# Application of Derivatives · Mathematics · JEE Advanced

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JEE Advanced 2023 Paper 1 Online
Let $Q$ be the cube with the set of vertices $\left\{\left(x_1, x_2, x_3\right) \in \mathbb{R}^3: x_1, x_2, x_3 \in\{0,1\}\right\}$. Let $F$ be the se...
JEE Advanced 2020 Paper 1 Offline
Consider the rectangles lying the region $$\left\{ {(x,y) \in R \times R:0\, \le \,x\, \le \,{\pi \over 2}} \right.$$ and $$\left. {0\, \le \,y\, \le... JEE Advanced 2017 Paper 1 Offline Which of the following options is the only INCORRECT combination? JEE Advanced 2017 Paper 1 Offline Which of the following options is the only CORRECT combination? JEE Advanced 2017 Paper 1 Offline Which of the following options is the only CORRECT combination? JEE Advanced 2016 Paper 1 Offline The least value of a$$ \in R$$for which$$4a{x^2} + {1 \over x} \ge 1,$$, for all$$x>0$$. is JEE Advanced 2013 Paper 2 Offline Let$$f:\left[ {0,1} \right] \to R$$(the set of all real numbers) be a function. Suppose the function$$f$$is twice differentiable,$$f(0) = f(1)=0$... JEE Advanced 2013 Paper 2 Offline Let $$f:\left[ {0,1} \right] \to R$$ (the set of all real numbers) be a function. Suppose the function $$f$$ is twice differentiable, $$f(0) = f(1)=0... IIT-JEE 2012 Paper 2 Offline Let$$f\left( x \right) = {\left( {1 - x} \right)^2}\,\,{\sin ^2}\,\,x + {x^2}$$for all$$x \in IR$$and let$$g\left( x \right) = \int\limits_1^x {... IIT-JEE 2012 Paper 2 Offline Let $$f\left( x \right) = {\left( {1 - x} \right)^2}\,\,{\sin ^2}\,\,x + {x^2}$$ for all $$x \in IR$$ and let $$g\left( x \right) = \int\limits_1^x {... IIT-JEE 2008 Paper 1 Offline The total number of local maxima and local minima of the function$$f(x) = \left\{ {\matrix{ {{{(2 + x)}^3},} & { - 3 ... IIT-JEE 2007 The tangent to the curve $$y = {e^x}$$ drawn at the point $$\left( {c,{e^c}} \right)$$ intersects the line joining the points $$\left( {c - 1,{e^{c -... IIT-JEE 2007 If a continuous function$$f$$defined on the real line$$R$$, assumes positive and negative values in$$R$$then the equation$$f(x)=0$$has a root i... IIT-JEE 2007 If a continuous function$$f$$defined on the real line$$R$$, assumes positive and negative values in$$R$$then the equation$$f(x)=0$$has a root i... IIT-JEE 2007 If a continuous function$$f$$defined on the real line$$R$$, assumes positive and negative values in$$R$$then the equation$$f(x)=0$$has a root i... IIT-JEE 2005 Screening If$$P(x)$$is a polynomial of degree less than or equal to$$2$$and$$S$$is the set of all such polynomials so that$$P(0)=0$$,$$P(1)=1$$and$$P... IIT-JEE 2004 Screening If $$f\left( x \right) = {x^3} + b{x^2} + cx + d$$ and $$0 < {b^2} < c,$$ then in $$\left( { - \infty ,\infty } \right)$$ IIT-JEE 2004 Screening If $$f\left( x \right) = {x^a}\log x$$ and $$f\left( 0 \right) = 0,$$ then the value of $$\alpha$$ for which Rolle's theorem can be applied in $$\lef... IIT-JEE 2003 Screening In$$\left[ {0,1} \right]$$Languages Mean Value theorem is NOT applicable to IIT-JEE 2003 Screening Tangent is drawn to ellipse$${{{x^2}} \over {27}} + {y^2} = 1\,\,\,at\,\left( {3\sqrt 3 \cos \theta ,\sin \theta } \right)\left( {where\,\,\theta \... IIT-JEE 2002 Screening The length of a longest interval in which the function $$3\,\sin x - 4{\sin ^3}x$$ is increasing, is IIT-JEE 2002 Screening The point(s) in the curve $${y^3} + 3{x^2} = 12y$$ where the tangent is vertical, is (are) IIT-JEE 2001 Screening If $$f\left( x \right) = x{e^{x\left( {1 - x} \right)}},$$ then $$f(x)$$ is IIT-JEE 2001 Screening The triangle formed by the tangent to the curve $$f\left( x \right) = {x^2} + bx - b$$ at the point $$(1, 1)$$ and the coordinate axex, lies in the fi... IIT-JEE 2001 Screening Let $$f\left( x \right) = \left( {1 + {b^2}} \right){x^2} + 2bx + 1$$ and let $$m(b)$$ be the minimum value of $$f(x)$$. As $$b$$ varies, the range o... IIT-JEE 2000 Screening Consider the following statements in $$S$$ and $$R$$ $$S:$$ $$\,\,\,$$$ Both $$\sin \,\,x$$ and $$\cos \,\,x$$ are decreasing functions in the interv...
IIT-JEE 2000 Screening
If the normal to the curve $$y = f\left( x \right)$$ and the point $$(3, 4)$$ makes an angle $${{{3\pi } \over 4}}$$ with the positive $$x$$-axis, the...
