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## 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 $$f(x) = {\tan ^{ - 1}} - {1 \over 2}\,ln \,x\,on\,\left[ {{1 \over {\sqrt 3 }},\sqrt 3 ... WB JEE 2021 Tangent is drawn at any point P(x, y) on a curve, which passes through (1, 1). The tangent cuts X-axis and Y-axis at A a... WB JEE 2020 A particle is projected vertically upwards. If it has to stay above the ground for 12 sec, then WB JEE 2020 Two particles A and B move from rest along a straight line with constant accelerations f and h, respectively. If A takes... WB JEE 2019 Let$$f(x) = \cos \left( {{\pi \over x}} \right),x \ne 0$$, then assuming k as an integer, WB JEE 2018 A particle is in motion along a curve 12y = x3. The rate of change of its ordinate exceeds that of abscissa in... WB JEE 2018 Two particles move in the same straight line starting at the same moment from the same point in the same direction. The ... WB JEE 2017 If the line ax + by + c = 0, ab$$ \ne $$0, is a tangent to the curve xy = 1$$-$$2x, then WB JEE 2017 ## MCQ (Single Correct Answer) More A particle moving in a straight line starts from rest and the acceleration at any time t is$$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$$.Then WB JEE 2020 If the tangent to the curve y2 = x3 at (m2, m3) is also a normal to the curve at (m2, m3), then the value of mM is... WB JEE 2020 If the radius of a spherical balloon increases by 0.1%, then its volume increases approximately by WB JEE 2019 The normal to the curve$$y = {x^2} - x + 1$$, drawn at the points with the abscissa$${x_1} = 0$$,$${x_2} = - 1$$and... WB JEE 2018 A ladder 20 ft long leans against a vertical wall. The top end slides downwards at the rate of 2 ft per second. The rate... WB JEE 2018 The law of motion of a body moving along a straight line is x =$${1 \over 2}$$vt. x being its distance from a fixed po... WB JEE 2018 The value of K in order that f(x) = sin x$$-$$cos x$$-$$kx + 5 decreases for all positive real values of x is given ... WB JEE 2017 The chord of the curve$$y = {x^2} + 2ax + b$$, joining the points where x =$$\alpha$$and x =$$\beta$$, is parallel t... WB JEE 2017 Let,$$F(x) = {e^x},G(x) = {e^{ - x}}$$and$$H(x) = G(F(x))$$, where x is a real variable. Then,$${{dH} \over {dx}}$$... WB JEE 2017 The acceleration of a particle starting from rest moving in a straight line with uniform acceleration is 8m/sec2. The ti... WB JEE 2011 The co-ordinates of the point on the curve$$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$$at (2, 1) is WB JEE 2009 A particle is projected vertically upwards and is at a height h after t1 seconds and again after t2 seconds then... WB JEE 2008 ## Subjective More If the area of a rectangle is 64 square units, find the minimum value possible for its perimeter. WB JEE 2011 Prove that the centre of the smallest circle passing through origin and whose centre lies on y = x + 1 is$$\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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