Mathematics – Important Question Bank for ( JAC ) Jharkhand HSC 2016 Examination

1.A manufacturing company makes two models A and B of product. Each piece of model A requires 9 labour hours for fabricating and 1 labour hour for finishing. Each piece of model B requires 12 labour hours for fabricating and 3 labour hours for finishing. For fabricating and finishing the maximum labour hours are available 180 and 30 respectively. The company makes a profit of Rs.  8000 on each piece of model A and Rs. 12000 on each piece of model B. How many pieces of model A and B should be manufactured per week to realise a maximum profit? What is the maximum profit per week?

2. A dietician wishes to mix together two kind of foods X and Y in such a way that the mixture contains at least 10 units of vitamine A, 12 units of vitamin B and 8 units of vitamin C. The vitamin contents of one kg food is given below :-

3. One kg of food X costs Rs. 16 and one kg of food Y costs Rs. 20. Find the least cost of the mixture which will produce the required diet.

4. Find the equation of the plane passing through there points (1,1,0),(1,2,1) and ( 2,2, 1)

5. Find the co-ordinates of the point where the line through (3, 4, 5) and (2, 3, 1) − crosses the plane

2_x + y + z = 7

6. Using matrics solve the following system of equations ;

3x – 2y + 3z = 8, 2x + y – z = 1, 4x – 3y + 2z = 4.

7. Find the area of the region enclosed by the parabola x² = y, st line y = x = + 2 and x – axis.

8. Two Cards are drawn simultaneously from a well-Shuffled pack of 52 Cards. Find the mean and variance of the number of aces.

9. Find the direction ratios of the straight line joining A (5,-3,8) and B (2,-1,4).

10. Find the angle between the straight lines whose direction ratios are 1,2,-1 and 1,2,-2.

11. Write the equation of the xy plane.

12. Find the distance of the point (1,-2,1) from the plane 3x-y+z = 4.

13. Find the angle between the planes. X+y+2z=6 and 2x-y+z =9

14. Find the equation of the plane passing through the line of intersection of the planes 3x-2y+z = 5 and x-y+2z = 3 and containing the point (1,2,3).

15. Fine the direction ratios of the normal to the plane 3x-7y+8z =11

16. Find the point on the curve y = x2 – 4_x + 5 , where the tangent is parallel to x – axis

17. For given Parabola  y = x ( x− 2)² , find

1. Slope of the chord joining two points (2,0) and (4,4).
2. Value of x, when slope of the tangent = slope of the chord
3. Equation of the tangent at the obtained point

18. The radius of a circle is increases uniformly at the rate of 3 cm./sec. Find the rate of increase in area of the circle when its radius is 10 cm.

19. Solve the differential equation

(x² + xy)dy = (x² + y²)dx

20. In a bolt factory, three machinist A,B and C manufacture 25 % , 35 % and 40 % of the total production respectively. Of their respective outputs 5% , 4% and 2% are defective

(i) A bolt is drown at random. Find the probability that it is produced by machine A.

(ii) A bolt is drown at random. Find the probability that it is produced by machine C.

(iii) Find the probability of drawing a defective bolt, given that its is produced by machine A

(iv) Find the probability of drawing a defective bolt, given that its is produced by machine B.

(v) Find the probability of drawing a defective bolt, given that its is produced by machine C.

(vi) A bolt is drown at random and its is found to be defective. Find the probability that it was manufactured by machine A

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