Previous Year Papers

Download Solved Question Papers Free for Offline Practice and view Solutions Online.

Test Series

Take Zigya Full and Sectional Test Series. Time it out for real assessment and get your results instantly.

Test Yourself

Practice and master your preparation for a specific topic or chapter. Check you scores at the end of the test.

171. A group consists of 4 girls and 7 boys. In how many ways can a team of 5 members be selected if the team has:
(i) no girl (ii) at least one boy and one girl (iii) at least 3 girls.

Total number of boys and girls in the group = 4 girls + 7 boys = 11
Number of boys and girls in the team = 5
(i) The team consists of no girl,
$rightwards double arrow$ The team consists of 0 girl + 5 boys

∴ Number of selections = $straight C presuperscript 4 subscript 0 cross times straight C presuperscript 7 subscript 5 space equals space 1 space cross times space fraction numerator 7 cross times 6 cross times 5 factorial over denominator 5 factorial space 2 factorial end fraction equals 21$
Hence, the number of teams formed = 21

(ii) The team consists of at least 1 boy and 1 girl.
Options are:
The team consists of 1 girl + 4 boys
Number of selections = $space space straight C presuperscript 4 subscript 1 cross times straight C presuperscript 7 subscript 4 space equals space 4 cross times fraction numerator 7 factorial over denominator 3 factorial space 4 factorial end fraction equals 4 cross times fraction numerator 7 cross times 6 cross times 5 over denominator 3 factorial end fraction$
= 4 x 7 x 5 = 140.
Or
The team consists of 2 girls + 3 boys

$rightwards double arrow$ Number of selections = $straight C presuperscript 4 subscript 2 cross times straight C presuperscript 7 subscript 3 space equals space fraction numerator 4 factorial over denominator 2 factorial space 2 factorial end fraction cross times fraction numerator 7 factorial over denominator 4 factorial space 3 factorial end fraction$

= $fraction numerator 4 cross times 3 over denominator 2 cross times 1 end fraction cross times fraction numerator 7 cross times 6 cross times 5 over denominator 3 cross times 2 cross times 1 end fraction equals 6 cross times 35 equals 210.$
Or
The team consists of 3 girls + 2 boys
$rightwards double arrow$ Number of selections = $straight C presuperscript 4 subscript 3 cross times straight C presuperscript 7 subscript 2 space equals space fraction numerator 4 factorial space over denominator 3 factorial space space 1 factorial end fraction cross times fraction numerator 7 factorial over denominator 5 factorial space space 2 factorial end fraction$
= $4 cross times fraction numerator 7 cross times 6 over denominator 2 end fraction equals 84.$
Or
The team consists of 4 girls + 1 boy.
$rightwards double arrow$ Number of selections = $straight C presuperscript 4 subscript 4 cross times straight C presuperscript 7 subscript 1 space equals space 1 cross times 7 equals 7$
Hence, the total number of teams that can be formed = 140 + 210 + 84 + 7 = 441

(iii) The team consists of at least 3 girls
Options are:
The team consists of 3 girls + 2 boys.
$rightwards double arrow$ Number of selections = $<pre>uncaught exception: mkdir(): Permission denied (errno: 2) in /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php at line #56mkdir(): Permission denied in file: /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php line 56 #0 [internal function]: _hx_error_handler(2, 'mkdir(): Permis...', '/home/config_ad...', 56, Array) #1 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php(56): mkdir('/home/config_ad...', 493) #2 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/FolderTreeStorageAndCache.class.php(110): com_wiris_util_sys_Store->mkdirs() #3 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/RenderImpl.class.php(231): com_wiris_plugin_impl_FolderTreeStorageAndCache->codeDigest('mml=<math xmlns...') #4 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/TextServiceImpl.class.php(59): com_wiris_plugin_impl_RenderImpl->computeDigest(NULL, Array) #5 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/service.php(19): com_wiris_plugin_impl_TextServiceImpl->service('mathml2accessib...', Array) #6 {main}</pre>$
Or
The team consists of 4 girls + 1 boy.
$rightwards double arrow$ Number of selections = $straight C presuperscript 4 subscript 4 cross times straight C presuperscript 7 subscript 1 space equals space 1 cross times 7 space equals space 7$
Hence, the total number of teams that can be formed = 84 + 7 = 91

200 Views

Short Answer Type

172.

Determine the number of 5-card combinations out of a deck of 52 cards if each selection of 5 cards has exactly one king.

90 Views

Long Answer Type

173.

What is the number of ways of choosing 4 cards from a pack of 52 cards? In how many of these :

(i) four cards are of the same suit?

(ii) four cards belongs to different suit?

(iii) are face cards?

(iv) two are red cards and two are black cards?

(v) cards are of the same colour?

137 Views

Short Answer Type

174.

How many chords can be drawn through 21 points on a circle?

142 Views

175.

How many straight lines can be formed with 7 points, 3 of which are colinear.

103 Views

176. Find the number of triangles formed by 9 points lying on the circumference of a circle.

114 Views

177. Find the number of triangles formed by 12 points, 5 of which are collinear.

92 Views

178.

If $straight C presuperscript straight n minus 1 end presuperscript subscript straight r colon straight C presuperscript straight n subscript straight r colon straight C presuperscript straight n plus 1 end presuperscript subscript straight r space equals space 6 colon 9 colon 13 comma$ Find n and r.

89 Views

179. In an examination, a question paper consists of 12 questions, divided into two parts i.e., Part I and Part II containing 5 and 7 questions respectively. A student is required to attempt 8 questions in all, selecting at least 3 from each part. In how many ways can the student select his questions?

111 Views

180. From a class of 25 students, 10 are to be chosen for an excursion party. There are three students who decide that either all of them will join or none of them will join. In how many ways can the excursion party be chosen?

99 Views