The value of x if \(\begin{vmatrix} 0 & 1 & 0 \\ x & 2 & x \\ 1 & 3 & x \end{vmatrix}=0\) is_________.

(a)

0, - 1

(b)

0, 1

(c)

- 1, 1

(d)

- 1, - 1

If A is square matrix of order 3, then |kA| is________.

(a)

k|A|

(b)

-k|A|

(c)

k³|A|

(d)

-k³|A|

If any three rows or columns of a determinant are identical then the value of the determinant is ________.

(a)

0

(b)

2

(c)

1

(d)

3

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

(a)

3

(b)

6

(c)

5

(d)

4

The term containing x³ in the expansion of (x - 2y)⁷ is _________.

(a)

3^rd

(b)

4^th

(c)

5^th

(d)

6^th

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

(a)

7/5

(b)

-7/5

(c)

5/7

(d)

-9/7

The degree measure of \(\frac{\pi}{8}\) is ______.

(a)

20^o60^'

(b)

22^o30^'

(c)

20^o60^'

(d)

20^o30^'

The value of \(\frac{1}{cosec(-45^o)}\) is _______.

(a)

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

(b)

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

(c)

\(\sqrt2\)

(d)

\(-\sqrt2\)

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

(a)

(0,0)

(b)

(1,0)

(c)

(0,1)

(d)

(1,1)

If demand and the cost function of a firm are p = 2–x and c = 2x² + 2x + 7 then its profit function is ________.

(a)

x² + 7

(b)

x² - 7

(c)

- x² + 7

(d)

- x² - 7

The dividend received on 200 shares of face value Rs.100 at 8% is ________.

(a)

Rs. 1600

(b)

Rs. 1000

(c)

Rs. 1500

(d)

Rs. 800

Example of contingent annuity is _______.

(a)

Installments of payment for a plot of land

(b)

An endowment fund to give scholarships to a student

(c)

Personal loan from a bank

(d)

All the above

When calculating the average growth of economy, the correct mean to use is?

(a)

Weighted mean

(b)

Arithmetic mean

(c)

Geometric mean

(d)

Harmonic mean

Probability that at least one of the events A, B occur is _________.

(a)

\(P(A\cup B)\)

(b)

\(P(A\cap B)\)

(c)

P(A/B)

(d)

\((A\cup B)\)

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 which influences the values or is used for prediction is called________.

(a)

Dependent variable

(b)

Independent variable

(c)

Explained variable

(d)

Regressed

The term regression was introduced by ________.

(a)

R.A Fisher

(b)

Sir Francis Galton

(c)

Karl Pearson

(d)

Croxton and Cowden

A solution which maximizes or minimizes the given LPP is called ______.

(a)

a solution

(b)

a feasible solution

(c)

an optimal solution

(d)

none of these

Network problems have advantage in terms of project _______.

(a)

Scheduling

(b)

Planning

(c)

Controlling

(d)

All the above

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

Solve: \(\begin{vmatrix}2& x&3\\4&1&6\\1&2&7 \end{vmatrix}=0\)

Expand the following by using binomial theorem.\(\left( x+\frac { 1 }{ y } \right) ^{ 7 }\)

If 4(nC₂) = (n + 2)C₃ , find n

Convert the following degree measure into radian measure 60^o

Evaluate: \(\underset { x\rightarrow 1 }{ lim } \frac { { x }^{ 3 }-1 }{ x-1 } \)

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.

The total cost function for the production of x units of an item is given by c = 10 - 4x³ + 3x⁴ find the (i) average cost function (ii) marginal cost function (iii) marginal average cost fuction.

If A \(= \begin{bmatrix} 1 & -1 \\2 & 3 \end{bmatrix}\) show that A² - 4A + 5I₂ = 0 and also find A^-1.

If \(A=\left[ \begin{matrix} 2 & 4 \\ -3 & 2 \end{matrix} \right] \)then, find A ^-1.

Find n, if \(\frac{1}{9!}+\frac{1}{10!}=\frac{n}{11!}\)

Solve : \(\tan^{-1}2x+\tan^{-1}3x=\frac{\pi}{4}\)

Express each of the following as the product of sine and cosine sinA + sin2A

Differentiate sin² x with respect to x².

Find the stationary value and the stationary points f(x) = x² + 2x – 5.

Evaluate:\(\begin{vmatrix} 1&a&a^2-bc\\1&b&b^2-ca\\1&c&c^2-ab \end{vmatrix}\)

Solve by using matrix inversion method:
2x + 5y = 1
3x + 2y = 7

By the principle of mathematical induction, prove the following.
5²ⁿ - 1 is divisible by 24, for all \(n\in N\) .

Draw the graph of the following functions : f(x) = 16 - x²

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?

Verify the relationship among AM, GM and HM for the following data

X	7	10	13	16	19	22	25	28
f	10	22	24	28	19	9	12	16

For the given lines of regression 3X – 2Y = 5 and X – 4Y = 7. Find
(i) Regression coefficients
(ii) Coefficient of correlation