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## Marks 1

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$$\mathop {\lim }\limits_{n \to \infty } \left( {\sqrt {{n^2} + n} - \sqrt {{n^2} + 1} } \right)\,\,$$ is ________.
GATE IN 2016
A straight line of the form $$y=mx+c$$ passes through the origin and the point $$(x, y)=(2,6).$$ The value of $$m$$ is
GATE IN 2016
The double integral $$\,\,\int_0^a {\int_0^y {f\left( {x,y} \right)\,dx\,dy\,\,\,} }$$ is equivalent to
GATE IN 2015
Given $$x\left( t \right) = 3\,\sin \,\left( {1000\pi t} \right)\,\,$$ and $$\,\,y\left( t \right) = 5\cos \,\left( {100... GATE IN 2014 The series$$\,\,\sum\limits_{m = 0}^\alpha {{1 \over {{4^m}}}{{\left( {x - 1} \right)}^{2m}}\,\,\,} $$converges for GATE IN 2011 Given$$y = {x^2} + 2x + 10\,\,\,$$the value of$$\,\,{\left. {{{dy} \over {dx}}} \right|_{x = 1}}\,\,$$is equal to GATE IN 2008$$\,\mathop {Lim}\limits_{x \to 0} {{\sin x} \over x}\,\,\,$$is GATE IN 2008 The value of$$\,\int\limits_0^\infty {\int\limits_0^\infty {{e^{ - {x^2}}}{e^{ - {y^2}}}} dx\,dy\,\,\,\,} $$is GATE IN 2007 Consider the function$$\,\,f\left( x \right) = {\left| x \right|^3},\,\,\,$$where$$x$$is real. Then the function$$f...
GATE IN 2007
For real $$x,$$ the maximum value of $${{{e^{Sin\,x}}} \over {{e^{Cos\,x}}}}\,\,$$ is
GATE IN 2007
$$f = {a_0}\,{x^n} + {a_1}\,{x^{n - 1}}\,y + - - + \,{a_{n - 1}}\,x\,{y^{n - 1}} + {a_n}\,{y^n}$$ where $$\,\,{a_i}\... GATE IN 2005 The value of the integral$$\int\limits_{ - 1}^1 {{1 \over {{x^2}}}dx} \,\,\,$$is GATE IN 2005$$\mathop {Lim}\limits_{x \to {\pi \over 4}} \,\,{{Sin\,\,2\left( {x - {\pi \over 4}} \right)} \over {x - {\pi \over ...
GATE IN 2001
$$\mathop {Lim}\limits_{x \to 0} \,{1 \over {10}}\,\,{{1 - {e^{ - j5x}}} \over {1 - {e^{ - jx}}}} = \_\_\_\_.$$
GATE IN 1999

## Marks 2

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The angle between two vectors $${X_1} = {\left[ {\matrix{ 2 &amp; 6 &amp; {14} \cr } } \right]^T}$$ and $${X_2} =... GATE IN 2017 Let$$\,\,f:\left[ { - 1, - } \right] \to R,\,\,$$where$$\,f\left( x \right) = 2{x^3} - {x^4} - 10.$$The minimum valu... GATE IN 2016 The maximum value of$$f\left( x \right) = {x^3} - 9{x^2} + 24x + 5$$in the interval$$\left[ {1,6} \right]$$is GATE IN 2012 Consider the function$$\,\,y = {x^2} - 6x + 9.\,\,\,$$The maximum value of$$y$$obtained when$$x$$varies over the i... GATE IN 2008 The expression$${e^{ - ln\,x}}$$for$$x &gt; 0 is equal to
GATE IN 2008

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