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#### Term 1 Five Mark Model Questions

12th Standard EM

Reg.No. :
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Time : 02:00:00 Hrs
Total Marks : 50
10 x 5 = 50
1. Solve the equations 2x + 3y = 7, 3x + 5y = 9 by Cramer’s rule.

2. The price of 3 Business Mathematics books, 2 Accountancy books and one Commerce book is Rs840. The price of 2 Business Mathematics books, one Accountancy book and one Commerce book is Rs 570. The price of one Business Mathematics book, one Accountancy book and 2 Commerce books is Rs 630. Find the cost of each book by using Cramer’s rule.

3. Evaluate $\int { \frac { 7x-1 }{ { x }^{ 2 }-5x+6 } dx }$

4. A company produces 50,000 units per week with 200 workers. The rate of change of productions with respect to the change in the number of additional labour x is represented as 300 - 5x1/2 If 64 additional labours are employed, find out the additional number of units, the company can produce.

5. Solve 3extan ydx +(1 + ex)sec2ydy = 0 given y(0) = $\frac { \pi }{ 4 }$

6. Using Newton’s formula for interpolation estimate the population for the year 1905
from the table:

 Year 1891 1901 1911 1921 1931 Population 98.752 1,32,285 1,68,076 1,95,670 2,46,050
7. If f (x) is defined by f(x)=k2-2x, 0$\le$x<$\infty$is a density function. Determine the constant k and also find mean.

8. One fifth percent of the the blades produced by a blade manufacturing factory turn out to be defective. The blades are supplied in packets of 10. Use Poisson distribution to calculate the approximate number of packets containing no defective, one defective and two defective blades respectively in a consignment of 1,00,000 packets (e–0.2 =.9802)

9. An ambulance service claims that it takes on the average 8.9 minutes to reach its destination in emergency calls. To check on this claim, the agency which licenses ambulance services has them timed on 50 emergency calls, getting a mean of 9.3 minutes with a standard deviation of 1.6 minutes. What can they conclude at the level of significance

10. the Laspeyre’s, Paasche’s and Fisher’s price index number for the following data. Interpret on the data.

 Commodities Price Quandity 2000 2010 2000 2010 Rice 38 35 6 7 Wheat 12 18 7 10 Rent 10 15 10 15 Fuel 25 30 12 16 Miscellaneous 30 33 8 10