IIT-JEE 2000 Screening
Let $$f\left( x \right) = \int {{e^x}\left( {x - 1} \right)\left( {x - 2} \right)dx.}$$ Then $$f$$ decreases in the interval
IIT-JEE 2000 Screening
Let $$f\left( x \right) = \left\{ {\matrix{ {\left| x \right|,} & {for} & {0 < \left| x \right| \le 2} \cr {1,} & {for} & {... IIT-JEE 2000 Screening For all$$x \in \left( {0,1} \right)$$IIT-JEE 1999 The function$$f(x)={\sin ^4}x + {\cos ^4}x$$increases if IIT-JEE 1998 The number of values of$$x$$where the function$$f\left( x \right) = \cos x + \cos \left( {\sqrt 2 x} \right)$$attains its maximum is IIT-JEE 1998 If$$f\left( x \right) = {{{x^2} - 1} \over {{x^2} + 1}},$$for every real number$$x$$, then the minimum value of$$f$$IIT-JEE 1997 If$$f\left( x \right) = {x \over {\sin x}}$$and$$g\left( x \right) = {x \over {\tan x}}$$, where$$0 < x \le 1$$, then in this interval IIT-JEE 1995 Screening The function$$f\left( x \right) = {{in\,\left( {\pi + x} \right)} \over {in\,\left( {e + x} \right)}}$$is IIT-JEE 1995 Screening On the interval$$\left[ {0,1} \right]$$the function$${x^{25}}{\left( {1 - x} \right)^{75}}$$takes its maximum value at the point IIT-JEE 1995 Screening The slope of the tangent to a curve$$y = f\left( x \right)$$at$$\left[ {x,\,f\left( x \right)} \right]$$is$$2x+1$$. If the curve passes through t... IIT-JEE 1994 The function defined by$$f\left( x \right) = \left( {x + 2} \right){e^{ - x}}$$IIT-JEE 1994 Which one of the following curves cut the parabola$${y^2} = 4ax$$at right angles? IIT-JEE 1987 The smallest positive root of the equation,$$\tan x - x = 0$$lies in IIT-JEE 1987 Let$$f$$and$$g$$be increasing and decreasing functions, respectively from$$\left[ {0,\infty } \right)$$to$$\left[ {0,\infty } \right)$$. Let$$...
IIT-JEE 1986
Let $$P\left( x \right) = {a_0} + {a_1}{x^2} + {a_2}{x^4} + ...... + {a_n}{x^{2n}}$$ be a polynomial in a real variable $$x$$ with $$0 < {a_0} &l... IIT-JEE 1983 If$$a+b+c=0$$, then the quadratic equation$$3a{x^2} + 2bx + c = 0$$has IIT-JEE 1983$$AB$$is a diameter of a circle and$$C$$is any point on the circumference of the circle. Then IIT-JEE 1983 The normal to the curve$$\,x = a\left( {\cos \theta + \theta \sin \theta } \right)$$,$$y = a\left( {\sin \theta - \theta \cos \theta } \right)$$a... IIT-JEE 1983 If$$y = a\,\,In\,x + b{x^2} + x$$has its extreamum values at$$x=-1$$and$$x=2$$, then ## MCQ (More than One Correct Answer) JEE Advanced 2022 Paper 2 Online Let$$ \alpha=\sum\limits_{k = 1}^\infty {{{\sin }^{2k}}\left( {{\pi \over 6}} \right)} $$Let g:[0,1] \rightarrow \mathbb{R} be the function d... JEE Advanced 2019 Paper 2 Offline Let f : R$$ \to $$R be given by$$f(x) = (x - 1)(x - 2)(x - 5)$$. Define$$F(x) = \int\limits_0^x {f(t)dt} $$, x > 0Then which of the following opt... JEE Advanced 2019 Paper 2 Offline Let,$$f(x) = {{\sin \pi x} \over {{x^2}}}$$, x > 0Let x1 < x2 < x3 < ... < xn < ... be all the points of local maximum of f and y1 ... JEE Advanced 2017 Paper 2 Offline f : R$$ \to $$R is a differentiable function such that f'(x) > 2f(x) for all x$$ \in $$R, and f(0) = 1 then JEE Advanced 2017 Paper 2 Offline If$$f(x) = \left| {\matrix{ {\cos 2x} & {\cos 2x} & {\sin 2x} \cr { - \cos x} & {\cos x} & { - \sin x} \cr {\sin x} &...
JEE Advanced 2016 Paper 2 Offline
Let f: R $$\to \left( {0,\infty } \right)$$ and g : R $$\to$$ R be twice differentiable functions such that f'' and g'' are continuous functions on...
JEE Advanced 2015 Paper 2 Offline
Let $$f, g :$$ $$\left[ { - 1,2} \right] \to R$$ be continuous functions which are twice differentiable on the interval $$(-1, 2)$$. Let the values of...
JEE Advanced 2013 Paper 2 Offline
The function $$f(x) = 2\left| x \right| + \left| {x + 2} \right| - \left| {\left| {x + 2} \right| - 2\left| x \right|} \right|$$ has a local minimum o...
JEE Advanced 2013 Paper 1 Offline
A rectangular sheet of fixed perimeter with sides having their lengths in the ratio $$8:15$$ is converted into an open rectangular box by folding afte...
IIT-JEE 2012 Paper 2 Offline
If $$f\left( x \right) = \int_0^x {{e^{{t^2}}}} \left( {t - 2} \right)\left( {t - 3} \right)dt$$ for all $$x \in \left( {0,\infty } \right),$$ then
IIT-JEE 2009 Paper 2 Offline
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