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

The inventor of input-output analysis is ________.

The possible out comes when a coin is tossed five times _________.

Number of words with or without meaning that can be formed using letters of the word "EQUATION" , with no repetition of letters is _____.

The double ordinate passing through the focus is _______.

The equation of directrix of the parabola y² = - x is _______.

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

If \(\alpha\) and \(\beta\) be between 0 and \(\frac{\pi}{2}\) and if \(\cos(\alpha+\beta)=\frac{12}{13}\) and \(\sin(\alpha-\beta)=\frac{3}{5}\) then \(\sin2\alpha\) is  _____.

If \(f\left( x \right) =\begin{cases} { x }^{ 2 }-4x\quad ifx\ge 2 \\ x+2\quad ifx<2 \end{cases}\), then f(5) is _______.

\(\frac{d}{dx}(5e^x-2logx)\) is equal to ________.

Marginal revenue of the demand function p = 20–3x is _______.

The demand function is always _______.

The annual income on 500 shares of face value Rs.100 at 15% is _______.

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

The mean of the values 11,12,13,14 and 15 is _________.

If two events A and B are dependent then the conditional probability of P(B/A) is _________.

Example for positive correlation is______.

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

Maximize: z = 3x₁ + 4x₂ subject to 2x₁ + x₂ ≤ 40, 2x₁+ 5x₂ ≤ 180, x₁, x₂ ≥ 0. In the LPP, which one of the following is feasible corner point?

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

Find the minors and cofactors of all the elements of the following determinants. \(\begin{bmatrix} 1&-3&2\\4&-1&2\\3&5&2 \end{bmatrix}\)

Find the values of A and B if \(\frac { 1 }{ \left( { x }^{ 2 }-1 \right) } =\frac { A }{ x-1 } +\frac { B }{ x+1 } \)

Find the cartesian equation of the circle whose parametric equations are x = 3 cos\(\theta\), y = 3 sin\(\theta,\) \(0\le \theta \le 2\pi \) 

Prove that \(\cos18^o-\sin18^o=\sqrt{2}.\sin27^o\)

Determine whether the following functions are odd or even?
f(x) = x + x²

A certain manufacturing concern has the toal cost function C = \({1\over5}x^2-6x+100\).Find when the tatal cost is minimum.

What is the amount of perpetual annuity of Rs. 50 at 5% compound interest per year?

The price of a commodity increased by 5% from 2004 to 2005, 8% from 2005 to 2006 and 77% from 2006 to 2007. Calculate the average increase from 2004 to 2007?

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

A producer has 30 and 17 units of labour and capital respectively which he can use to produce two types of goods X and Y. To produce one unit of X, 2 unit of labour and 3 units of capital are required. Similarly, 3 units of labour and 1 unit of capital is required to produce one unit of Y. If X and Yare priced at HOO and H20 per unit respectively, how should the producer use his resources to maximize the total revenue? Formulate the LPP for the above.

Find the minor and cofactor of each element of the determinant\(\left| \begin{matrix} 1 & -2 \\ 4 & 3 \end{matrix} \right| \)

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

For what value of k does 12x² + 7xy + ky² + 13x - y + 3 = 0 represents a pair of straight lines?

Convert the following into the product of trigonometric functions cos75^o + cos 45^o

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

Find the elasticity of supply for the supply law \(x={p\over p+5}\) when p = 20 and interpret your result.

A man wishes to pay back his depts of Rs.3783 due after 3 years by 3 equal yearly instalments. Find the amount of each instalments,money being worth 5% p.a. compounded annually

Calculate GM for the following table gives the weight of 31 persons in sample survey.

Find the regression co-efficient of x on y from the following data. \(\sum\)X=20, \(\sum\)Y=40, \(\sum\)XY=300, \(\sum\)X²=150, \(\sum\)Y²=345, N=5. Find the value of x when y=5

Solve the following LPP graphically. Maximize \(Z={ x }_{ 1 }+{ x }_{ 2 }\)
Subject to the constraints \({ x }_{ 1 }-{ x }_{ 2 }\le -1,{ -x }_{ 1 }+{ x }_{ 2 }\le 0\quad and\quad { x }_{ 1 }+{ x }_{ 2 }\ge 0\)

Find adjoint of \(A=\left[ \begin{matrix} 1 & -2 & -3 \\ 0 & 1 & 0 \\ -4 & 1 & 0 \end{matrix} \right] \)

Resolve into partial fractions for the following : \(\frac{x-2}{(x+2)(x-1)^2}\)

Using the principle of mathematical induction, prove that 1.3 + 2.3² + 3.3³ + ... + n.3ⁿ =\(\frac { (2n-1){ 3 }^{ n+1 }+3 }{ 4 } for\ all\ n\in N\)

As the number of units produced increases from 500 to 1000 and the total cost of production increases from. Rs 6000 to Rs 9000. Find the relationship between the cost (y) and the number of units produced (x) if the relationship is linear.

Prove that cos 20° cos 40° cos 60° cos 80⁰ = \(\frac { 1 }{ 16 } \)

If  \(sin\left( { sin }^{ -1 }\left( \frac { 1 }{ 5 } \right) +{ cos }^{ -1 }(x) \right) =1\)  then find the value of x

Draw the graph of f(x) = a^x, \(a\ne 1\) and a > 0

Find the stationary values and stationary points for the function f(x) = 2x³ + 9x² + 12x + 1

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

Equal amounts are invested in 12% stock at 95 (brokerage). If 12% stock brought at Rs.120 more by way of dividend income than the other, find the amount invested in each stock?

A, B and C was 50%, 30% and 20% of the cars in a service station respectively. They fail to clean the glass in 5% , 7% and 3% of the cars respectively. The glass of a washed car is checked. What is the probability that the glass has been cleaned?

Calculate coefficient of correlation from the following data

A company is producing three products P₁, P₂ and P₃, with profit contribution of Rs.20, Rs.25 and Rs.15 per unit respectively. The resource requirements per unit of each of the products and total availability are given below.

Formulate the above as a linear programming model.

Calculate the earliest start time, earliest finish time, latest start time and latest finish time of each activity of the project given below and determine the critical path of the project and duration to complete the project.