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Binomial Theorem

Short Answer Type

61.

Write the general term in the expansion of:
$<pre>uncaught exception: mkdir(): Permission denied (errno: 2) in /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php at line #56mkdir(): Permission denied in file: /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php line 56 #0 [internal function]: _hx_error_handler(2, 'mkdir(): Permis...', '/home/config_ad...', 56, Array) #1 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php(56): mkdir('/home/config_ad...', 493) #2 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/FolderTreeStorageAndCache.class.php(110): com_wiris_util_sys_Store->mkdirs() #3 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/RenderImpl.class.php(231): com_wiris_plugin_impl_FolderTreeStorageAndCache->codeDigest('mml=<math xmlns...') #4 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/TextServiceImpl.class.php(59): com_wiris_plugin_impl_RenderImpl->computeDigest(NULL, Array) #5 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/service.php(19): com_wiris_plugin_impl_TextServiceImpl->service('mathml2accessib...', Array) #6 {main}</pre>$

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62.

115 Views

63.

Write the general term in the expansion of:
$open parentheses 2 straight x plus 1 over straight x close parentheses to the power of 5$

102 Views

64.

Write the general term in the expansion of:
$open parentheses fraction numerator 4 straight x over denominator 5 end fraction minus fraction numerator 5 over denominator 2 straight x end fraction close parentheses to the power of 6$

120 Views

65.

Write the general term in the expansion of:
$space open parentheses straight x plus fraction numerator 1 over denominator 2 straight x end fraction close parentheses to the power of 2 straight m end exponent$

100 Views

66. Find the 4^th term in the expansion of (x- 2y)^12.

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67.

Find the 13^th term in the expansion of $open parentheses 9 straight x minus fraction numerator 1 over denominator 3 square root of straight x end fraction close parentheses to the power of 18 comma space straight x not equal to 0$

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68.

Find 3^rd term in the expansion of $open parentheses 3 straight x minus straight y cubed over 6 close parentheses to the power of 4$

102 Views

69.

Find 5^th term in the expansion of $<pre>uncaught exception: mkdir(): Permission denied (errno: 2) in /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php at line #56mkdir(): Permission denied in file: /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php line 56 #0 [internal function]: _hx_error_handler(2, 'mkdir(): Permis...', '/home/config_ad...', 56, Array) #1 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php(56): mkdir('/home/config_ad...', 493) #2 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/FolderTreeStorageAndCache.class.php(110): com_wiris_util_sys_Store->mkdirs() #3 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/RenderImpl.class.php(231): com_wiris_plugin_impl_FolderTreeStorageAndCache->codeDigest('mml=<math xmlns...') #4 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/TextServiceImpl.class.php(59): com_wiris_plugin_impl_RenderImpl->computeDigest(NULL, Array) #5 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/service.php(19): com_wiris_plugin_impl_TextServiceImpl->service('mathml2accessib...', Array) #6 {main}</pre>$

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70. Find the r^th term from the end in the expansion of (x + a)ⁿ.

In the expansion of $left parenthesis straight x plus straight a right parenthesis to the power of straight n colon$

$straight p to the power of th space term space from space end space equals space straight T subscript straight n minus straight p plus 2 end subscript$

$rightwards double arrow$ $straight r to the power of th space term space from space end space equals space straight T subscript straight n minus straight r plus 2 end subscript$

∴ $straight T subscript straight n minus straight r plus 2 end subscript equals straight C presuperscript straight n subscript straight n minus straight r plus 1 end subscript space left parenthesis straight x right parenthesis to the power of straight n minus straight n plus straight r minus 1 end exponent. space straight a to the power of straight n minus straight r plus 1 end exponent$

$equals straight C presuperscript straight n subscript straight n minus straight r plus 1 end subscript space straight x to the power of straight r minus 1 end exponent. space straight a to the power of straight n minus straight r plus 1 end exponent$