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.
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.
Find the intervals in which f(x) = sin 3x – cos 3x, 0 < x < Ï€, is strictly increasing or strictly decreasing.
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.
Find the particular solution of the differential equation (1 – y2) (1 + log x) dx + 2xy dy = 0, given that y = 0 when x = 1.
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.
Find graphically, the maximum value of z = 2x + 5y, subject to constraints given below:
2x + 4y ≤ 8
3x + y ≤ 6
x + y ≤ 4
x≥ 0, y ≤ 0.6
If A is a square matrix such that A2 = I, then find the simplified value of (A -1)3 + (A +1)3 – 7A.
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).
If a line makes angles 90 °, 60 ° and θ with x, y and z axis respectively, where θ is acute, then find θ.
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.
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
Find the vector equation of a plane which is at a distance , of 5 units from the origin and its normal vector is
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.
