JEE MATHEMATICS MCQ: TANGENTS & NORMALS

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Application +4 | -1

Let y be the number of people in a village at time

t

. Assume that the rate of change of the population is proportional to the number of people in the village at any time and further assume that the population never increase in time. Then, the population of the village at any fixed

t

is given by

View answer and explanation

Correct option: B

y = c{e^{kt}},

for some constants

c \ge 0

and

k \le 0

Option B (

y = c{e^{kt}},

for some constants

c \ge 0

and

k \le 0

) is correct because it represents exponential decay, which aligns with a population that never increases.

More Questions from TANGENTS & NORMALS

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The complete set of value of '

a

' for which there exists at least one line that is tangent to the graph of the curve

y=x^3-a x

at one point and normal to the graph at another point is given by The point of intersection of the tangents drawn to the curve

x^2 y=1-y

at the points where it is met by the curve

x y=1-y

, is given by Let

C

be the curve

y^3-3 x y+2=0

. If

H

is the set of points on the curve

\mathrm{C}

where the tangent is parallel to

x

-axis and

V

is the set of points on

C

where the tangent is parallel to

y

-axis, then The curve

y-e^{x y}+x=0

has a vertical tangent at the point: If normal to the curve

y = f\left( x \right)

is parallel to

x

-axis, then The tangents to the curve

x = a\left( {\theta - \sin \theta } \right),\;y = a\left( {1 + \cos \theta } \right)

at the points

\theta = \left( {2k + 1} \right)\pi ,\;k \in Z

are parallel to: