# Application of Derivatives · Mathematics · WB JEE

Start Practice## MCQ (Single Correct Answer)

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...