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 is an invertible matrix of order 2, then det (A^-1) be equal to ________.

(a)

det (A)

(b)

\({{1}\over{det(A)}}\)

(c)

1

(d)

0

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

(a)

3

(b)

6

(c)

5

(d)

4

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 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

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

(a)

\(\sqrt3\)

(b)

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

(c)

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

(d)

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

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

The graph of y = e^x intersect the y-axis at _______.

(a)

(0,0)

(b)

(1,0)

(c)

(0,1)

(d)

(1,1)

\(\frac{d}{dx}(a^x)=\) ________.

(a)

\(\frac { 1 }{ x\log e^a}\)

(b)

a^a

(c)

x log_e^a

(d)

a^x log_e^a

The demand function is always _______.

(a)

Increasing function

(b)

Decreasing function

(c)

Non-decreasing function

(d)

Undefined function

If R = 5000 units / year, C₁ = 20 paise , C₃ = Rs. 20 then EOQ is _______.

(a)

5000

(b)

100

(c)

1000

(d)

200

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

Let a sample space of an experiment be S = { E₁,E₂,....., E_n} Then \(\sum _{ i=1 }^{ n }{ P({ E }_{ t }) } \) is equal to _________.

(a)

0

(b)

1

(c)

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

(d)

\(\frac { 1 }{ 3 } \)

Probability of an impossible event is _________.

(a)

1

(b)

0

(c)

0.2

(d)

0.5

Correlation co-efficient lies between ______.

(a)

0 to ∞

(b)

-1 to +1

(c)

-1 to 0

(d)

-1 to ∞

The coefficient of correlation describes ________.

(a)

the magnitude and direction

(b)

only magnitude

(c)

only direction

(d)

no magnitude and no direction

In the context of network, which of the following is not correct?

(a)

A network is a graphical representation

(b)

A project network cannot have multiple initial and final nodes

(c)

An arrow diagram is essentially a closed network

(d)

An arrow representing an activity may not have a length and shape

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

Find |AB| if \(A=\begin{bmatrix} 3&-1\\2&1 \end{bmatrix} \) and \(B =\begin{bmatrix} 3&0\\1&-2 \end{bmatrix}\)

If nP_r = 360, find n and r.

Find the acute angle between the lines 2x - y + 3 = 0 and x + y + 2 = 0.

In any quadrilateral ABCD, prove that sin (A + B) + sin (C + D) = 0

Differentiate the following functions with respect to x, \(x^{\frac{3}{2}}\)

Find the maximum and minimum values of x³-6x²+7

Find the number of shares which will give an annual income of Rs. 3,600 from 12% stock of face value Rs. 100.

A die is thrown twice and the sum of the number appearing is observed to be 6. What is the conditional probability that the number 4 has appeared at least once?

From the following data calculate the correlation coefficient Σxy = 120, Σx² = 90, Σy² = 640

Draw a network diagram for the project whose activities and their predecessor relationships are given below

Activity	A	B	C	D	E	F
Predecessor activity	-	-	D	A	B	C

Find the inverse of each of the following matrices \(\left[ \begin{matrix} 1 & 2 & 3 \\ 0 & 2 & 4 \\ 0 & 0 & 5 \end{matrix} \right] \)

Find the term independent of x in the expansion of \({ \left( x-\frac { 2 }{ { x }^{ 2 } } \right) }^{ 15 }\)

Find the slope of the lines which make an angle of 45° with the line 3x - y + 5 = 0.

Prove that  \(2\sin ^{ 2 }{ \frac { \pi }{ 6 } } +\ cosec ^{ 2 }{ \frac { 7\pi }{ 6 } } \cos ^{ 2 }{ \frac { \pi }{ 3 } } =\frac { 3 }{ 2 } \)

Differentiate the following with respect to x : x³ e^x

For the production function P = \(4L^{ \frac { 3 }{ 4 } }K^{ \frac { 1 }{ 4 } }\) verify Euler’s theorem.

