Today, we are posting the Mathematics– Important Questions Bank for Jharkhand Board HSC 2016 Examination to make life easy for all you HSC students.
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 :
Food  vitamine  A  B  C  X   1  2  3  Y   2  2  1 

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 coordinates 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 x^{2} = y, st line y = x = + 2 and x – axis.
8. Two Cards are drawn simultaneously from a wellShuffled 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 3xy+z = 4.
13. Find the angle between the planes. X+y+2z=6 and 2xy+z =9
14. Find the equation of the plane passing through the line of intersection of the planes 3x2y+z = 5 and xy+2z = 3 and containing the point (1,2,3).
15. Fine the direction ratios of the normal to the plane 3x7y+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
 Slope of the chord joining two points (2,0) and (4,4).
 Value of x, when slope of the tangent = slope of the chord
 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
(x^{2} + xy)dy = (x^{2} + y^{2})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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