Buds Public School , Dubai
Grade 12 Bio & IT Mathematics Worksheet
SET –I Submn Date:On or before 28/11/17
SECTION – A
1. Evaluate dx.
2. Find the value of .
3. Find the value of cot.
4. Write the vector equation of the line = =.
SECTION – B
5. Show that = .
6. Find if y=log()
7. Solve : given that y = 1 when x = 0.
8. Write the differential equation representing the family of curves where m and c are arbitrary constants.
9. Let a=i+4j+2k,b=3i-2j+7k and c=2i-j+4k ,find a vector p which is perpendicular to both a and b and p.c =18.
10. Find the position vector of a point R which divides the line joining the two points P(i+2j-k) and Q(-i+j+k) in the ratio 2:1 (i) internally (ii) externally.
11. If a,b,c are unit vectors such that a+b+c = 0 then find the value of a.b+b.c+c.a.
12. Find the equation of the plane through the intersection of the planes x+3y+6=0 and 3x-y-4z=0 and whose perpendicular distance from the origin is unity.
SECTION – C
13. If then prove that
14. Prove that =.
15. If then prove that
16. 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 2 cm/sec.How fast is its height on the wall decreasing when the foot of the ladder is 4m away from the wall?
17. Evaluate dx OR dx.
18. Evaluate dx.
19. Find the area of the region bounded by x2 =4y , y=2 , y = 4 and the Y-axis in the first quadrant.
20. If = 3 then express in the form
where .
21. Find the vector and Cartesian equation of the line passing through the point parallel to the planes + ) = 5 and + ) = 6.
22. One kind of cake requires 200g of flour and 25 g of fat, and another kind of cake requires 100g of flour and 50g of fat. Find the maximum number of cakes which can be made from 5 kg of flour and 1 kg of fat assuming that there is no shortage of other ingredients .Formulate the above as a linear programming problem and solve it graphically.
23. Prove that is an increasing function in .
OR
Find the equation of tangent to the curve .
SECTION – D
24. If (x-a)2 + (y-b)2 = c2, for some c prove that is a constant independent of a and b .
25. Evaluate: dx
OR
Find + ) dx
26. . Evaluate : using limit as a sum.
27. A dietician wishes to mix two types of foods in such a way that vitamin contents of the
mixture contain at least 8 units of vitamin A and 10 units of vitamin C . Food I contains 2 units/ kg of vitamin A and 1 unit / kg of vitamin C . Food II contains 1 unit/ kg of vitamin A and 2 units / kg of vitamin C. It costs Rs.50 per kg to purchase food ‘ I’ and Rs . 70 per Kg to Purchase food ‘II’. Formulate this problem as a linear programming problem to minimize the cost of such a mixture.
28. Show that the height of the closed cylinder of given surface and maximum volume is equal to the diameter of the base.
29. Using integration, find the area of the triangle whose vertices are (2,5),(4,7) and (6,2).
SET -II
SECTION – A
1. Find the value of cot .
2. Find the area of the region bounded by the curve y2 = x, the line x=1 and x=4.
3. Find the order and degree of the differential equation y’’’+y2+= 0.
4. Evaluate .
SECTION – B
5. Solve:.
6. Find
7. Solve : given that y = 1 when x = 0.
8. Form the differential equation of the family of circles in the second quadrant and touching the coordinate axes.
SECTION – C
9. Find the area of the greatest rectangle that can be included in an ellipse .
(OR )
Find the equation of the tangents to the curve which passes through the point (.
SECTION – D
10. Using integration ,find the area bounded by the lines
11. . Evaluate : using limit as a sum.
12. . A farmer has a supply of chemical fertilizer of type A which contains 10 % of nitrogen and 35 % of phosphoric acid, and type B contains 6 % of nitrogen and 10 % phosphoric acid. After testing the soil conditions of the field, it was found that at least 14 kg of nitrogen and 14 kg of phosphoric acid is required for producing food crop. The fertilizer of type A costs Rs 5 per kg and type B costs Rs 3 per kg. How many kg of each type of the fertilizer should be used to meet the requirement at the minimum cost? Using LPP, solve the above Problem graphically.
13. Show that the altitude of a closed right circular cone maximum volume that can be inscribed in a sphere of radius R is .
14. Evaluate :
15. Evaluate :
16. Evaluate :
17. Evaluate :
18. Evaluate :
19. Evaluate :
20. Evaluate :
21. Evaluate : a)
22. Evaluate : as limit of sum
23. Evaluate :
24. Evaluate :
25. Evaluate :
26. Show that the normal at any point to the curve is at a constant distance from the origin.
27. Find the equation of tangents to the curve which passes through the point ( , 0) .
28. a) Find the intervals in which the function f given by is
i) Increasing ii ) decreasing
b) The length of a rectangle is decreasing at the rate of 5 cm / min and the width y is increasing at the rate of 4 cm / min . When x = 8 cm and y = 6 cm , find the rate of change of
i) the perimeter , ii) the area of the rectangle.
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