If A is 3 \(\times\) 3 matrix and |A| = 4, then |A^-1| is equal to ________.

(a)

\({{1}\over{4}}\)

(b)

\({{1}\over{16}}\)

(c)

2

(d)

4

If \(\triangle=\begin{vmatrix} {a}_{11} & {a}_{12} & {a}_{13} \\ {a}_{21} & {a}_{22} & {a}_{23} \\ {a}_{31} & {a}_{32} & {a}_{33} \end{vmatrix}\) and A_ij is cofactor of a_ij, then value of \(\triangle\) is given by ________.

(a)

a₁₁ A₃₁ + a₁₂ A₃₂ + a₁₃ A₃₃

(b)

a₁₁ A₁₁ + a₁₂ A₂₁ + a₁₃ A₃₁

(c)

a₂₁ A₁₁ + a₂₂ A₁₂ + a₂₃ A₁₃

(d)

a₁₁ A₁₁ + a₂₁ A₂₁ + a₃₁ A₃₁

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 slope of the line 7x + 5y - 8 = 0 is _______.

(a)

7/5

(b)

-7/5

(c)

5/7

(d)

-9/7

The eccentricity of the parabola is _______.

(a)

3

(b)

2

(c)

0

(d)

1

The value of \(\frac{3 \tan 10^{\circ}-\tan ^3 10^{\circ}}{1-3 \tan ^2 10^{\circ}}\) is _______,

(a)

\(\frac{1}{\sqrt3}\)

(b)

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

(c)

\(\frac{\sqrt3}2\)

(d)

\(\frac{1}{\sqrt2}\)

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

(a)

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

(b)

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

(c)

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

(d)

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

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

(a)

(0,0)

(b)

(1,0)

(c)

(0,1)

(d)

(1,1)

The range of f(x) = |x|, for all \(x\in R\), is ________.

(a)

(0, \(\infty \))

(b)

(0, \(\infty \))

(c)

(-\(\infty \), \(\infty \))

(d)

(1, \(\infty \))

The demand function is always _______.

(a)

Increasing function

(b)

Decreasing function

(c)

Non-decreasing function

(d)

Undefined function

if q = 1000 + 8p₁ - p₂ then, \(\frac { \partial q }{ \partial { p }_{ 1 } } \) is _______.

(a)

-1

(b)

8

(c)

1000

(d)

1000 - p₂

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

When an observation in the data is zero, then its geometric mean is

(a)

Negative

(b)

Positive

(c)

Zero

(d)

Cannot be calculated

The events A and B are independent if _________.

(a)

\(P\left( A\cap B \right) =0\)

(b)

\(P\left( A\cap B \right) =P(A)\times P(B)\)

(c)

\(P\left( A\cup B \right) =P(A)+P(B)\)

(d)

\(P\left( A\cup B \right) =P(A)\times P(B)\)

The correlation coefficient ________.

(a)

r = ±\(\sqrt { { b }_{ xy }\times { b }_{ yx } } \)

(b)

r = \(\frac { 1 }{ { b }_{ xy }\times { b }_{ yx } } \)

(c)

r = b_xy x b_yx

(d)

r = ±\(\sqrt { \frac { 1 }{ { b }_{ xy }\times { b }_{ yx } } } \)

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

One of the conditions for the activity (i, j) to lie on the critical path is_______.

(a)

E_j - E_i = L_j - L_i = t_ij

(b)

E_i - E_j = L_j - L_i = t_ij

(c)

E_j - E_i = L_i - L_j = t_ij

(d)

E_j - E_i = L_j - L_i ≠ t_ij

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

Show that \(\left[ \begin{matrix} 8 & 2 \\ 4 & 3 \end{matrix} \right] \)is non – singular.

If P(n) is the statement "2³ⁿ -1 is a multiple of 7" then show that P (5) is true.

Find the equation of the circle with centre at (3, –1) and radius is 4 units.

If \(\cos x=-\frac{1}{2}\) and \(\pi , find the value of \(4\tan^2x-3cosec^2x\)

Evaluate \(\underset { x\rightarrow \frac { 1 }{ 2 } }{ lim } \frac { { 4x }^{ 2 }-1 }{ 2x-1 } \)

A tour operator charges Rupees 136 per passenger with a discount of 40 paisa for each passenger in excess of 100. The operator requires at least 100 passengers to operate the tour. Determine the number of passenger that will maximize the amount of money the tour operator receives.

A person pays Rs 64,000 per annum for 12 years at the rate of 10% per year. Find the annuity [(1.1)¹² = 3.3184]

A person purchases tomatoes from each of the 4 places at the rate of 1kg., 2kg., 3kg., and 4kg. per rupee respectively. On the average, how many kilograms has he purchased per rupee?

Calculate the correlation coefficient from the following data
N = 9, ΣX = 45, ΣY = 108, ΣX² = 285, ΣY² = 1356, ΣXY = 597

Develop a network based on the following information:

Activity:	A	B	C	D	E	F	G	H
Immediate predecessor:	-	-	A	B	C, D	C, D	E	F

Solve: 2x + 5y = 1 and 3x + 2y = 7 using matrix method.

