GATE Overflow - Recent questions tagged cartesian-coordinates
https://gateoverflow.in/tag/cartesian-coordinates
Powered by Question2AnswerGATE2016 EC-3: GA-10
https://gateoverflow.in/110855/gate2016-ec-3-ga-10
<p>A straight line is fit to a data set (ln $x, y$). This line intercepts the abscissa at ln $x = 0.1$ and has a slope of $-0.02$. What is the value of y at $x = 5$ from the fit?</p>
<ol style="list-style-type:upper-alpha">
<li>$-0.030$ </li>
<li>$-0.014$</li>
<li>$0.014$</li>
<li>$0.030$</li>
</ol>Numerical Abilityhttps://gateoverflow.in/110855/gate2016-ec-3-ga-10Wed, 25 Jan 2017 08:55:55 +0000GATE2016 EC-3: GA-9
https://gateoverflow.in/110853/gate2016-ec-3-ga-9
<p>Find the area bounded by the lines $3x + 2y=14, 2x - 3y = 5$ in the first quadrant.</p>
<ol style="list-style-type:upper-alpha">
<li>$14.95$</li>
<li>$15.25$</li>
<li>$15.70$</li>
<li>$20.35$</li>
</ol>Numerical Abilityhttps://gateoverflow.in/110853/gate2016-ec-3-ga-9Wed, 25 Jan 2017 08:52:14 +0000ISI2011-PCB-A-4a
https://gateoverflow.in/48049/isi2011-pcb-a-4a
Consider six distinct points in a plane. Let $m$ and $M$ denote the minimum and maximum distance between any pair of points. Show that $M/m \geq \sqrt{3}$.Numerical Abilityhttps://gateoverflow.in/48049/isi2011-pcb-a-4aFri, 03 Jun 2016 02:38:42 +0000GATE2014 AE: GA-4
https://gateoverflow.in/40303/gate2014-ae-ga-4
<p>If $y=5x^2+3$, then the tangent at $x=0$, $y=3$</p>
<ol start="1" style="list-style-type:upper-alpha">
<li>passes through $x=0,y=0$</li>
<li>has a slope of $+1$</li>
<li>is parallel to the $x$-axis</li>
<li>has a slope of $-1$</li>
</ol>Numerical Abilityhttps://gateoverflow.in/40303/gate2014-ae-ga-4Tue, 16 Feb 2016 06:19:31 +0000GATE2012 AE: GA-9
https://gateoverflow.in/40220/gate2012-ae-ga-9
<p>Two points $(4, p)$ and $(0, q)$ lie on a straight line having a slope of $3/4$. The value of $( p – q)$ is</p>
<ol style="list-style-type:upper-alpha">
<li>$-3$</li>
<li>$0$</li>
<li>$3$</li>
<li>$4$</li>
</ol>Numerical Abilityhttps://gateoverflow.in/40220/gate2012-ae-ga-9Mon, 15 Feb 2016 19:48:23 +0000TIFR2015-A-13
https://gateoverflow.in/29586/tifr2015-a-13
<p>Imagine the first quadrant of the real plane as consisting of unit squares. A typical square has $4$ corners: $(i, j), (i+1, j), (i+1, j+1),$and $(i, j+1)$, where $(i, j)$ is a pair of non-negative integers. Suppose a line segment $l$ connecting $(0, 0)$ to $(90, 1100)$ is drawn. We say that $l$ passes through a unit square if it passes through a point in the interior of the square. How many unit squares does $l$ pass through?</p>
<ol style="list-style-type:lower-alpha">
<li>$98,990$</li>
<li>$9,900$</li>
<li>$1,190$</li>
<li>$1,180$</li>
<li>$1,010$</li>
</ol>Numerical Abilityhttps://gateoverflow.in/29586/tifr2015-a-13Sat, 05 Dec 2015 08:55:53 +0000TIFR2014-A-13
https://gateoverflow.in/26390/tifr2014-a-13
<p>Let $L$ be a line on the two dimensional plane. $L'$s intercepts with the $X$ and $Y$ axes are respectively $a$ and $b$. After rotating the co-ordinate system (and leaving $L$ untouched), the new intercepts are $a'$ and $b'$ respectively. Which of the following is TRUE?</p>
<ol style="list-style-type: lower-alpha;">
<li>$\frac{1}{a}+\frac{1}{b}=\frac{1}{a}+\frac{1}{b}$.</li>
<li>$\frac{1}{a^{2}}+\frac{1}{b^{2}}=\frac{1}{a'^{2}}+\frac{1}{b'^{2}}$.</li>
<li>$\frac{b}{a^{2}}+\frac{a}{b^{2}}=\frac{b'}{a'^{2}}+\frac{a}{b'^{2}}$.</li>
<li>$\frac{b}{a}+\frac{a}{b}=\frac{b'}{a'}+\frac{a'}{b'}$.</li>
<li>None of the above.</li>
</ol>
Numerical Abilityhttps://gateoverflow.in/26390/tifr2014-a-13Sat, 14 Nov 2015 05:42:09 +0000TIFR2013-B-9
https://gateoverflow.in/25675/tifr2013-b-9
<p>Suppose $n$ straight lines are drawn on a plane. When these lines are removed, the plane falls apart into several connected components called regions. $A$ region $R$ is said to be convex if it has the following property: whenever two points are in $R$, then the entire line segment joining them is in $R$. Suppose no two of the n lines are parallel. Which of the following is true?</p>
<ol style="list-style-type:lower-alpha">
<li>$O (n)$ regions are produced, and each region is convex.</li>
<li>$O (n^{2})$ regions are produced but they need not all be convex.</li>
<li>$O (n^{2})$ regions are produced, and each region is convex.</li>
<li>$O (n \log n)$ regions are produced, but they need not all be convex.</li>
<li>All regions are convex but there may be exponentially many of them.</li>
</ol>Numerical Abilityhttps://gateoverflow.in/25675/tifr2013-b-9Fri, 06 Nov 2015 14:14:54 +0000GATE2007-IT-80
https://gateoverflow.in/3532/gate2007-it-80
<p>Let $P_{1},P_{2},\ldots,P_{n}$ be $n$ points in the $xy-$plane such that no three of them are collinear. For every pair of points $P_{i}$ and $P_{j}$, let $L_{ij}$ be the line passing through them. Let $L_{ab}$ be the line with the steepest gradient amongst all $\frac{n(n -1)}{2}$ lines.</p>
<p>Which one of the following properties should necessarily be satisfied ?</p>
<ol style="list-style-type:upper-alpha">
<li>$P_{a}$ and $P_{b}$ are adjacent to each other with respect to their $x$-coordinate</li>
<li>Either $P_{a}$ or $P_{b}$ has the largest or the smallest $y$-coordinate among all the points</li>
<li>The difference between $x$-coordinates $P_{a}$ and $P_{b}$ is minimum</li>
<li>None of the above</li>
</ol>Linear Algebrahttps://gateoverflow.in/3532/gate2007-it-80Thu, 30 Oct 2014 21:48:48 +0000