#### Important 2 Mark Creative Questions (New Syllabus) 2020

12th Standard

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Time : 01:00:00 Hrs
Total Marks : 20

Part A

10 x 2 = 20
1. Solve: 2x + 3y = 4 and 4x + 6y = 8 using Cramer's rule.

2. If f'(x) = 8x3 -2x2, f(2) = 1, find f(x)

3. If the marginal revenue for a commodity is MR = 9 - 6x2 + 2x, find the total revenue function.

4. Form the differential equation of family of rectangular hyperbolas whose asymptotes are the Co-ordinate axes.

5. If f(0) = 5, f(1) = 6, f(3) = 50, find f(2) by using Lagrange's formula.

6. An unbiased die is rolled. If the random variable X is defined as
X(w) = {1, the outcome w is an even number
{0, if the outcome w is an odd number
Find the probability distribution of X.

7. A continuous random variable. X has the p.d.f. defined by $f(x)=\left\{\begin{array}{l} C e^{-a x}, \quad 0<x<\infty \\ 0, \quad \text { elsewhere } \end{array}\right.$ Find the value of C if a> 0

8. If 10 coins are tossed, find the probability that exactly 5 heads appears.

9. A sample of 400 students is found to have mean height of 171.38 cms, Can it reasonable be regarded as a sample from a large population with mean height of 171.17 cms and standard deviation of 3.3 cms (Test at 5% level)

10. The following is the pay-off matrix (in rupees) for three strategies and three states of nature. Select a strategy using maximin principle.