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At present a firm is manufacturing 2000 items. It is estimated that the rate of change of production p with respect to additional nuber of workers x is given by `(dp)/(dx)=100-12sqrtx.` If the firm employes 25 more workers, then the new level of production of items is

A

2500

B

3000

C

3500

D

4500

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The correct Answer is:
C
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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 (dP)/(dx)=100-12sqrt(x.) If the firm employs 25 more workers,then the new level of production of items is (1)3000(2)3500(3)4500(4)2500

The rate of a reaction, which may also be called its velocity or speed, can be defined with relation to the concentration of any of the reacting substances, or to that of any product of the reaction. If the species chosen is a reactant which has a concentration c at time t the rate is - dc/dt, while the rate with reference to a product having a concentration x at time t is dx/dt. Any concentration units may be used for expressing the rate, thus, if moles per liter are employed for concentration and seconds for the time, the units for the rate are moles "liter"^(-1) sec^(-1) . For gas reactions pressure units are sometimes used in place of concentrations, so that legitimate units for the rate would be (mm. Hg) sec^(-1) and atm. sec^(-1) The order of a reaction concerns the dependence of the rate upon the concentrations of reacting substances, thus, if the rate is found experimentally to be proportional to the alpha^(th) power of the concentration of one of the reactants A, to the beta^(th) power of the concentration of a second reactant B, and so forth, via., rate kC_(A)^(alpha) C_(B)^(beta)" " (1) the over-all order of the reaction is simply n = alpha +beta + ---------(2) Such a reaction is said to be of the alpha^(th) order with respect to the substance A, the beta^(th) order with respect to B and so on... (Laidler, K. J., & Glasstone, S. (1948). Rate, order and molecularity in chemical kinetics. Journal of Chemical Education, 25(7), 383.) In the following questions, a statement of assertion followed by a statement of reason is given. Choose the correct answer out of the following choices on the basis of the above passage. Assertion: Rate of reaction is a measure of change in concentration of reactant with respect to time. Reason: Rate of reaction is a measure of change in concentration of product with respect to time.

The rate of a reaction, which may also be called its velocity or speed, can be defined with relation to the concentration of any of the reacting substances, or to that of any product of the reaction. If the species chosen is a reactant which has a concentration c at time t the rate is - dc/dt, while the rate with reference to a product having a concentration x at time t is dx/dt. Any concentration units may be used for expressing the rate, thus, if moles per liter are employed for concentration and seconds for the time, the units for the rate are moles "liter"^(-1) sec^(-1) . For gas reactions pressure units are sometimes used in place of concentrations, so that legitimate units for the rate would be (mm. Hg) sec^(-1) and atm. sec^(-1) The order of a reaction concerns the dependence of the rate upon the concentrations of reacting substances, thus, if the rate is found experimentally to be proportional to the alpha^(th) power of the concentration of one of the reactants A, to the beta^(th) power of the concentration of a second reactant B, and so forth, via., rate kC_(A)^(alpha) C_(B)^(beta)" " (1) the over-all order of the reaction is simply n = alpha +beta + ---------(2) Such a reaction is said to be of the alpha^(th) order with respect to the substance A, the beta^(th) order with respect to B and so on... (Laidler, K. J., & Glasstone, S. (1948). Rate, order and molecularity in chemical kinetics. Journal of Chemical Education, 25(7), 383.) In the following questions, a statement of assertion followed by a statement of reason is given. Choose the correct answer out of the following choices on the basis of the above passage. Assertion: For a reaction: P +2Q to Products, Rate =k [P]^(1//2)[Q]^(1) so the order of reaction is 1.5 Reason: Order of reaction is the sum of stoichiometric coefficients of the reactants.

India's manufacturing growth fell to its lowestin more than two years in September, 2011 , reinforcing fears that an extended period of high policy-rates is hurting growth, accqrding to a closely vatched index. The HSBC India Purch:asing Managers' Index (PMI), based one survey of over 500 companies, fell to 50.4 from 52.6 in August and 53.6 in July. It was the lowest since March 2009, when the reading was below 5-0, indicating contraction. September's index also recorded the biggest one-month fall since November 2008. The sub index for new orders, which reflects future output, declined for the sixth successive month, while export orders fell for a third month on the back of weakness in global economy. The Reserve Bank of India (RBI) last week indicate·d it was not done yet with monetary pocicy tightening as inflation was still high. The bank has already raised rates 12 times since March 201 Oto tame inflation, which is at a.13-month high of9. 78%. Economists expect the RBI toraise rates 6ne'more time but warn that target¥d growth will be hard .to achieve if the slump continues. "This ( fall in PMI) was driven by weaker orders, with export orders still contracting due to the weaker global economic conditions," HSBC said in a press release quoting its chief economist for India & ASEAN. PMI is considered a fairly good indicator of manufacturing · activity the world over, but in the case of India, the large contribution of the unorganised sector yields a low correlation 1 with industrial growth. However, the Index for Industrial Production (IIP) has been showing a weakening trend, having slipped to a 21-month low of 3.3% in July. The core sector, which consists of eight infrastructure industries and has a combined weight of 37.9% in the IIP, also grew at only3.5% in August. The PMI data is in line with the suffering manufacturing activity in India as per other estimates. Producers are seeing that demand conditions are softening and the outlook is uncertain, therefore they are producing less. Employment in the manufacturing sector ·declined for the second consecutive month, indicating it too was under pressure. This could be attributed to lower requirement of staff and rise in resignations as higher wage requests go unfulfilled, the HSBC statement said. On the inflation front, input prices rose at an 11-month low rate, but despite signs of softening they still remain at historically high levels. While decelerating slightly, the readings for input and output priGes suggest that inflation pressures remain firmly in place. Most economists feel the RBI is close to the end of its rate hike cycle. Even the weekly -Wholesale Price Index . (WPI) estimates have started showing signs of softening, having fallen more than one percentage point. The PMI is based on surveys of

ARIHANT MATHS-DIFFERENTIAL EQUATION -Exercise (Questions Asked In Previous 13 Years Exam)
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  4. Let f:[0,1]rarrR (the set of all real numbers) be a function. Suppose ...

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  5. Let f:[0,1]rarrR (the set of all real numbers) be a function. Suppose ...

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  6. Let f:[0,1]toR (the set of all real numbers ) be a function. Suppose t...

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  7. If y(x) satisfies the differential equation y^(prime)-ytanx=2xs e c...

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  8. Let y^(prime)(x)+y(x)g^(prime)(x)=g(x)g^(prime)(x),y(0),x in R , wher...

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  9. Let f: RvecR be a continuous function which satisfies f(x)= int0^xf(t...

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  10. For the following question, choose the correct answer from the codes (...

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  11. If a curve y=f(x) passes through the point (1,-1) and satisfies the di...

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  12. Let y(x) be the solution of the differential equation (xlogx)(dy)/(dx)...

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  13. Let the population of rabbits surviving at a time t be governed by ...

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  17. Let I be the purchase value of an equipment and V(t) be the value afte...

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