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WB JEE

Application of Derivatives

Mathematics

Previous Years Questions

MCQ (More than One Correct Answer)

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From a balloon rising vertically with uniform velocity v ft/sec a piece of stone is let go. The height of the balloon ab...
WB JEE 2022
The greatest and least value of $$f(x) = {\tan ^{ - 1}} - {1 \over 2}\,ln \,x\,on\,\left[ {{1 \over {\sqrt 3 }},\sqrt 3 ...
WB JEE 2021
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 a...
WB JEE 2020
A particle is projected vertically upwards. If it has to stay above the ground for 12 sec, then
WB JEE 2020

MCQ (Single Correct Answer)

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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...
WB JEE 2022
If the tangent at the point P with co-ordinates (h, k) on the curve y2 = 2x3 is perpendicular to the straight line 4x = ...
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...
WB JEE 2021
Consider the curve $$y = b{e^{ - x/a}}$$, where a and b are non-zero real numbers. Then
WB JEE 2020
In open interval $$\left( {0,\,{\pi \over 2}} \right)$$
WB JEE 2020
Let $$f(x) = {x^{13}} + {x^{11}} + {x^9} + {x^7} + {x^5} + {x^3} + x + 12$$.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
The acceleration of a particle starting from rest moving in a straight line with uniform acceleration is 8m/sec2. The ti...
WB JEE 2011
The co-ordinates of the point on the curve $$y = {x^2} - 3x + 2$$ where the tangent is perpendicular to the straight lin...
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 equation of normal of $${x^2} + {y^2} - 2x + 4y - 5 = 0$$ at (2, 1) 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) i...
WB JEE 2010
Angle between y2 = x and x2 = y at the origin is
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 i...
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
The Rolle's theorem is applicable in the interval $$-$$1 $$\le$$ x $$\le$$ 1 for the function
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 b...
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 projected vertically upwards and is at a height h after t1 seconds and again after t2 seconds then...
WB JEE 2008

Subjective

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If the area of a rectangle is 64 square units, find the minimum value possible for its perimeter.
WB JEE 2011
Prove that the centre of the smallest circle passing through origin and whose centre lies on y = x + 1 is $$\left( { - {...
WB JEE 2010
A train moving with constant acceleration takes t seconds to pass a certain fixed point and the front and back end of th...
WB JEE 2009

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