The chance that doctor A will diagnise the disease X correctly is 60%. The chance that a patient will die by his treatment after correct diagnosis is 40% and the chance of death after wrong diagnosis is 70%. A patient of doctor A who had disease X died. The probability that his disease was diagnosed correctly is
(A) `5/13`
(B) `6/13`
(C) `2/13`
(D) `1/13`

A purse contains 2 six-sided dice. One is a normal fair die, while the other has two 1s two 3s,and two 5s. A die is picked up and rolled. Because of some secret magnetic attraction of the unfair die, there is 75% chance of picking the unfair die and a 25% chance of picking a fair die. The dice is rolled and shows up the face 3. The probability that a fair die was picked up is (a) 1/7 (b) 1/4 (c) 1/6 (d) 1/24

Column I, Column II If the probability of getting at least one head is at least 0.8 in n trials, then value of n can be, p. 2 One mapping is selected at random from all mappings of the set s={1,2,3, ... ,n} into itself. If the probability that the mapping being one-one is 3/32, then the value of n is, q. 3 If m is selected at random from set {1,2,..., 10} and the probability that the quadratic equation 2x^2+2m x+m+1=0 has real roots is k , then value of 5k is more than, r. 4 A man firing at a distant target as 20% chance of hitting the target in one shoot. If P be the probabililty of hitting the target in "n" attempts , where 20 P^2-13 P+2lt=0, then the ratio of maximum and minimum value of n is less than, s. 5

Ram was a daily wage worker in a factory. He was suffering from Cancer. On hearing this, most of his co-workers, started avoiding him under the impression that it was a contagious disease. When Prof. Srivastava came to know about this, case, he took him to a leading radiologist, who examined him and told that it was at the beginning stage. He advised that it could be easily cured and also certified that it was not a communicable disease. After this, Ram was given proper treatment by the doctor and got cured completely. (1) How is mean life of a radioactive element related to its half life? (2) A radioactive sample has activity of 10,000 disintegrations per second after 20 hours . After next 10 hours, its activity reduces to 5,000 dps. Find out its half - life and initial activity.

For his 18th birthday in February Peter plants to turn a hut in the garden of his parents into a swimming pool with an artifical beach. In order to estimate the consts for heating the water and the house , peter obtains the data for the natural gas combustion and its price. What is the total energy (in MJ) needed for Peter's "winter swimming pool" calculated in 1.3 and 1.4? How much natural gas will he need, if the gas heater has an efficiency of 90.0% ? What are the different costs for the use of either natural gas or electricity ? Use the values given by PUC for your calculations and assume 100% efficiency for the electric heater. Table 1: Composition of natural gas {:("Chemical substance","mol fraction x",D_(1)H^(@)(KJ mol^(-1))^(-1),S^(@)(J mol^(-1)K^(-1))^(-1),C_(p)^(@)(J mol^(-1)K^(-1))^(-1)),(CO_(2(g)),0.0024,-393.5,213.6,37.1),(N_(2(g)) ,0.0134,0.0,191.6,29.1),(CH_(2(g)),0.9732,-74.6,186.3,35.7),(C_(2)H_(3 (g)),0.0110,-84.0,229.2,52.2),(H_(2)O_(g),-,-285.8,70.0,75.3),(H_(2)O_(g),-,-241.8,188.8,33.6),(H_(2)O_(g),-,0.0,205.2,29.4):} Equation J=E(A.Deltat)^(-1) =!! lambda "wall" . DeltaT. d^(-1) , where J= energy flow E along a temperature gradient (wall direction Z) par area A and time Deltat , d-wall thickness , lambda wall -heat conductivity , DeltaT - difference in temperature between the inside and the outside of the house.

For the circle C with the equation x^(2) + y^(2) - 16x - 12y + 64 = 0 match the List I with the List II given below, {:(,"List I",,"List II"),((i),"The equation of the polar",(A),y = 0),(,"of (-5, 1) with respect to C",,),((ii),"The equation of the tangent",(B),y = 6),(,"at (8, 0) to C",,),((iii),"The equation of the normal",(C),x + y = 7),(,"at (2, 6) to C",,),((iv),"The equation of the diameter",(D),13x + 5y = 98),(,"of C through (8, 12)",,),(,,(E),x = 8):} The correct match is