At present, a firm is manufacturing 2000 items. It is estimated that the rate of change of production P w.r.t. additional number of workers x is given by `(d P)/(dx)=100-12sqrt(xdot)` If the firm employs 25 more workers, then the new level of production of items is (1) 3000 (2) 3500 (3) 4500 (4) 2500

Differentiate the functions given w.r.t. x: sqrt(((x-1)(x-2))/((x-3)(x-4)(x-5)))

has four statements (A,B,C and D) given in Coumn-I and five statements (P,Q,R,S and T) given in Column-II. Any given statement in Column-I can have correct matching with one or more statement(s) given in Column-II. {:(Column-I,Column-II),((A)"A rectangular box has volume 48,and the sum of",(P)1),("length of the twelve edges of the box is 48. The largest",),("integer that could be the length of an edge of the box,is",),((B)"The number of zeroes at the end in the product of first",(Q)2),("20 prime numbers, is"(p),),((C)"The number of solutions of" 2^(2x)-3^(2y)=55 "in which x and y",(R)3),("are integers,is"(0),(S)4),((D)"The number" (7+5sqrt(2))^(1//3)+(7-5sqrt(2))^(1//3)"is equal to",(T)6):}

When an object moves through a fluid, as when a ball falls through air or a glass sphere falls through water te fluid exerts a viscous foce F on the object this force tends to slow the object for a small sphere of radius r moving is given by stoke's law, F_(w)=6pietarv . in this formula eta in the coefficient of viscosity of the fluid which is the proportionality constant that determines how much tangential force is required to move a fluid layer at a constant speed v, when the layer has an area A and is located a perpendicular distance z from and immobile surface. the magnitude of the force is given by F=etaAv//z . For a viscous fluid to move from location 2 to location 1 along 2 must exceed that at location 1, poiseuilles's law given the volumes flow rate Q that results from such a pressure difference P_(2)-P_(1) . The flow rate of expressed by the formula Q=(piR^(4)(P_(2)-P_(1)))/(8etaL) poiseuille's law remains valid as long as the fluid flow is laminar. For a sfficiently high speed however the flow becomes turbulent flow is laminar as long as the reynolds number is less than approximately 2000. This number is given by the formula R_(e)=(2overline(v)rhoR)/(eta) In which overline(v) is the average speed rho is the density eta is the coefficient of viscosity of the fluid and R is the radius of the pipe. Take the density of water to be rho=1000kg//m^(3) Q. If the sphere in previous question has mass of 1xx10^(-5)kg what is its terminal velocity when falling through water? (eta=1xx10^(-3)Pa-s) A. 1.3m/s B. 3.4m/s C. 5.2m/s D. 6.5m/s

When an object moves through a fluid, as when a ball falls through air or a glass sphere falls through water te fluid exerts a viscous foce F on the object this force tends to slow the object for a small sphere of radius r moving is given by stoke's law, F_(w)=6pietarv . in this formula eta in the coefficient of viscosity of the fluid which is the proportionality constant that determines how much tangential force is required to move a fluid layer at a constant speed v, when the layer has an area A and is located a perpendicular distance z from and immobile surface. the magnitude of the force is given by F=etaAv//z . For a viscous fluid to move from location 2 to location 1 along 2 must exceed that at location 1, poiseuilles's law given the volumes flow rate Q that results from such a pressure difference P_(2)-P_(1) . The flow rate of expressed by the formula Q=(piR^(4)(P_(2)-P_(1)))/(8etaL) poiseuille's law remains valid as long as the fluid flow is laminar. For a sfficiently high speed however the flow becomes turbulent flow is laminar as long as the reynolds number is less than approximately 2000. This number is given by the formula R_(e)=(2overline(v)rhoR)/(eta) In which overline(v) is the average speed rho is the density eta is the coefficient of viscosity of the fluid and R is the radius of the pipe. Take the density of water to be rho=1000kg//m^(3) Q. Calculate the highest average speed that blood (rho~~1000kg//m^(3) ) could have and still remain in laminar flow when it flows through the arorta (R=8xx10^(-3)m ) Take the coeffiicient of viscosity of blood to be 4xx10^(-3)Pa-s

When an object moves through a fluid, as when a ball falls through air or a glass sphere falls through water te fluid exerts a viscous foce F on the object this force tends to slow the object for a small sphere of radius r moving is given by stoke's law, F_(w)=6pietarv . in this formula eta in the coefficient of viscosity of the fluid which is the proportionality constant that determines how much tangential force is required to move a fluid layer at a constant speed v, when the layer has an area A and is located a perpendicular distance z from and immobile surface. the magnitude of the force is given by F=etaAv//z . For a viscous fluid to move from location 2 to location 1 along 2 must exceed that at location 1, poiseuilles's law given the volumes flow rate Q that results from such a pressure difference P_(2)-P_(1) . The flow rate of expressed by the formula Q=(piR^(4)(P_(2)-P_(1)))/(8etaL) poiseuille's law remains valid as long as the fluid flow is laminar. For a sfficiently high speed however the flow becomes turbulent flow is laminar as long as the reynolds number is less than approximately 2000. This number is given by the formula R_(e)=(2overline(v)rhoR)/(eta) In which overline(v) is the average speed rho is the density eta is the coefficient of viscosity of the fluid and R is the radius of the pipe. Take the density of water to be rho=1000kg//m^(3) Q. Blood vessel is 0.10 m in length and has a radius of 1.5xx10^(-3) m blood flows at rate of 10^(-7)m^(3)//s through this vessel. The pressure difference that must be maintained in this flow between the two ends of the vessel is 20 Pa what is the viscosity sufficient of blood?

