InterviewSolution
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InterviewSolution
This section includes InterviewSolutions, each offering curated multiple-choice questions to sharpen your knowledge and support exam preparation. Choose a topic below to get started.
| 1. |
An airforce plane is ascending vertically atthe rate of 100 km/h. If the radius of the earth is `rk m ,`how fast is the area of the earth, visible from the plane, increasing at 3minutes after it started ascending? Given that the visible area `A`at height `h`is given by `A=2pir^2h/(r+h)`. |
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Answer» Let say h=height and A= area `(dh)/dt=100` `A=(2pir^2h)/(r+h` `(dA)/(dt)=(dA)/(dh)(dh)/(dt)` `=2pir^2d/dh(h/(r+h))*100` `=2pir^2[((r+h)-h)/(f+h)^2]*100` `=(200pir^3)/(r+h)^2` `h=100/60*3=5km` `(dA)/(dt)=(200pir^3)/(r+5)^2``km^2`/h. |
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| 2. |
If the area of circle increases at a uniform rate, then prove that theperimeter varies inversely as the radius. |
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Answer» Area of a circle, `A = pir^2` `:. (dA)/dt = 2pir (dr)/dt` It is given that area of circle increases at uniform rate. `:. (dA)/dt = k`, where `k` is a constant. `=> 2pir (dr)/dt = k` `=> (dr)/dt = k/(2pir)` Now, perimeter of the circle `P = 2pir` `:. (dP)/dt = 2pi(dr)/dt` `=> (dP)/dt = (2pi)(k/(2pir)) = k/r` Thus, rate of change of perimeter varies inversely with the radius. |
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| 3. |
A ladder 13m long leans against a wall. The foot of the ladder ispulled along the ground away from the wall, at the rate of 1.5m/sec. How fastis the angle `theta`betweenthe ladder and the ground is changing when the foot of the ladder is 12m awayfrom the wall. |
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Answer» `tan theta = y/x` `sin theta = y/13` differentiating wrt t `cos theta* (d theta)/dt = ((dy)/dt)/13` `12/13*(d theta)/dt = (dy/dt)/13` `(d theta)/dt = (dy/dt)/12` eqn (1) now, `x^2 + y^2 = 13^2` `2xdy/dt + 2ydy/dt = 0` `2*12*1.5 = -2*5*dy/dt` `dy/dt = 24*1.5/-10= 36/-10` putting in eqn (1) `(d theta)/dt = -36/(10*12) = -0.3`rad/sec |
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