#### Sample 3 Mark Creative Questions (New Syllabus) 2020

12th Standard

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Time : 01:00:00 Hrs
Total Marks : 30

Part A

10 x 3 = 30
1. Show that the equations x + 2y = 3, y - z = 2, x + y + z = 1 are consistent and have infinite sets of solution.

2. Evaluate $\int { \frac { cos2x-cos2\alpha }{ cosx-cos\alpha } } dx$

3. Find the area under the demand curve xy = 1 bounded by the ordinates x = 3, x = 9 and x-axis

4. Solve: (x2-yx2)dy + (y2+xy2)dx = 0

5. Find the number of men getting wages between Rs. 30 and Rs. 35 from the following table.

 Wages (x) 20 - 30 30 - 40 40 - 50 50 - 60 No. of men (y) 9 30 35 42
6. A player tosses two unbiased coins. He wins Rs. 5 if two heads appear, Rs. 2 if one head appear and Rs.1 if no head appear. Find the expected amount to win.

7. A die is thrown 120 times and getting 1 or 5 is considered a success. Find the mean and variance of the number of successes.

8. The mean life time of 50 electric bulbs produced by a manufacturing company is estimated to be 825 hours with the S.D. of 110 hours. If II is the mean life time of all the bulbs produced by the company, test the hypothesis that μ = 900 hours at 5% level of significance.

9. Calculate the seasonal indices for the following data by the method of simple average.

 Year Quarters I II III IV 1994 78 66 84 80 1995 76 74 82 78 1996 72 68 80 70 1997 74 70 84 74 1998 76 74 86 82
10. Determine an initial basic feasible solution to the following transportation problem using North West corner rule.