If \(A=\left[\begin{array}{rr} 2 & 3 \\ 1 & -6 \end{array}\right] \text { and } B=\left[\begin{array}{rr} -1 & 4 \\ 1 & -2 \end{array}\right],\) then verify adj (AB) = (adj B) (adj A).

Evaluate the following using binomial theorem: (101)⁴

If the lines x + y = 6 and x + 2y = 4 are diameters of the circle, and the circle passes through the point (2, 6)  then find its equation.

Find \(\frac{dy}{dx}\)  of the following functions: x = a (\(\theta\) - sin \(\theta\)), y = a (1 - cos \(\theta\))

A company has to supply 1000 item per month at a uniform rate and for each time, a production run is started with the cost of Rs. 200. Cost of holding is Rs. 20 per item per month. The number of items to be produced per run has to be ascertained. Determine the total of setup cost and average inventory cost if the run size is 500, 600, 700, 800. Find the optimal production run size using EOQ formula.

What amount should be deposited annually so that after 16 years a person receives Rs. 1,67,160 if the interest rate is 15% [(1.15)¹⁶ = 9.358]

Calculate mean deviation about median for the following data:

Class	0-10	10-20	20-30	30-40	40-50
Frequency	5	8	15	16	6

If two regression co-efficient are 2 and 0.45, what will be the co-efficient of correlation?

A company produces two types of pens A and B. Pen A is of superior quality and pen B is of lower quality. Profits on pens A and B are Rs. 5 and Rs. 3 per pen respectively. Raw materials required for each pen A is twice as that of pen B. The supply of raw material is sufficient only for 1000 pens per day. Pen A requires a special clip and only 400 such clips are available per day. For pen B, only 700 clips are available per day. Formulate this problem as a linear programming problem.

1. Data on readership of a magazine indicates that the proportion of male readers over 30 years old is 0.30 and the proportion of male reader under 30 is 0.20. If the proportion of readers under 30 is 0.80. What is the probability that a randomly selected male subscriber is under 30?

2. Solve the following LPP by graphical method Minimize z = 5x₁ + 4x₂ Subject to constraints 4x₁ + x₂ ≥ 40 ; 2x₁ + 3x₂ ≥ 90 and x₁, x₂ > 0.

1. Differentiate (sec x -1) (sec x +1)

2. A company buys in lots of 500 boxes which is a 3 month supply. The cost per box is Rs. 125 and the ordering cost in Rs. 150. The inventory carrying cost is estimated at 20% of unit value.
   (i) Determine the total amount cost of existing inventory policy
   (ii) Determine EOQ in units
   (iii) How much money could be saved by applying the economic order quantity?

1. Differentiate the following with respect to x \(\sqrt { \frac { (x-1)(x-2) }{ (x-3)({ x }^{ 2 }+x+1) } } \)

2. A computer while calculating the correlation co-efficient between two variables x and y from 25 pairs of observations, obtained the following results. \(\sum\)x=125, \(\sum\)x²=650, \(\sum\)y=100, \(\sum\)y²=460, xy=508. It was later found out that it had copied down two pairs as while the correct values are 

   x	y
   6	14
   8	6

    

   x	y
   8	12
   6	8

   Obtain the correlation co-efficient for the correct value.

1. Find the equation of the parabola whose vertex is (0, 0) passing through the point (2, 3) and axis is along X-axis.

2. If  z = 4x⁶ - 8x³ - 7x + 6xy + 8y + x³y⁵, find 
   (i) \({\partial^2z\over \partial y^2}\) (ii)\(\partial^2 z\over \partial x\partial y\)(iii) \(\partial^2z\over \partial y\partial x\)

1. If a parabolic reflector is 20 cm in diameter and 5 cm deep, find the focus.

2. Equal amounts are invested in 10% stock at 89 and 7% stock at 90 (1% brokerage paid in both transactions). If 10% stock bought Rs. 100 more by way of dividend income than the other, find the amount invested in each stock.

1. If \(A=\left[ \begin{matrix} 1 & tan\quad x \\ -tan\quad x & \quad \quad \quad 1 \end{matrix} \right] \), then show that A^TA^-1 = \(\left[ \begin{matrix} cos\quad 2x & -sin2x \\ sin\quad 2x & cos2x \end{matrix} \right] .\)

2. Prove that:  \(\frac { \sin { \left( 180-\theta \right) } \cos { \left( 90+\theta \right) } \tan { \left( 270-\theta \right) \cot { \left( 360-\theta \right) } } }{ \sin { \left( 360-\theta \right) \cot { \left( 360+\theta \right) \sin { \left( 270-\theta \right) \csc { \left( -\theta \right) } } } } } =-1\)

1. Resolve into partial fractions for the following : \(\frac{1}{\left(x^2+4\right)(x+1)}\)

2. As the number of units manufactured increases from 6000 to 8000, the total cost of production increases from Rs. 33,000 to Rs. 40,000. Find the relationship between the cost (y) and the number of units made (x) if the relationship is linear.