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1. Solve the following problem graphically and maximise. Z = 8000x + 12000 y. Subject to constraints : 3x+4y ≤ 60 x +3y ≤ 30, x ≥ 0 , y ≥ 0.

2. A man is known to speak truth 3 out of 4 times. He throws a die and reports that it a six. Find the probability that it is actually a Six.

3. Find area of the region bounded by the two parabolas 2 y x = and 2 y x

4. Find the maximum value of 2x^{3} – 24x + 107 in the interval [1,3].

5.Solve the following problem graphically. Minimize and maximize. Z = 3x + 9y

Subject to the constraints: x + 3y ≤ 60.

X+ y ≥ 10, x ≤ y , x ≥ 0. Y ≥ 0

6. Solve the system of linear emanation. Using matrix method

2x + 3y +3z = 5, x – 2 y+ z = – 4, 3x – y – 2 z = 3

7. A card from a pack of 52 card is lost. From the remaining cards of the pack, two cards are drawn and are found to be both diamonds. Find the probability of the lost card being a diamond.

8. Find co-ordinates of the point where the line through (3,-4,-5) and (2,-3,1) crosses the plane 2x + y +z = 7

9. Find the local maximum and local minima, If any of the given function. Find also the local maximum and the local minimum values us the case may be. *f*(x) = x^{3} – 6x^{2} + 9x +15

10. A die is thrown three times. Events A and B are defined as below.

A → 4 on the third throw

B → 6 on first and 5 on the second throw Find the probability of A given that B has already occurred.

11. Find the intervals in which the function *f*(x) = 4x^{3} – 6x^{2} – 72 x + 30 is

(a) strictly increasing

(b) strictly decreasing.

12. If f : R+R be given by *f*(x) = (3 – x^{3}) ^{1/3 }then find of (x)

13. Given that the two numbers appearing on throwing two dice are different. Find the probability of the event the sum of numbers on the dice is 4.

14. A ladder 5m long is leaning against a wall. The bottom of the ladder is pulled along the ground, away from the wall at the rate of 2cm/S. How fast is its height on the wall decreasing when the foot of the ladder is 4m away from the wall?

15. Find the intervals in which the function is strictly increasing or strictly Decreasing. *f*(x) = (x + 1)^{3 }(x – 3) ^{3}

16. Differentiate the function with respect to x . x ^{sin x} + (sin x) ^{cos x}

17. Find the slope of the tangent to the curve y= 3x^{4} – 4x at x = 4

18. Let * be the binary operation on N given by a*b = L.C.M. of a and b. Find the value of (5*7).

19. Find direction cosines of a line which makes equal angles with the coordinate axes.

20. Consider a binary operation * on the set [1,2,3,4,5] defined as a*b = a. Find the value of (2*3) * (4*5)

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