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JEE Advanced

Differentiation

Mathematics

Previous Years Questions

MCQ (More than One Correct Answer)

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Let $$f:R \to R,\,g:R \to R$$ and $$h:R \to R$$ be differentiable functions such that $$f\left( x \right)= {x^3} + 3x + ...
JEE Advanced 2016 Paper 1 Offline

MCQ (Single Correct Answer)

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Let $$f:\left[ {0,2} \right] \to R$$ be a function which is continuous on $$\left[ {0,2} \right]$$ and is differentiable...
JEE Advanced 2014 Paper 2 Offline
Let $$f$$ and $$g$$ be real valued functions defined on interval $$(-1, 1)$$ such that $$g''(x)$$ is continuous, $$g\lef...
IIT-JEE 2008
Let $$g\left( x \right) = \log f\left( x \right)$$ where $$f(x)$$ is twice differentible positive function on $$\left( {...
IIT-JEE 2008
Let $$\,\,\,$$$$f\left( x \right) = 2 + \cos x$$ for all real $$X$$. STATEMENT - 1: for eachreal $$t$$, there exists a...
IIT-JEE 2007
$${{{d^2}x} \over {d{y^2}}}$$ equals
IIT-JEE 2007
If $$f(x)$$ is a twice differentiable function and given that $$f\left( 1 \right) = 1;f\left( 2 \right) = 4,f\left( 3 \r...
IIT-JEE 2005 Screening
If $$y$$ is a function of $$x$$ and log $$(x+y)-2xy=0$$, then the value of $$y'(0)$$ is equal to
IIT-JEE 2004 Screening
Let $$f:\left( {0,\infty } \right) \to R$$ and $$F\left( x \right) = \int\limits_0^x {f\left( t \right)dt.} $$ If $$F\l...
IIT-JEE 2001 Screening
If $${x^2} + {y^2} = 1$$ then
IIT-JEE 2000
If $$y = {\left( {\sin x} \right)^{\tan x}},$$ then $${{dy} \over {dx}}$$ is equal to
IIT-JEE 1994
Let $$f(x)$$ be a quadratic expression which is positive for all the real values of $$x$$. If $$g(x)=f(x)+f''(x)$$, then...
IIT-JEE 1990
If $${y^2} = P\left( x \right)$$, a polynomial of degree $$3$$, then $$2{d \over {dx}}\left( {{y^3}{{{d^2}y} \over {d{x^...
IIT-JEE 1988

Numerical

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Let $$f\left( \theta \right) = \sin \left( {{{\tan }^{ - 1}}\left( {{{\sin \theta } \over {\sqrt {\cos 2\theta } }}} \r...
IIT-JEE 2011 Paper 1 Offline
If the function $$f\left( x \right) = {x^3} + {e^{{x \over 2}}}$$ and $$g\left( x \right) = {f^{ - 1}}\left( x \right)$$...
IIT-JEE 2009

Subjective

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If$$\,\,\,$$ $$y = {{a{x^2}} \over {\left( {x - a} \right)\left( {x - b} \right)\left( {x - c} \right)}} + {{bx} \over {...
IIT-JEE 1998
Find $${{{dy} \over {dx}}}$$ at $$x=-1$$, when $${\left( {\sin y} \right)^{\sin \left( {{\pi \over 2}x} \right)}} + {{...
IIT-JEE 1991
If $$x = \sec \theta - \cos \theta $$ and $$y = {\sec ^n}\theta - {\cos ^n}\theta $$, then show that $$\left( {{x^2} ...
IIT-JEE 1989
If $$\alpha $$ be a repeated root of a quadratic equation $$f(x)=0$$ and $$A(x), B(x)$$ and $$C(x)$$ be polynomials of d...
IIT-JEE 1984
Let $$f$$ be a twice differentiable function such that $$f''\left( x \right) = - f\left( x \right),$$ and $$f'\left( x...
IIT-JEE 1982
Let $$y = {e^{x\,\sin \,{x^3}}} + {\left( {\tan x} \right)^x}$$. Find $${{dy} \over {dx}}$$
IIT-JEE 1981
Given $$y = {{5x} \over {3\sqrt {{{\left( {1 - x} \right)}^2}} }} + {\cos ^2}\left( {2x + 1} \right)$$; Find $${{dy} \ov...
IIT-JEE 1980
Find the derivative of $$$f\left( x \right) = \left\{ {\matrix{ {{{x - 1} \over {2{x^2} - 7x + 5}}} & {when\,\,x...
IIT-JEE 1979
Find the derivative of $$\sin \left( {{x^2} + 1} \right)$$ with respect to $$x$$ first principle.
IIT-JEE 1978

Fill in the Blanks

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If $$x{e^{xy}} = y + {\sin ^2}x,$$ then at $$x = 0,{{dy} \over {dx}} = ..............$$
IIT-JEE 1996
If $$f\left( x \right) = \left| {x - 2} \right|$$ and $$g\left( x \right) = f\left[ {f\left( x \right)} \right]$$, then ...
IIT-JEE 1990
The derivative of $${\sec ^{ - 1}}\left( {{1 \over {2{x^2} - 1}}} \right)$$ with respect to $$\sqrt {1 - {x^2}} $$ at $$...
IIT-JEE 1986
If $$f\left( x \right) = {\log _x}\left( {In\,x} \right),$$ then $$f'\left( x \right)$$ at $$x=e$$ is ................
IIT-JEE 1985
If $${f_r}\left( x \right),{g_r}\left( x \right),{h_r}\left( x \right),r = 1,2,3$$ are polynomials in $$x$$ such that $$...
IIT-JEE 1985
If $$y = f\left( {{{2x - 1} \over {{x^2} + 1}}} \right)$$ and $$f'\left( x \right) = \sin {x^2}$$, then $${{dy} \over ...
IIT-JEE 1982

True or False

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The derivative of an even function is always an odd function.
IIT-JEE 1983

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