#### 5 Marks Revision Test

11th Standard

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Time : 02:30:00 Hrs
Total Marks : 100
20 x 5 = 100
1. Suppose the inter-industry flow of the product of two industries are given as under.

 Production sector Consumption sector Domestic demand Total output X Y X 30 40 50 120 Y 20 10 30 60

Determine the technology matrix and test Hawkin's -Simon conditions for the viability of the system. If the domestic demand changes to 80 and 40 units respectively, what should be the gross output of each sector in order to meet the new demands.

2. An amount of Rs. 5000 is put into three investment at the rate of interest of 6%, 7% and 8% per annum respectively. The total annual income is Rs. 358. If the combined income from the first two investment is Rs. 70 more than the income from the third, find the amount of each investment by matrix method.

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

4. Using binomial theorem, find the value of ${ \left( \sqrt { 2 } +1 \right) }^{ 5 }+{ \left( \sqrt { 2 } -1 \right) }^{ 5 }$

5. Show by the principle of mathematical induction that 23n–1 is a divisible by 7, for all $n \in N$.

6. 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.

7. An arch is in the form of a parabola with its axis vertical. The arch is 10 m high and 5 m wide at the base. How side is 2 m from the vertex of the parabola?

8. Prove that  $\frac { \sin { \left( { 180 }^{ o }+A \right) \cos { \left( { 90 }^{ o }-A \right) \tan { \left( { 270 }^{ o }-A \right) } } } \quad \quad }{ \sec { \left( { 540 }^{ o }-A \right) \cos { \left( { 360 }^{ o }+A \right) \ cosec { \left( { 270 }^{ o }+A \right) } } } } =-\sin { A } \cos ^{ 2 }{ A }$

9. Prove that cos 4x = 1 - 8 sin2x cos2x.

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

11. Examine the following functions for continuity at indicated points
$f(x)=\left\{\begin{array}{cl} \frac{x^2-4}{x-2}, & \text { if } x \neq 2 \\ 0, & \text { if } x=2 \end{array} \right.$ at x = 2

12. Differentiate the following with respect to x.
(i) xx
(ii) (log x)cos x

13. Verify the relationship of elasticity of demand, average revenue and marginal revenue for the demand law p = 50 - 3x.

14. The following table gives the annual demand and unit price of 3 items

Items Annual Demand (units) Unit Price Rs
A 800 0.02
B 400 1.00
C 13,800 0.20

Ordering cost is Rs. 5 per order and holding cost is 10% of unit price.
Determine the following:
(i) EOQ in units
(ii) Minimum average cost
(iii) EOQ in rupees
(iv) EOQ in years of supply
(v) Number of orders per year.

15. A man invests Rs 13,500 partly in 6% of Rs 100 shares at Rs 140 and the remaining in 5% of Rs 100 shares at Rs 125. If his total income is Rs 560, how much has he invested in each?

16. The first of three urns contains 7 White and 10 Black balls, the second contains 5 White and 12 Black balls and third contains 17 White balls and no Black ball. A person chooses an urn at random and draws a ball from it. And the ball is found to be White. Find the probabilities that the ball comes from
(i) the first urn
(ii) the second urn
(iii) the third urn

17. Find the Quartile deviation.

 Wages (Rs) 20-30 30-40 40-50 50-60 60-70 No. of labourers 3 5 20 10 5
18. Calculate coefficient of correlation for the ages of husbands and their respective wives:

 Age of husbands 23 27 28 29 30 31 33 35 36 39 Age of wives 18 22 23 24 25 26 28 29 30 32
19. You are given the following data:

 Details X Y Arithmetic Mean 36 85 Standard Deviation 11 8

If the Correlation coefficient between X and Y is 0.66, then find (i) the two regression coefficients, (ii) the most likely value of Y when X = 10

20. Solve the following LPP. Maximize Z = 2 x1 + 5x2 subject to the conditions x1+ 4x2 ≤ 24. 3x1+x2 ≤ 21, x1+x2 ≤ 9 and x1, x2 ≥ 0.