Show that the altitude of the right circular cone of maximum volume that can be inscribed in a sphere of radius r is 4r/3. Also find maximum volume in terms of volume of the sphere.
Two schools P and Q want to award their selected students on the values of Discipline, Politeness and Punctually. The school P wants to award Rs x each, y each and Rs z each for the three respective values to its 3,2 and 1 students with a total award money of Rs 1,000. School Q wants to spend Rs 1,500 to award its 4,1 and 3 students on the respective values (by giving the same award money for the three values as before). If the total amount of awards for one prize on each value is Rs 600, using matrices, find the award money for each value. Apart from the above three values, suggest one more value for awards.
Find the differential equation representing the family A of curves Ï… = A/r + B, where A and B are arbitrary r constants.
Solve the differential equation: (tan-1 y-x)dy = (1 + y2) dx.
Solution. Same as solution Q. 23 (OR) Set 1 (Outside Delhi) up to eq.
x = tan-1 y -1 + ce -tan-1 y
OR
A dealer in rual area wishes to purchase a number of sewing machines. He has only Rs 5,760 to invest and has space for at most 20 items for storage. An electronic sewing machine cost him Rs 360 and a manually operated sewing machine Rs 240. He can sell an electronic sewing machine at a profit of Rs 22 and a manually operated sewing machine at a profit of Rs 18. Assuming that he can sell all the items that he can buy, how should he invest his money in order to maximize his profit ? Make it as a LPP and solve it graphically.
If A is a square matrix such that A2 = I, then find the simplified value of (A -1)3 + (A +1)3 – 7A.
Find the vector equation of a plane which is at a distance , of 5 units from the origin and its normal vector is
Find the vector and cartesian equations of the line through the point (1,2, – 4) and perpendicular to the two lines.
Three persons A, B and C apply for a job of Manager in a Private Company. Chances of their selection (A, B and C) are in the ratio 1:2:4. The probabilities that A, B and C can introduce changes to improve profits of the , company are 0.8,0.5 and 0.3 respectively. If the change does not take place, find the probability that it is due to the appointment of C.
Show that the altitude of the right circular cone of maximum volume that can be inscribed in a sphere of radius r is 4r/3. Also find maximum volume in terms of volume of the sphere.
Using integration find the area of the region {(x, y): x2 +y2 ≤2ax, y2 ≥ ax, x,y≥ 0}
Three Schools A, B and C organized a mela for collecting funds for helping the rehabilitation of flood victims. They sold hand made fans, mats and plates from recycled material at a cost of Rs 25, Rs 100 and Rs 50 each. The number of articles sold are given below:
Find the fund collected by each school separately by selling the above articles. Also find the total funds collected for the purpose. Write one value generated by the above situation.
Find the local maxima and local minima, of the function f(x) = sin x – cos x, 0 < x < 2Ï€. Also find the local maximum and local minimum values.
A card from a pack of 52 playing cards is lost. From the remaining cards of the pack three cards are drawn at random (without replacement) and are found to be all spades. Find the probability of the lost card being a . spade. [6]
Find the particular solution of the differential equation (1 – y2) (1 + log x) dx + 2xy dy = 0, given that y = 0 when x = 1.
Let/: N -> N be a function defined as/(x) = 9x2 + 6x-5. Show that: N—>S, where S is the range off, is invertible. Find the inverse of f and hence find f-1 (43) and f-1(163).
