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

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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)$$... IIT-JEE 2009 ## Subjective More If$$\,\,\,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 $$f\left( x \right) = \left\{ {\matrix{ {{{x - 1} \over {2{x^2} - 7x + 5}}} &amp; {when\,\,x... IIT-JEE 1979 Find the derivative of$$\sin \left( {{x^2} + 1} \right)$$with respect to$$x$$first principle. IIT-JEE 1978 ## Fill in the Blanks More If$$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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