GATE2009 q22 - Revision history

Arjun Suresh at 11:38, 15 July 2014

2014-07-15T11:38:31Z

Arjun Suresh at 12:54, 14 July 2014

2014-07-14T12:54:57Z

Arjun Suresh at 12:37, 14 July 2014

2014-07-14T12:37:10Z

Arjun Suresh at 12:35, 14 July 2014

2014-07-14T12:35:46Z

Arjun Suresh at 12:30, 14 July 2014

2014-07-14T12:30:00Z

Arjun Suresh at 12:28, 14 July 2014

2014-07-14T12:28:24Z

Arjun Suresh at 12:27, 14 July 2014

2014-07-14T12:27:57Z

Arjun Suresh at 12:27, 14 July 2014

2014-07-14T12:27:12Z

Arjun Suresh at 12:26, 14 July 2014

2014-07-14T12:26:22Z

Arjun Suresh at 12:24, 14 July 2014

2014-07-14T12:24:47Z

← Older revision		Revision as of 11:38, 15 July 2014
Line 65:		Line 65:

	[[Category: GATE2009]]		[[Category: GATE2009]]
−	[[Category: Graph Theory questions]]	+	[[Category: Graph Theory questions from GATE]]

← Older revision		Revision as of 12:54, 14 July 2014
Line 59:		Line 59:
	of group from $d$, so $d$ is a generator.		of group from $d$, so $d$ is a generator.

−	$c$ and $d$ are generators. So option <b>(C)</b> is correct.	+	Thus $c$ and $d$ are generators. So option <b>(C)</b> is correct.

@@ Line 53: / Line 53: @@
 		 on repeated application of $b$ on itself. So it is not a generator.
-		Now for $c$, $c*c = b$. Then $(c*c)*c = b*c = d$. Then $(c*c*c)*c = d*c = a$. Then $(c*c*c*c)*c = a*c = c$. So we see that we have generated
+		Now for $c$, $c*c = b$. Then $(c*c)*c = b*c = d$. Then $(c*c*c)*c = d*c = a$. Then $(c*c*c*c)*c = a*c = c$. We see that we have generated
-		 all elements of group. So $c$ is a generator.
+		 all elements of group, so $c$ is a generator.
-		For $d$, $d*d = b$. Then $(d*d)*d = b*d = c$. Then $(d*d*d)*d = c*d = a$. Then $(d*d*d*d)*d = a*d = d$. So we have generated all elements
+		For $d$, $d*d = b$. Then $(d*d)*d = b*d = c$. Then $(d*d*d)*d = c*d = a$. Then $(d*d*d*d)*d = a*d = d$. We have generated all elements
 		 of group from $d$, so $d$ is a generator.
-		So $c$ and $d$ are generators. So option <b>(C)</b> is correct.
+		$c$ and $d$ are generators. So option <b>(C)</b> is correct.

@@ Line 34: / Line 34: @@
 |}
 		Which one of the following choices is correct?
-		<br>
-		<b>(A) </b>a, b are generators
+		(A) $a, b$ are generators
-		&nbsp;
-		<b>(B) </b>b, c are generators
+		(B) $b, c$ are generators
-		<br>
-		<b>(C) </b>c, d are generators
+		(C) $c, d$ are generators
-		&nbsp;
-		<b>(D) </b>d, a are generators
+		(D) $d, a$ are generators
 ==={{Template:Author|Happy Mittal|{{mittalweb}} }}===
 An element is a generator for a cyclic group if on repeated applications of it upon itself, it can generate all
 		elements of group.
-		<br>
-		For example here : a*a = <b>a</b>, then (a*a)*a = a*a = <b>a</b>, and so on. Here we see that no matter how many times we apply a on itself,
+		For example here : $a*a = a$, then $(a*a)*a = a*a = a$, and so on. Here we see that no matter how many times we apply $a$ on itself,
-		we can't generate any other element except a, so a is not a generator.
+		we can't generate any other element except $a$, so $a$ is not a generator.
-		<br>
-		Now for b, b*b = <b>a</b>. Then (b*b)*b = a*b = <b>b</b>. Then (b*b*b)*b = b*b = <b>a</b>, and so on. Here again we see that we can only generate a and b
+		Now for $b$, $b*b = a$. Then $(b*b)*b = a*b = b$. Then $(b*b*b)*b = b*b = a$, and so on. Here again we see that we can only generate $a$ and $b$
-		 on repeated application of b on itself. So it is not a generator.
+		 on repeated application of $b$ on itself. So it is not a generator.
-		<br>
-		Now for c, c*c = <b>b</b>. Then (c*c)*c = b*c = <b>d</b>. Then (c*c*c)*c = d*c = <b>a</b>. Then (c*c*c*c)*c = a*c = <b>c</b>. So we see that we have generated
+		Now for $c$, $c*c = b$. Then $(c*c)*c = b*c = d$. Then $(c*c*c)*c = d*c = a$. Then $(c*c*c*c)*c = a*c = c$. So we see that we have generated
-		 all elements of group. So c is a generator.
+		 all elements of group. So $c$ is a generator.
-		<br>
-		For d, d*d = <b>b</b>. Then (d*d)*d = b*d = <b>c</b>. Then (d*d*d)*d = c*d = <b>a</b>. Then (d*d*d*d)*d = a*d = <b>d</b>. So we have generated all elements
+		For $d$, $d*d = b$. Then $(d*d)*d = b*d = c$. Then $(d*d*d)*d = c*d = a$. Then $(d*d*d*d)*d = a*d = d$. So we have generated all elements
-		 of group from d, so d is a generator.
+		 of group from $d$, so $d$ is a generator.
-		<br>
-		So c and d are generators. So option <b>(C)</b> is correct.
+		So $c$ and $d$ are generators. So option <b>(C)</b> is correct.

@@ Line 10: / Line 10: @@
 |-
 !a
-|b
+|a
-| a
+| b
 | d
 |-
 !b
 | b
 | a
 |-
 !c
 | c
 | b
 | a
 |-
@@ Line 30: / Line 30: @@
 | d
 | c
 | b
 |}
 		Which one of the following choices is correct?

@@ Line 21: / Line 21: @@
 | a
 |-
-|d
+!c
 | d
 | c

@@ Line 9: / Line 9: @@
 ! d
 |-
-|b
+!a
 |b
 | a
@@ Line 15: / Line 15: @@
 | c
 |-
-|c
+!b
 | c
 | d

@@ Line 1: / Line 1: @@
 For the composition table of a cyclic group shown below
-{| {{table}}
 {| class="wikitable"
 ! a
 ! b
@@ Line 12: / Line 9: @@
 ! d
 |-
-| b
+|b
 | a
 | d
 | c
 |-
 | c
 | d
@@ Line 22: / Line 21: @@
 | a
 |-
 | d
 | c

@@ Line 1: / Line 1: @@
 For the composition table of a cyclic group shown below
-		<table>
+		{| class="wikitable"
-  <tr>
+! a
-    <th>a</th>
+! b
-    <th>b</th>
+! c
-    <th>c</th>
+! d
-    <th>d</th>
+|-
-  </tr>
+| b
-  <tr>
+| a
-    <td>b</td>
+| d
-    <td>a</td>
+| c
-    <td>d</td>
+|-
-    <td>c</td>
+| c
-  </tr>
+| d
-  <tr>
+| b
-    <td>c</td>
+| a
-    <td>d</td>
+|-
-    <td>b</td>
+| d
-    <td>a</td>
+| c
-  </tr>
+| b
-  <tr>
+| a
-    <td>d</td>
+|}
 		Which one of the following choices is correct?
 		<br>