A sum of Rs.1000 is deposited at the beginning of each quarter in a S.B. account that pays C.I 8% compounded quarterly. Find the account at the end of 3 years.

From the following data compute the value of Harmonic Mean.

Marks	10	20	30	40	50
No. of students	20	30	50	15	5

Find the co-variance and co-efficient of correlation for the following data:
n=10, \(\sum\)x=50, \(\sum\)y=-30, \(\sum\)x²=290, \(\sum\)y²=300 and \(\sum\)xy=-115.

Solve the following LPP graphically. ∴ Maximize Z = 3x₁ + 4x₂  subject to the constraints x₁ + x₂ ≤ 4 and x₁,x₂ ≥ 0.

1. Two commodities A and B are produced such that 0.4 tonne of A and 0.7 tonne of B are required to produce a tonne of A. Similarly 0.1 tonne of A and 0.7 tonne of B are needed to produce a tonne of B. Write down the technology matrix. If 68 tonnes of A and 10.2 tonnes of B are required, find the gross production of both of them.

2. By the principle of mathematical induction, prove the following.
   4 + 8 + 12 + ...... + 4n = 2n(n + 1), for all \(n\in N\).

1. Resolve into partial factors : \(\frac { { x }^{ 2 }+x+1 }{ { x }^{ 2 }+2x+1 } \)

2. The profit Rs.y accumulated in thousand in x months is given by y = -x²  + 10x - 15. Find the best time to end the project.

1. Prove that \(\frac { 4tan\ x(1-{ tan }^{ 2 }x) }{ 1-6{ tan }^{ 2 } x+{ tan }^{ 4 } x } =tanx\)

2. If cosA =\(\frac{4}{5}\)and cosB =\(\frac{12}{13}\),\(\frac{3 \pi}{2}<(A, B)<2 \pi\), find the value of sin(A - B)

1. If \(y={ \left( x+\sqrt { 1+{ x }^{ 2 } } \right) }^{ m }\), then show that (1 + x)² y₂ + xy₁ - m² = 0.

2. A monopolist has a demand curve x = 106 – 2p and average cost curve AC = 5 + \(\frac { x }{ 50 } \) where p is the price per unit output and x is the number of units of output. If the total revenue is R = px, determine the most profitable output and the maximum profit.

1. What is the maximum slope of the tangent to the curve y = - x³ + 3x² +  9x - 27 and at what point is it?

2. a bank pays 8% interest compounded quarterly. Determine the equal deposits to be made at the end of each quarter for 3 years so as to receive Rs.300 at the end of 3 years.

1. Calculate the geometric mean of the data given below giving the number of families and the income per head of different classes of people in a village of Kancheepuram District.

   Class of people	No. of Families	Income per head in 1990 (Rs)
   Landlords	1	1000
   Cultivators	50	80
   Landless labourers	25	40
   Money- lenders	2	750
   School teachers	3	100
   Shop-keepers	4	150
   Carpenters	3	120
   Weavers	5	60

2. The heights ( in cm.) of a group of fathers and sons are given below

   Heights of fathers:	158	166	163	165	167	170	167	172	177	181
   Heights of Sons:	163	158	167	170	160	180	170	175	172	175

   Find the lines of regression and estimate the height of son when the height of the father is 164 cm.

1. Draw a network diagram for the following activities.

   Activity code	A	B	C	D	E	F	G	H	I	J	K
   Predecessor activity	-	A	A	A	B	C	C	C,D	E,F	G,H	I,J

2. A manufacturer produces two types of steel trunks. He has two machine A and B. For completing, the first type of the trunk requires 3 hours on machine A and 2 hours on machine B, whereas the second type of the trunk requires 3 hours on machine A and 3 hours on machine B. Machines A and B can work at the most for 18 hours and 14 hours per day respectively. He earns a profit of Rs.30 andRs.40 per trunk of the first type and second type respectively. How many trunks of the each type must he make each day to make maximum profit?