From a lot of 15 bulbs which include 5 defectives, a sample of 4 bulbs is drawn one by one with replacement. Find the probability distribution of number of defective bulbs. Hence find the mean of the distribution.
Let D be the event of drawing a defective bulb and X denote the variable showing the number of defective bulbs in 4 draws. Then
P(D)=5/15
Using integration find the area of the region {(x, y): x2 +y2 ≤2ax, y2 ≥ ax, x,y≥ 0}
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 ?
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.
Let N denote the set of all natural numbers and R be the relation on N x N defined by (a, b) R(c, d) if ad (b + c) = bc (a + d). Show that R is an equivalence relation.
Using integration find the area of the triangle formed by positive x-axis and tangent and normal to the circle x2 + y2= 4 at (1, √3).
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 equation of normal at any point on the curve x = 3 cost t – cos3 t and y = 3 sin t – sin3 t is 4(ycos3 t- sin3t) = 3 sin 4t.
If A is a square matrix such that A2 = I, then find the simplified value of (A -1)3 + (A +1)3 – 7A.
An unbiased coin is tossed 4 times. Find the mean and variance of the number of heads obtained.
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 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
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 vector equation of a plane which is at a distance , of 5 units from the origin and its normal vector is