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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
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The greatest and least value of $$f(x) = {\tan ^{ - 1}} - {1 \over 2}\,ln \,x\,on\,\left[ {{1 \over {\sqrt 3 }},\sqrt 3 ...
WB JEE 2021
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Tangent is drawn at any point P(x, y) on a curve, which passes through (1, 1). The tangent cuts X-axis and Y-axis at A a...
WB JEE 2020
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A particle is projected vertically upwards. If it has to stay above the ground for 12 sec, then
WB JEE 2020
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Two particles A and B move from rest along a straight line with constant accelerations f and h, respectively. If A takes...
WB JEE 2019
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Let $$f(x) = \cos \left( {{\pi \over x}} \right),x \ne 0$$, then assuming k as an integer,
WB JEE 2018
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A particle is in motion along a curve 12y = x3. The rate of change of its ordinate exceeds that of abscissa in...
WB JEE 2018
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Two particles move in the same straight line starting at the same moment from the same point in the same direction. The ...
WB JEE 2017
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If the line ax + by + c = 0, ab $$ \ne $$ 0, is a tangent to the curve xy = 1 $$-$$ 2x, then
WB JEE 2017
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MCQ (Single Correct Answer)
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A particle moving in a straight line starts from rest and the acceleration at any time t is $$a - k{t^2}$$ where a and k...
WB JEE 2022
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If the tangent at the point P with co-ordinates (h, k) on the curve y2 = 2x3 is perpendicular to the straight line 4x = ...
WB JEE 2021
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Two particles A and B move from rest along a straight line with constant accelerations f and f' respectively. If A takes...
WB JEE 2021
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Consider the curve $$y = b{e^{ - x/a}}$$, where a and b are non-zero real numbers. Then
WB JEE 2020
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In open interval $$\left( {0,\,{\pi \over 2}} \right)$$
WB JEE 2020
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Let $$f(x) = {x^{13}} + {x^{11}} + {x^9} + {x^7} + {x^5} + {x^3} + x + 12$$.Then
WB JEE 2020
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If the tangent to the curve y2 = x3 at (m2, m3) is also a normal to the curve at (m2, m3), then the value of mM is...
WB JEE 2020
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If the radius of a spherical balloon increases by 0.1%, then its volume increases approximately by
WB JEE 2019
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The normal to the curve $$y = {x^2} - x + 1$$, drawn at the points with the abscissa $${x_1} = 0$$, $${x_2} = - 1$$ and...
WB JEE 2018
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A ladder 20 ft long leans against a vertical wall. The top end slides downwards at the rate of 2 ft per second. The rate...
WB JEE 2018
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The law of motion of a body moving along a straight line is x = $${1 \over 2}$$ vt. x being its distance from a fixed po...
WB JEE 2018
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The value of K in order that f(x) = sin x $$-$$ cos x $$-$$ kx + 5 decreases for all positive real values of x is given ...
WB JEE 2017
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The chord of the curve $$y = {x^2} + 2ax + b$$, joining the points where x = $$\alpha$$ and x = $$\beta$$, is parallel t...
WB JEE 2017
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Let, $$F(x) = {e^x},G(x) = {e^{ - x}}$$ and $$H(x) = G(F(x))$$, where x is a real variable. Then, $${{dH} \over {dx}}$$ ...
WB JEE 2017
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The acceleration of a particle starting from rest moving in a straight line with uniform acceleration is 8m/sec2. The ti...
WB JEE 2011
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The co-ordinates of the point on the curve $$y = {x^2} - 3x + 2$$ where the tangent is perpendicular to the straight lin...
WB JEE 2010
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The point in the interval [0, 2$$\pi$$], where $$f(x) = {e^x}\sin x$$ has maximum slope, is
WB JEE 2010
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The equation of normal of $${x^2} + {y^2} - 2x + 4y - 5 = 0$$ at (2, 1) is
WB JEE 2010
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If the normal to the curve y = f(x) at the point (3, 4) makes an angle 3$$\pi$$/4 with the positive x-axis, then f'(3) i...
WB JEE 2010
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Angle between y2 = x and x2 = y at the origin is
WB JEE 2009
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If the rate of increase of the radius of a circle is 5 cm/sec., then the rate of increase of its area, when the radius i...
WB JEE 2009
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The distance covered by a particle in t seconds is given by x = 3 + 8t $$-$$ 4t2. After 1 second its velocity will be...
WB JEE 2009
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The Rolle's theorem is applicable in the interval $$-$$1 $$\le$$ x $$\le$$ 1 for the function
WB JEE 2009
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A particle is moving in a straight line. At time t, the distance between the particle from its starting point is given b...
WB JEE 2009
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The equation of the tangent to the conic $${x^2} - {y^2} - 8x + 2y + 11 = 0$$ at (2, 1) is
WB JEE 2009
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A particle is projected vertically upwards and is at a height h after t1 seconds and again after t2 seconds then...
WB JEE 2008
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If the area of a rectangle is 64 square units, find the minimum value possible for its perimeter.
WB JEE 2011
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Prove that the centre of the smallest circle passing through origin and whose centre lies on y = x + 1 is $$\left( { - {...
WB JEE 2010
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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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