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Binomial Theorem

Short Answer Type

51. How many terms do the expansion of the following have?

left parenthesis 1 minus 2 straight x plus straight x squared right parenthesis to the power of 7

113 Views

52. Expand using Binomial Theorem.

open parentheses 1 plus straight x over 2 minus straight x over 2 close parentheses to the power of 4 comma space straight x not equal to 0

128 Views

Long Answer Type

53. Find the co-efficient of x⁵ in the product (1 + 2x)⁶ (1 -x)⁷ using Binomial theorem.

117 Views

54. Find the co-efficient of a⁴ in the product (1 + 2a)⁴ (2 - a)⁵ using Binomial Theorem.

104 Views

Short Answer Type

55. Using Binomial Theorem, expand the following expression:

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162 Views

56. Using Binomial Theorem, expand the following expression:

<pre>uncaught exception: <b>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</b><br /><br />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<br />#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>

173 Views

57. Expand the following expression, using Binomial Theorem:

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110 Views

58. Expand the following expression, using Binomial Theorem:

left parenthesis 1 plus straight x plus straight x squared right parenthesis cubed

101 Views

59.
Find the co-efficient of $straight x squared$ in the expansion of $open parentheses 3 straight x minus 1 over straight x close parentheses to the power of 6.$

Suppose $straight T subscript straight r plus 1 end subscript$ contains $space straight x squared.$
$straight T subscript straight r plus 1 end subscript space equals space straight C presuperscript 6 subscript straight r left parenthesis 3 straight x right parenthesis to the power of 6 minus straight r space end exponent open parentheses negative 1 over straight x close parentheses to the power of straight r$
Power of x = (6 - r) - r
= 6 - 2r
Power of x required = 2
∴ 6 - 2r = 2 or r = 2
$straight T subscript straight r plus 1 end subscript space equals space straight T subscript 3 space equals space straight C presuperscript 6 subscript 2 space end subscript left parenthesis 3 straight x right parenthesis to the power of 4 space open parentheses negative 1 over straight x close parentheses squared$
$<pre>uncaught exception: mkdir(): Permission denied (errno: 2) in /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php at line #56mkdir(): Permission denied in file: /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php line 56 #0 [internal function]: _hx_error_handler(2, 'mkdir(): Permis...', '/home/config_ad...', 56, Array) #1 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php(56): mkdir('/home/config_ad...', 493) #2 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/FolderTreeStorageAndCache.class.php(110): com_wiris_util_sys_Store->mkdirs() #3 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/RenderImpl.class.php(231): com_wiris_plugin_impl_FolderTreeStorageAndCache->codeDigest('mml=<math xmlns...') #4 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/TextServiceImpl.class.php(59): com_wiris_plugin_impl_RenderImpl->computeDigest(NULL, Array) #5 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/service.php(19): com_wiris_plugin_impl_TextServiceImpl->service('mathml2accessib...', Array) #6 {main}</pre>$
Hence, co-efficient of $straight x squared equals 1215$