord

(b)

latus rectum

(c)

directrix

(d)

axis

The value of \(\sin15^o\) is ______.

(a)

\(\frac{\sqrt{3}+1}{2\sqrt{2}}\)

(b)

\(\frac{\sqrt{3}-1}{2\sqrt{2}}\)

(c)

\(\frac{\sqrt3}{\sqrt2}\)

(d)

\(\frac{\sqrt3}{2\sqrt2}\)

The value of \(\sin(-420^o)\) is _______.

(a)

\(\frac{\sqrt3}{2}\)

(b)

\(-\frac{\sqrt3}{2}\)

(c)

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

(d)

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

The value of sin 15^o cos 15^o is ______.

(a)

1

(b)

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

(c)

\(\frac{\sqrt3}{2}\)

(d)

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

If sin A + cos A = 1, then sin 2A is equal to _______.

(a)

1

(b)

2

(c)

0

(d)

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

\(\sec^{-1}\frac{2}{3}+cosec^{-1}\frac{2}{3}=\) ______.

(a)

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

(b)

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

(c)

\(\pi\)

(d)

\(-\pi\)

If f(x) = \(\frac{1-x}{1+x}\) then f(-x) is equal to _______.

(a)

-f(x)

(b)

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

(c)

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

(d)

f(x)

The graph of f(x) = e^x is identical to that of ________.

(a)

f(x) = a^x, a > 1

(b)

f(x) = a^x, a < 1

(c)

f(x) = a^x, 0 < a < 1

(d)

y = ax +b, a \(\ne\) 0

If f(x) = x² and g(x) = 2x + 1 then (fg)(0) is ________.

(a)

0

(b)

2

(c)

1

(d)

4

For what value of x, f(x) = \(\frac{x+2}{x-1}\) is not continuous?

(a)

-2

(b)

1

(c)

2

(d)

-1

If the function f(x) is continuous at x = a if \(\lim _{ x\rightarrow a }{ f\left( x \right) } \) is equal to ________.

(a)

f(-a)

(b)

f\((\frac{1}{a})\)

(c)

2f(a)

(d)

f(a)

If the demand function is said to be inelastic, then _______.

(a)

|η_d| > 1

(b)

|η_d| = 1

(c)

|η_d| < 1

(d)

|η_d| = 0

Relationship among MR, AR and η_d is ______.

(a)

\({ n }_{ d }=\frac { AR }{ AR-MR } \)

(b)

η_d =  AR - MR

(c)

MR = AR = η_d

(d)

\(AR=\frac { MR }{ {ηd } } \)

Profit P(x) is maximum when ________.

(a)

MR = MC

(b)

MR = 0

(c)

MC = AC

(d)

TR = AC

If u = 4x² + 4xy + y² + 32 + 16 , then \(\frac { \partial ^{ 2 }u }{ \partial y\partial x } \) is equal to ________.

(a)

8x + 4y + 4

(b)

4

(c)

2y + 32

(d)

0

The demand function is always _______.

(a)

Increasing function

(b)

Decreasing function

(c)

Non-decreasing function

(d)

Undefined function

The dividend received on 200 shares of face value Rs.100 at 8% is ________.

(a)

Rs. 1600

(b)

Rs. 1000

(c)

Rs. 1500

(d)

Rs. 800

If a man received a total dividend of Rs. 25,000 at 10% dividend rate on a stock of face value Rs.100, then the number of shares purchased.

(a)

3500

(b)

4500

(c)

2500

(d)

300

If ‘a’ is the annual payment, ‘n’ is the number of periods and ‘i’ is compound interest for Rs. 1 then future amount of the annuity is  _______.

(a)

A = \(\frac{a}{i}(1+i)(1+i)^n-1]\)

(b)

A = \(\frac{a}{i}[(1+i)^n-1]\)

(c)

P = \(\frac{a}{i}\)

(d)

P = \(\frac{a}{i}(1+i)[1-(1+i)^{-n}]\)

An annuity in which payments are made at the beginning of each payment period is called _______.

