The co-factor of -7 in the determinant \(\begin{vmatrix} 2 & -3 & 5 \\ 6 & 0 & 4 \\ 1 & 5 & -7 \end{vmatrix}\) is________.

(a)

-18

(b)

18

(c)

-7

(d)

7

If \(\triangle=\begin{vmatrix} 1 & 2 & 3 \\ 3 & 1 & 2 \\ 2 & 3 & 1 \end{vmatrix}\) then \(\begin{vmatrix} 3 & 1 & 2 \\ 1 & 2 & 3 \\ 2 & 3 & 1 \end{vmatrix}\) is ________.

(a)

\(\triangle\)

(b)

-\(\triangle\)

(c)

3\(\triangle\)

(d)

-3\(\triangle\)

adj (AB) is equal to ________.

(a)

adj A adj B

(b)

adj A^T adj B^T

(c)

adj B adj A

(d)

adj B^T adj A^T

If A and B are non-singular matrix then, which of the following is incorrect?

(a)

A² = I Iimplies A^-1 = A

(b)

I^-1 = I

(c)

If AX = B, then X = B^-1 A

(d)

If A is square matrix of order 3 then |adj A|= |A|²

If A is a square matrix of order 3 and IAI = 3 then | adj A| is equal to ________.

(a)

81

(b)

27

(c)

3

(d)

9

The number of diagonals in a polygon of n seates is equal to _______.

(a)

nC₂

(b)

nC₂ - 2

(c)

nC₂ - n

(d)

nC₂ - 1

The greatest positive integer which divide n(n + 1) (n + 2) (n + 3) for n \(\in\) N is ________.

(a)

2

(b)

6

(c)

20

(d)

24

For all n > 0, nC₁ + nC₂ + nC₃ + ... +nC_n is equal to _______

(a)

2n

(b)

2ⁿ- 1

(c)

n²

(d)

n² - 1

The number of ways to arrange the letters of the word "CHEESE" is ______.

(a)

120

(b)

240

(c)

720

(d)

6

Thirteen guests has participated in a dinner. The number of handshakes happened in the dinner is __________.

(a)

715

(b)

78

(c)

286

(d)

13

The angle between the pair of straight lines x² - 7xy + 4y² = 0 _______.

(a)

\(tan^{-1}\left(1\over 3\right)\)

(b)

\(tan^{-1}\left(1\over 2\right)\)

(c)

\(tan^{-1}\left(\sqrt{33}\over 5\right)\)

(d)

\(tan^{-1}\left(5\over\sqrt{33}\right)\)

Length of the latus rectum of the parabola y² = - 25x is _______.

(a)

25

(b)

-5

(c)

5

(d)

-25

Combined equation of co-ordinate axes is _______.

(a)

x²-y² = 0

(b)

x²+y² = 0

(c)

xy = c

(d)

xy = 0

If the circle touches x axis, y axis and the line x = 6 then the length of the diameter of the circle is _______.

(a)

6

(b)

3

(c)

12

(d)

4

The eccentricity of the parabola is _______.

(a)

3

(b)

2

(c)

0

(d)

1

If \(\tan\theta=\frac{1}{\sqrt5}\) and \(\theta\) lies in the first quadrant, then \(\cos\theta\) is _______.

(a)

\(\frac{1}{\sqrt6}\)

(b)

\(\frac{-1}{\sqrt6}\)

(c)

\(\frac{\sqrt5}{\sqrt6}\)

(d)

\(\frac{-\sqrt5}{\sqrt6}\)

The value of \(\cos(-480^o)\) is ________.

(a)

\(\sqrt3\)

(b)

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

(c)

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

(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 \(\tan A=\frac{1}{2}\) and \(\tan B=\frac{1}{3}\) then tan(2A + B) is equal to ______.

(a)

1

(b)

2

(c)

3

(d)

4

\(\sin\left(\cos^{-1}\frac{3}{5}\right)\) is _____.

(a)

\(\frac{3}{5}\)

(b)

\(\frac{5}{3}\)

(c)

\(\frac{4}{5}\)

(d)

\(\frac{5}{4}\)

The graph of the line y = 3 is _______.

