# Application of Derivatives · Mathematics · WB JEE

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WB JEE 2008
A particle is projected vertically upwards and is at a height h after t1 seconds and again after t2 seconds then
WB JEE 2009
The equation of the tangent to the conic $${x^2} - {y^2} - 8x + 2y + 11 = 0$$ at (2, 1) is
WB JEE 2009
A particle is moving in a straight line. At time t, the distance between the particle from its starting point is given by x = t $$-$$ 6t2 + t3. Its ac...
WB JEE 2009
The Rolle's theorem is applicable in the interval $$-$$1 $$\le$$ x $$\le$$ 1 for the function
WB JEE 2009
The distance covered by a particle in t seconds is given by x = 3 + 8t $$-$$ 4t2. After 1 second its velocity will be
WB JEE 2009
If the rate of increase of the radius of a circle is 5 cm/sec., then the rate of increase of its area, when the radius is 20 cm, will be
WB JEE 2009
Angle between y2 = x and x2 = y at the origin is
WB JEE 2010
If the normal to the curve y = f(x) at the point (3, 4) makes an angle 3$$\pi$$/4 with the positive x-axis, then f'(3) is
WB JEE 2010
The equation of normal of $${x^2} + {y^2} - 2x + 4y - 5 = 0$$ at (2, 1) is
WB JEE 2010
The point in the interval [0, 2$$\pi$$], where $$f(x) = {e^x}\sin x$$ has maximum slope, is
WB JEE 2010
The co-ordinates of the point on the curve $$y = {x^2} - 3x + 2$$ where the tangent is perpendicular to the straight line y = x are
WB JEE 2011
The acceleration of a particle starting from rest moving in a straight line with uniform acceleration is 8m/sec2. The time taken by the particle to mo...
WB JEE 2023
A missile is fired from the ground level rises x meters vertically upwards in t sec, where $$x = 100t - {{25} \over 2}{t^2}$$. The maximum height reac...
WB JEE 2023
The portion of the tangent to the curve $${x^{{2 \over 3}}} + {y^{{2 \over 3}}} = {a^{{2 \over 3}}},a > 0$$ at any point of it, intercepted between th...
WB JEE 2023
Given $$f(x) = {e^{\sin x}} + {e^{\cos x}}$$. The global maximum value of $$f(x)$$
WB JEE 2022
A particle moving in a straight line starts from rest and the acceleration at any time t is $$a - k{t^2}$$ where a and k are positive constants. The m...
WB JEE 2021
Two particles A and B move from rest along a straight line with constant accelerations f and f' respectively. If A takes m sec. more than that of B an...
WB JEE 2021
If the tangent at the point P with co-ordinates (h, k) on the curve y2 = 2x3 is perpendicular to the straight line 4x = 3y, then
WB JEE 2020
If the tangent to the curve y2 = x3 at (m2, m3) is also a normal to the curve at (m2, m3), then the value of mM is...
WB JEE 2020
Let $$f(x) = {x^{13}} + {x^{11}} + {x^9} + {x^7} + {x^5} + {x^3} + x + 12$$.Then
WB JEE 2020
In open interval $$\left( {0,\,{\pi \over 2}} \right)$$
WB JEE 2020
Consider the curve $$y = b{e^{ - x/a}}$$, where a and b are non-zero real numbers. Then
WB JEE 2019
If the radius of a spherical balloon increases by 0.1%, then its volume increases approximately by
WB JEE 2018
The law of motion of a body moving along a straight line is x = $${1 \over 2}$$ vt. x being its distance from a fixed point on the line at time t and ...
WB JEE 2018
A ladder 20 ft long leans against a vertical wall. The top end slides downwards at the rate of 2 ft per second. The rate at which the lower end moves ...
WB JEE 2018
The normal to the curve $$y = {x^2} - x + 1$$, drawn at the points with the abscissa $${x_1} = 0$$, $${x_2} = - 1$$ and $${x_3} = {5 \over 2}$$
WB JEE 2017
Let, $$F(x) = {e^x},G(x) = {e^{ - x}}$$ and $$H(x) = G(F(x))$$, where x is a real variable. Then, $${{dH} \over {dx}}$$ at x = 0 is
WB JEE 2017
The chord of the curve $$y = {x^2} + 2ax + b$$, joining the points where x = $$\alpha$$ and x = $$\beta$$, is parallel to the tangent to the curve at ...
WB JEE 2017
The value of K in order that f(x) = sin x $$-$$ cos x $$-$$ kx + 5 decreases for all positive real values of x is given by

## Subjective

WB JEE 2009
A train moving with constant acceleration takes t seconds to pass a certain fixed point and the front and back end of the train pass the fixed point w...
WB JEE 2010
Prove that the centre of the smallest circle passing through origin and whose centre lies on y = x + 1 is $$\left( { - {1 \over 2},{1 \over 2}} \right... WB JEE 2011 If the area of a rectangle is 64 square units, find the minimum value possible for its perimeter. ## MCQ (More than One Correct Answer) WB JEE 2023 A balloon starting from rest is ascending from ground with uniform acceleration of 4 ft/sec$$^2$$. At the end of 5 sec, a stone is dropped from it. If... WB JEE 2023 If$$f(x) = 3\root 3 \of {{x^2}} - {x^2}$$, then WB JEE 2022 From a balloon rising vertically with uniform velocity v ft/sec a piece of stone is let go. The height of the balloon above the ground when the stone ... WB JEE 2021 The greatest and least value of$$f(x) = {\tan ^{ - 1}} - {1 \over 2}\,ln \,x\,on\,\left[ {{1 \over {\sqrt 3 }},\sqrt 3 } \right]$$are WB JEE 2020 A particle is projected vertically upwards. If it has to stay above the ground for 12 sec, then WB JEE 2020 Tangent is drawn at any point P(x, y) on a curve, which passes through (1, 1). The tangent cuts X-axis and Y-axis at A and B respectively. If AP : BP ... WB JEE 2019 Two particles A and B move from rest along a straight line with constant accelerations f and h, respectively. If A takes m seconds more than B and des... WB JEE 2018 A particle is in motion along a curve 12y = x3. The rate of change of its ordinate exceeds that of abscissa in WB JEE 2018 Let$$f(x) = \cos \left( {{\pi \over x}} \right),x \ne 0$$, then assuming k as an integer, WB JEE 2017 If the line ax + by + c = 0, ab$$ \ne $$0, is a tangent to the curve xy = 1$$- 2x, then
WB JEE 2017
Two particles move in the same straight line starting at the same moment from the same point in the same direction. The first moves with constant velo...
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