(a)

Annuity due

(b)

An immediate annuity

(c)

perpetual annuity

(d)

none of these

The present value of the perpetual annuity of Rs. 2000 paid monthly at 10 % compound interest is _______.

(a)

Rs. 2,40,000

(b)

Rs. 6,00,000

(c)

Rs. 20,40,000

(d)

Rs. 2,00,400

The geometric mean of two numbers 8 and 18 shall be _________.

(a)

12

(b)

13

(c)

15

(d)

11.08

Harmonic mean is the reciprocal of _________.

(a)

Median of the values.

(b)

Geometric mean of the values.

(c)

Arithmetic mean of the reciprocal of the values.

(d)

Quartiles of the values.

Harmonic mean is better than other means if the data are for _________.

(a)

Speed or rates.

(b)

Heights or lengths.

(c)

Binary values like 0 and 1

(d)

Ratios or proportions.

If median = 45 and its coefficient is 0.25, then the mean deviation about median is _________.

(a)

11.25

(b)

180

(c)

0.0056

(d)

45

Probability of an impossible event is _________.

(a)

1

(b)

0

(c)

0.2

(d)

0.5

The variable which influences the values or is used for prediction is called________.

(a)

Dependent variable

(b)

Independent variable

(c)

Explained variable

(d)

Regressed

The regression coefficient of Y on X ________.

(a)

b_xy =\(\frac { N\Sigma dxdy-(\Sigma dx)(\Sigma dy) }{ N\Sigma dy^{ 2 }-(\Sigma dy)^{ 2 } } \)

(b)

b_yx =\(\frac { N\Sigma dxdy-(\Sigma dx)(\Sigma dy) }{ N\Sigma dy^{ 2 }-(\Sigma dy)^{ 2 } } \)

(c)

b_yx =\(\frac { N\Sigma dxdy-(\Sigma dx)(\Sigma dy) }{ N\Sigma dx^{ 2 }-(\Sigma dx)^{ 2 } } \)

(d)

b_xy =\(\frac { N\Sigma xy-(\Sigma x)(\Sigma y) }{ \sqrt { N\Sigma { x }^{ 2 }-(\Sigma x)^{ 2 }\times \sqrt { N\Sigma { y }^{ 2 }-(\Sigma y)^{ 2 } } } } \)

The lines of regression of X on Y estimates ________.

(a)

X for a given value of Y

(b)

Y for a given value of X

(c)

X from Y and Y from X

(d)

none of these

The person suggested a mathematical method for measuring the magnitude of linear relationship between two variables say X and Y is ________.

(a)

Karl Pearson

(b)

Spearman

(c)

Croxton and Cowden

(d)

Ya Lun Chou

The lines of regression intersect at the point ________.

(a)

(X,Y)

(b)

\(\left( \bar { X } ,\bar { Y } \right) \)

(c)

(0,0)

(d)

(σ_x, σ_y)

A solution which maximizes or minimizes the given LPP is called ______.

(a)

a solution

(b)

a feasible solution

(c)

an optimal solution

(d)

none of these

The minimum value of the objective function Z = x + 3y subject to the constraints 2x + y ≤ 20, x + 2y ≤ 20, x > 0 and y > 0 is ______.

(a)

10

(b)

20

(c)

0

(d)

5

Which of the following is not correct?

(a)

Objective that we aim to maximize or minimize

(b)

Constraints that we need to specify

(c)

Decision variables that we need to determine

(d)

Decision variables are to be unrestricted

The objective of network analysis is to ________.

(a)

Minimize total project cost

(b)

Minimize total project duration

(c)

Minimize production delays, interruption and conflicts

(d)

All the above

Given an L.P.P maximize Z = 2x₁ + 3x₂ subject to the constrains x₁ + x₂ ≤ 1, 5x₁ + 5x₂ ≥ 0 and x₁ ≥ 0, x₂ ≥ 0 using graphical method, we observe ______.

(a)

No feasible solution

(b)

unique optimum solution

(c)

multiple optimum solution

(d)

none of these