When an object moves through a fluid, as when a ball falls through air or a glass sphere falls through water te fluid exerts a viscous foce F on the object this force tends to slow the object for a small sphere of radius r moving is given by stoke's law, F_(w)=6pietarv . in this formula eta in the coefficient of viscosity of the fluid which is the proportionality constant that determines how much tangential force is required to move a fluid layer at a constant speed v, when the layer has an area A and is located a perpendicular distance z from and immobile surface. the magnitude of the force is given by F=etaAv//z . For a viscous fluid to move from location 2 to location 1 along 2 must exceed that at location 1, poiseuilles's law given the volumes flow rate Q that results from such a pressure difference P_(2)-P_(1) . The flow rate of expressed by the formula Q=(piR^(4)(P_(2)-P_(1)))/(8etaL) poiseuille's law remains valid as long as the fluid flow is laminar. For a sfficiently high speed however the flow becomes turbulent flow is laminar as long as the reynolds number is less than approximately 2000. This number is given by the formula R_(e)=(2overline(v)rhoR)/(eta) In which overline(v) is the average speed rho is the density eta is the coefficient of viscosity of the fluid and R is the radius of the pipe. Take the density of water to be rho=1000kg//m^(3) Q. What is the viscous force on a glass sphere of radius r=1mm falling through water (eta=1xx10^(-3)Pa-s) when the sphere has speed of 3m/s?

When an object moves through a fluid, as when a ball falls through air or a glass sphere falls through water te fluid exerts a viscous foce F on the object this force tends to slow the object for a small sphere of radius r moving is given by stoke's law, F_(w)=6pietarv . in this formula eta in the coefficient of viscosity of the fluid which is the proportionality constant that determines how much tangential force is required to move a fluid layer at a constant speed v, when the layer has an area A and is located a perpendicular distance z from and immobile surface. the magnitude of the force is given by F=etaAv//z . For a viscous fluid to move from location 2 to location 1 along 2 must exceed that at location 1, poiseuilles's law given the volumes flow rate Q that results from such a pressure difference P_(2)-P_(1) . The flow rate of expressed by the formula Q=(piR^(4)(P_(2)-P_(1)))/(8etaL) poiseuille's law remains valid as long as the fluid flow is laminar. For a sfficiently high speed however the flow becomes turbulent flow is laminar as long as the reynolds number is less than approximately 2000. This number is given by the formula R_(e)=(2overline(v)rhoR)/(eta) In which overline(v) is the average speed rho is the density eta is the coefficient of viscosity of the fluid and R is the radius of the pipe. Take the density of water to be rho=1000kg//m^(3) Q. Which of the following may be concluded from the information in the passage?

A solution which remains in equilibrium with undissolved solute , in contact , is said to be saturated . The concentration of a saturated solution at a given temperature is a called solubility . The product of concentration of ions in a saturated solution of an electrolyte at a given temperature is called solubility product (K_(sp)) . For the electrolyte A_(x),B_(y) with solubility S. The solubility product (K_(sp)) is given as K_(sp) = x^(x) xx y^(y) xx S^(x-y) . While calculating the solubility of a sparingly . soluable salt in the presence of some strong electrolyte containing a common ion , the common ion concentration is practically equal to that of strong electrolyte containing a common ion . the common ion soncentration is practically equal to that of strong electrolyte . If in a solution , the ionic product of an electroylte exceeds its K_(sp) value at a particular temperature , then precipitation occurs . If two or more electrolyte are presentt in the solution , then by the addition of some suitable reagent , precipitation generally occurs in increasing order of their k_(sp) values . Solubility of some sparingly soluable salts , is sometimes enhanced through complexation . While we are calculating the solubility of some sparingly or pH of an electrolyte , the nature of cation of anion should be checked carefully whether there ion (s) are capable of undergoing hydrolysis or not . If either or both of the ions are capable of undergoing hydrolysis , it should be taken into account in calculating the solubility . While calculating the pH of an amphiprotic species , it should be checked whether or not cation can undergo hydrolysis . Total a_(H^(-)) = sqrt(K_(a_(1)xxK_(a_(2)))) (if cation do not undergo hydrolysis ) a_(H^(+)) = sqrt(K_(a_(1))((K_(w))/(K_(b)) - K_(a_(2)))) (if cation also undergoes hydrolysis ) where symbols have usual meaning . Solubility of solids into liquids is a function of temperature alone but solubility of gases into liquids is a function of temperature as well as pressure . The effect of pressure on solubility of gases into liquids is governed by Henry's law . The solubility of PbSO_(4) in water is 0.0303 g/l at 25^(@)C , its solubility product at that temperature is

A firm manufactures 3 products A, B and C. the profits are Rs. 3, 2 and 4 respectively. The firm has 2 machines and below is the required processing time in minutes for each machine on each product. Machine Products A B C M_1 M_2 4 2 3 2 5 4 Machines M_1a n d\ M_2 have 2000 and 25000 machine minutes respectively. The firm must manufacture 100 As, 200B and 50Cs but not more 150 As. Set up a LPP to maximize the profit.