(a)

Parallel to x-axis

(b)

Parallel to y-axis

(c)

Passing through the origin

(d)

Perpendicular to x-axis

Which of the following function is neither even nor odd?

(a)

f(x) = x³ + 5

(b)

f(x) = x⁵

(c)

f(x) = x¹⁰

(d)

f(x) = x²

\(\lim _{ x\rightarrow \infty }{ \frac { \tan { \theta } }{ \theta } } =\)________.

(a)

1

(b)

\(\infty\)

(c)

\(-\infty\)

(d)

\(\theta\)

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 y = log x then y₂ = ________.

(a)

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

(b)

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

(c)

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

(d)

e²

Instantaneous rate of change of y = 2x² + 5x with respect to x at x = 2 is _________.

(a)

4

(b)

5

(c)

13

(d)

9

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

If u = \({ e }^{ { x }^{ 2 } }\) then \(\frac { \partial u }{ \partial x } \) is equal to _______.

(a)

\({ 2x }e^{ { x }^{ 2 } }\)

(b)

\({ e }^{ { x }^{ 2 } }\)

(c)

\({2 e }^{ { x }^{ 2 } }\)

(d)

0

Average cost is minimum when _______.

(a)

Marginal cost = Marginal revenue

(b)

Average cost = Marginal cost

(c)

Average cost = Marginal revenue

(d)

Average Revenue = Marginal cost

The demand function is always _______.

(a)

Increasing function

(b)

Decreasing function

(c)

Non-decreasing function

(d)

Undefined function

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

Purchasing price of one share of face value 100 available at a discount of \(9\frac{1}{2}\%\) with brokerage \(\frac{1}{2}\%\) is ________.

(a)

Rs. 89

(b)

Rs. 90

(c)

Rs. 91

(d)

Rs. 95

A person brought 100 shares of 9% stock of face value Rs. 100, at a discount of 10%, then the stock purchased is _______.

(a)

Rs. 9000

(b)

Rs. 6000

(c)

Rs. 5000

(d)

Rs. 4000

Rs. 5000 is paid as perpetual annuity every year and the rate of C.I 10 %. Then present value P of immediate annuity is _______.

(a)

Rs. 60,000

(b)

Rs. 50,000

(c)

Rs. 10,000

(d)

Rs. 80,000

A invested some money in 10% stock at Rs.96. If B wants to invest in an equally good 12% stock, he must purchase a stock worth of  _______.

(a)

Rs. 80

(b)

Rs. 115.20

(c)

Rs. 120

(d)

Rs. 125.40

The best measure of central tendency is _________.

(a)

Arithmetic mean

(b)

Harmonic mean

(c)

Geometric mean

(d)

Median

The harmonic mean of the numbers 2,3,4 is _________.

(a)

\(\frac { 12 }{ 13 } \)

(b)

2

(c)

\(\frac { 36 }{ 13 } \)

(d)

\(\frac { 13 }{ 36 } \)

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

The probability of drawing a spade from a pack of card is _________.

(a)

1/52

(b)

1/13

(c)

4/13

(d)

1/4

If the values of two variables move in same direction then the correlation is said to be ______.

(a)

Negative

(b)

positive

(c)

Perfect positive

(d)

No correlation

The variable whose value is influenced (or) is to be predicted is called ________.

(a)

dependent variable

(b)

independent variable

(c)

regressor

(d)

explanatory variable

The regression coefficient of X on Y ________.

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

(d)

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

If X and Y are two variates, there can be atmost ________.

(a)

One regression line

(b)

two regression lines

(c)

three regression lines

(d)

more regression lines

Scatter diagram of the variate values (X,Y) give the idea about ________.

(a)

functional relationship

(b)

regression model

(c)

distribution of errors

(d)

no relation

In a network while numbering the events which one of the following statement is false?

(a)

Event numbers should be unique

(b)

Event numbering should be carried out on a sequential basis from left to right

(c)

The initial event is numbered 0 or 1

(d)

The head of an arrow should always bear a number lesser than the one assigned at the tail of the arrow

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

Network problems have advantage in terms of project _______.

(a)

Scheduling

(b)

Planning

(c)

Controlling

(d)

All the above