The value of \(\begin{vmatrix} 2x+y & x & y \\ 2y+z & y & z \\ 2z+x & z & x \end{vmatrix}\) is ________.

(a)

xyz

(b)

x+y+z

(c)

2x+2y+2z

(d)

0

The value of n, when nP₂ = 20 is _______.

(a)

3

(b)

6

(c)

5

(d)

4

If kx² + 3xy - 2y² = 0 represent a pair of lines which are perpendicular then k is equal to _______.

(a)

1/2

(b)

-1/2

(c)

2

(d)

-2

The value of cos²45^o - sin²45^o is_______.

(a)

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

(b)

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

(c)

0

(d)

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

f(x) = - 5 , for all \(x\in R\), is a ________.

(a)

an identity function

(b)

modulus function

(c)

exponential function

(d)

constant function

Profit P(x) is maximum when ________.

(a)

MR = MC

(b)

MR = 0

(c)

MC = AC

(d)

TR = AC

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

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

(a)

12

(b)

13

(c)

15

(d)

11.08

If r(X,Y) = 0 the variables X and Y are said to be ______.

(a)

Positive correlation

(b)

Negative correlation

(c)

No correlation

(d)

Perfect positive correlation

In constructing the network which one of the following statement is false?

(a)

Each activity is represented by one and only one arrow. (i.e) only one activity can connect any two nodes

(b)

Two activities can be identified by the same head and tail events

(c)

Nodes are numbered to identify an activity uniquely. Tail node (starting point) should be lower than the head node (end point) of an activity

(d)

Arrows should not cross each other