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Let R be a region in the first quadrant of the xy plane enclosed by a closed curve C considered in counter-clockwise dir...
GATE EE 2022
Let $$f(x) = \int\limits_0^x {{e^t}(t - 1)(t - 2)dt}$$. Then f(x) decreases in the interval.
GATE EE 2022
Let $${\rm I} = c\int {\int {_Rx{y^2}dxdy,\,\,} }$$ where $$R$$ is the region shown in the figure and $$c = 6 \times {1... GATE EE 2017 Set 1 Let$$x$$and$$y$$be integers satisfying the following equations$$$2{x^2} + {y^2} = 34$x + 2y = 11$$The valu... GATE EE 2017 Set 2 Consider a function$$f\left( {x,y,z} \right)$$given by$$f\left( {x,y,z} \right) = \left( {{x^2} + {y^2} - 2{z^2}} \r...
GATE EE 2017 Set 2
Let $$\,{y^2} - 2y + 1 = x$$ and $$\,\sqrt x + y = 5.\,\,$$ The value of $$\,x + \sqrt y \,\,$$ equals ________. (Given...
GATE EE 2017 Set 2
The maximum value attained by the function $$f(x)=x(x-1) (x-2)$$ in the interval $$\left[ {1,2} \right]$$ is _________.
GATE EE 2016 Set 1
A particle, starting from origin at $$t=0$$ $$s,$$ is traveling along $$x$$-axis with velocity $$v = {\pi \over 2}\cos ... GATE EE 2014 Set 3 Let$$f\left( x \right) = x{e^{ - x}}.$$The maximum value of the function in the interval$$\left( {0,\infty } \right)...
GATE EE 2014 Set 1
Minimum of the real valued function $$f\left( x \right) = {\left( {x - 1} \right)^{2/3}}$$ occurs at $$x$$ equal to
GATE EE 2014 Set 2
A function $$y = 5{x^2} + 10x\,\,$$ is defined over an open interval $$x=(1,2).$$ At least at one point in this interval...
GATE EE 2013
The function $$f\left( x \right) = 2x - {x^2} + 3\,\,$$ has
GATE EE 2011
Roots of the algebraic equation $${x^3} + {x^2} + x + 1 = 0$$ are
GATE EE 2011
At $$t=0,$$ the function $$f\left( t \right) = {{\sin t} \over t}\,\,$$ has
GATE EE 2010
Consider the function $$f\left( x \right) = {\left( {{x^2} - 4} \right)^2}$$ where $$x$$ is a real number. Then the func...
GATE EE 2007
If $$S = \int\limits_1^\infty {{x^{ - 3}}dx}$$ then $$S$$ has the value
GATE EE 2005
For the function $$f\left( x \right) = {x^2}{e^{ - x}},$$ the maximum occurs when $$x$$ is equal to
GATE EE 2005
The area enclosed between the parabola $$y = {x^2}$$ and the straight line $$y=x$$ is _______.
GATE EE 2004
$$\mathop {Lim}\limits_{\theta \to 0} \,{{\sin \,m\,\theta } \over \theta },$$ where $$m$$ is an integer, is one of the...
GATE EE 1997
If $$f(0)=2$$ and $$f'\left( x \right) = {1 \over {5 - {x^2}}},$$ then the lower and upper bounds of $$f(1)$$ estimated...
GATE EE 1995
$$\mathop {Lim}\limits_{x \to \infty } \,x\sin {\raise0.5ex\hbox{\scriptstyle 1} \kern-0.1em/\kern-0.15em \lower0.25ex... GATE EE 1995 The volume generated by revolving the area bounded by the parabola$${y^2} = 8x$$and the line$$x=2$$about$$y$$-axis ... GATE EE 1994 The integration of$$\int {{\mathop{\rm logx}\nolimits} \,dx} $$has the value GATE EE 1994 ## Marks 2 More Let$$g\left( x \right) = \left\{ {\matrix{ { - x} &amp; {x \le 1} \cr {x + 1} &amp; {x \ge 1} \cr } } \righ...
GATE EE 2017 Set 2
A function $$f(x)$$ is defined as $$f\left( x \right) = \left\{ {\matrix{ {{e^x},x &lt; 1} \cr {\ln x + a{x^2} ... GATE EE 2017 Set 1 The value of the integral$$\,\,2\int_{ - \infty }^\infty {\left( {{{\sin \,2\pi t} \over {\pi t}}} \right)} dt\,\,$$i... GATE EE 2016 Set 2 Let$$\,\,S = \sum\limits_{n = 0}^\infty {n{\alpha ^n}} \,\,$$where$$\,\,\left| \alpha \right| &lt; 1.\,\,$$The val... GATE EE 2016 Set 1 The volume enclosed by the surface$$f\left( {x,y} \right) = {e^x}$$over the triangle bounded by the lines$$x=y;x...
GATE EE 2015 Set 2
The minimum value of the function $$f\left( x \right) = {x^3} - 3{x^2} - 24x + 100$$ in the interval $$\left[ { - 3,3} \... GATE EE 2014 Set 2 To evaluate the double integral$$\int\limits_0^8 {\left( {\int\limits_{y/2}^{\left( {y/2} \right) + 1} {\left( {{{2x -...
GATE EE 2014 Set 2
The maximum value of $$f\left( x \right) = {x^3} - 9{x^2} + 24x + 5$$ in the interval $$\left[ {1,6} \right]$$ is
GATE EE 2012
The value of the quantity, where $$P = \int\limits_0^1 {x{e^x}\,dx\,\,\,}$$ is
GATE EE 2010
If $$(x, y)$$ is continuous function defined over $$\left( {x,y} \right) \in \left[ {0,1} \right] \times \left[ {0,1} \r... GATE EE 2009 The integral$$\,\,{1 \over {2\pi }}\int\limits_0^{2\Pi } {Sin\left( {t - \tau } \right)\cos \tau \,d\tau \,\,\,} $$equ... GATE EE 2007 The expression$$V = \int\limits_0^H {\pi {R^2}{{\left( {1 - {h \over H}} \right)}^2}dh\,\,\,}  for the volume of a co...
GATE EE 2006

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