A source contains two phosphorous radio nuclides `"_15^32P` `(T_(1/2) = 14.3d)` and `"_15^33P``(T_(1/2) = 25.3d)`. Initially, 10% of the decays come from `"_15^33P`. How long one must wait until 90% do so?

A computer producing factory has only two plants T_(1) and T_(2). Plant T_(1) produces 20% and plant T_(2) produces 80% of the total computers produced . 7% of the computers produced in the factory turn out to be defective. It is known that P (computer turns out to be defective givent that it is produced in plant T_(1)) = 10 P ( computer turns out to be defective given that it is produced in plant T_(2)), where P (E) denotes the probability of an event E. A computer produced in the factory is randomly selected and it does not turn out to be defective. Then the probability that it is produced in plant T_(2) is

Football teams T_(1)and T_(2) have to play two games are independent. The probabilities of T_(1) winning, drawing and lossing a game against T_(2) are 1/2,1/6and 1/3, respectively. Each team gets 3 points for a win, 1 point for a draw and 0 point for a loss in a game. Let X and Y denote the total points scored by teams T_(1) and T_(2) respectively, after two games. P(X=Y) is

In figure S is a monochromatic point source emitting light of wavelength lambda=500 nm. A thin lens of circular shape and focal length 0.10 m is cut into two identical halves L_(1) and L_(2) by a plane passing through a doameter. The two halves are placed symmetrically about the central axis SO with a gap of 0.5 mm. The distance along the axis from A to L_(1) and L_(2) is 0.15 m , while that from L_(1) and L_(2) to O is 1.30 m. The screen at O is normal to SO. (a) If the 3^(rd) intensity maximum occurs at point P on screen, find distance OP.

In R^3 , let L be a straight line passing throughthe origin. Suppose that all points on L are at a constant distance from the two planes: P_1: x+2y-z+1=0 and P_2: 2x-y-z+1=0 . Let M be the locus of the feet of the perpendiculars drawn from the points on L t the plane P_1 . Which of the following point(s) lie(s) on M?

Phospheric acid (H_(3)PO_(4)) perpared in two step process . (1) P_(4)+5O_(2) to P_(4)O_(10)" "(2) P_(4)O_(10) + 6H_(2)O to 4H_(3)PO_(4) Well allow 62 g of phosphrous to react with exces oxygen which from P_(4)O_(10) in 85% yield . In the sep (2) reaction 90% yield of H_3)PO_(4) is obtained . Mass of H_(3) PO_(4) produced is :

How many terms of the A.P. 20, 19 1/3, 18 2/3, ……… must be taken so that their sum is 300?

Two closed vessels of equal volume containing air at pressure P_(1) and temperature T_(1) are connected to each other through a narrow tube. If the temperature in one of the vessels is now maintained at T_(1) and that in the other at T_(2) , what will be the pressure in the vessels?

Let O(0,0),A(2,0),a n dB(1 1/(sqrt(3))) be the vertices of a triangle. Let R be the region consisting of all those points P inside O A B which satisfy d(P , O A)lt=min[d(p ,O B),d(P ,A B)] , where d denotes the distance from the point to the corresponding line. Sketch the region R and find its area.

There are two types of fertilisers F_1 and F_2 . F_1 consists of 10% nitrogen and 6% phosphoric acid and F_2 consists of 5% nitrogen and 10% phosphoric acid. After testing the soil conditions, a farmer finds that she needs atleast 14 kg of nitrogen and 14 kg of phosphoric acid for her crop. If F_1 costs Rs 6/kg and F_2 costs Rs 5/kg, determine how much of each type of fertiliser should be used so that nutrient requirements are met at a minimum cost. What is the minimum cost?

Find the value of p so that the lines : l_1:(1-x)/3=(7y-14)/(2p)=(z-3)/2 and l_2: (7-7x)/(3p)=(y-5)/1=(6-z)/5 are at right angles. also find the equations of the line passing through (3,2,-4) and parallel to line l_1 .