Verified Solution • 2025–26 Session moderate

QJEEM13Maa1a7: JEE Main 2013 Mathematics - Class 12 JEEM13Maa1a7 Solution: At present, a firm is manufacturing items. It is estimated that …

At present, a firm is manufacturing 20002000 items. It is estimated that the rate of change of production P w.r.t. additional number of workers xx is given by dpdx=100−12x.{{dp} \over {dx}} = 100 - 12\sqrt x . If the firm employs 2525 more workers, then the new level of production of items is

Multiple Choice Options

  • A 25002500
  • B 30003000
  • C 35003500
  • D 45004500

Step-by-Step Verified Solution

Given, Rate of change is dpdx=100−12x{{dp} \over {dx}} = 100 - 12\sqrt x

⇒dP=(100−12x)dx\Rightarrow dP = \left( {100 - 12\sqrt x } \right)dx

By intergrating ∫dP=∫(100−12x)dx\int {dP = \int {\left( {100 - 12\sqrt x } \right)} } dx

∫dP=∫(100−12x)dx\int {dP} = \int {\left( {100 - 12\sqrt x } \right)} dx

P=100x−8x3/2+CP = 100x - 8{x^{3/2}} + C

Given, when x=0x=0 then P=2000P=2000

⇒C=2000\Rightarrow C = 2000

Now when xx =25=25

then P=100×25−8×(25)3/2+2000P = 100 \times 25 - 8 \times {\left( {25} \right)^{3/2}} + 2000

          \,\,\,\,\,\,\,\,\,\, =4500−1000=4500-1000

⇒P=3500\Rightarrow P = 3500

Related Learning Resources & Exam Preparation

JEE Main PYQ Question Bank
Browse year-wise authentic previous years' questions with solutions
Authentic CBT Mock Tests
Simulate official exam environment with live timer and percentile scoring