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.
Let the awards for Discipline, Politeness and Punctuality be Rs x, Rs y and Rs z respectively.
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
If a line makes angles 90 °, 60 ° and θ with x, y and z axis respectively, where θ is acute, then find θ.
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
A bag ‘A’ contains 4 black and 6 red balls and bag ‘B’ contains 7 black and 3 red balls. A die is thrown. If 1 or 2 appears on it, then bag A is chosen, otherwise bag B. If two balls are drawn at random (without replacement) from the selected bag, find the probability of one of them being red and another black.
An unbiased coin is tossed 4 times. Find the mean and variance of the number of heads obtained.
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 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.
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}
Find the coordinate of the point P where the line through A(3, -4,-5) and B (2, – 3,1) crosses the plane passing through three points L (2,2,1), M (3,0,1) and N (4, -1,0). Also, find the ratio in which P divides the line segment AB.
An urn contains 3 white and 6 red balls. Four balls are drawn one by one with replacement from the urn. Find the probability distribution of the number of red balls drawn. Also find mean and variance of the distribution.
The side of an equilateral triangle is increasing at the rate of 2 cm/s. At what rate is its area increasing when the side of the triangle is 20 cm ?
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.
