To dig a well of x dcm deep, one part of the total expenses varies directly with x and other part varies directly with `x^2`. If the expenses of digging well of 100 dcm depths are Rs 5000 and Rs 12000 respectively. Calculate the expenses of digging a well of 250 dcm depth.

To dig a well of x dcm deep , one part of the total expenses varies directly with x and other part varies directly with x^2 . If the expenses of digging wells of 100 dcm and 200 dcm depths are rs5000 and rs12000 respectively , calculate the expenses of digging a well of 250 dcm depth.

A variable is the sum of two such quantities one of which varies directly with x and the other varies directly with x^2 . If y =3 when x =1 and y=10 when x=2 , then find the relation between x and y .

The total expenses of a hostel are partly constant and partly vary directly as the number of boarders. When the number of boarders are 120 and 100 the total expenses are ₨.2,000 and ₨.1,700 respectively. What will be the number of boarders when the total expenses is ₨. 1.880?

The weekly expenses of a hostel are partly constant and partly vary directly as the number of inmates . If the expenses are rs 2000 when the number of inmates is 120 and rs 1700 when the number is 100 . Find the number of inmates when the expenses are rs 1880 .

A manufacturer produces three products x, y, z which he sells in two markets. Annual sales are indicated below: {:("Market",,"Products",),(I,"10,000","2,000","18,000"),(II,"6,000","20,000","8,000"):} (a) If unit sale prices of x, y and z are Rs. 2.50, Rs. 1.50 and Rs. 1.00, respectively, find the total revenue in each market with the help of matrix algebra. (b) If the unit costs of the above three commodities are Rs. 2.00, Rs. 1.00 and 50 paise respectively. Find the gross profit.

Electromagnetic waves propagate through free space or a medium as transverse waves. The electric and magnetic fields are perpendicular to each other as well as perpendicular to the direction of propagation of waves at each point. In the direction of wave propagation, electric field vecE and magnetic field vecB form a right-handed cartesian coordinate system. During the propagation of electromagnetic wave, total energy of electromagnetic wave is distributed equally between electric and magnetic fields. Since in_0 and mu_0 are permittivity and permeability of free space, the velocity of electromagnetic wave, c=(in_0 mu_0)^(-1//2) . Energy density i.e., energy in unit volume due to electric field at any point, u_E=1/2in_0E^2 Similarly, energy density due to magnetic field , u_M=1/(2mu_0)B^2 . If the electromagnetic wave propagates along x-direction, then the equations of electric and magnetic field are respectively. E=E_0sin(omegat-kx) and B=B_0sin(omegat-kx) Here, the frequency and the wavelength of oscillating electric and magnetic fields are f=omega/(2pi) and lambda=(2pi)/k respectively. Thus E_"rms"=E_0/sqrt2 and B_"rms"=B_0/sqrt2 , where E_0/B_0=c . Therefore, average energy density baru_E=1/2in_0E_"rms"^2 and baru_M=1/(2mu_0)B_"rms"^2 . The intensity of the electromagnetic wave at a point, I=cbaru=c(baru_E+baru_B) . To answer the following questions , we assume that in case of propagation of electromagnetic wave through free space, c=3xx10^8 m.s^(-1) and mu_0=4pixx10^(-7) H.m^(-1) If the peak value of electric field at a point in electromagnetic wave is 15 V . m^(-1) , then average electrical energy density (in j . m^(-3) )