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

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 space equals space left parenthesis straight a plus straight b right parenthesis to the power of straight n

rightwards double arrow

straight a equals fraction numerator 4 straight x over denominator 5 end fraction comma space straight b equals negative fraction numerator 5 over denominator 2 straight x end fraction comma space straight n equals 6

<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>

equals space straight C presuperscript 6 subscript straight r open parentheses fraction numerator 4 straight x over denominator 5 end fraction close parentheses to the power of 6 minus straight r end exponent. space open parentheses negative fraction numerator 5 over denominator 2 straight x end fraction close parentheses to the power of straight r

equals space left parenthesis negative 1 right parenthesis to the power of straight r space straight C presuperscript 6 subscript straight r space fraction numerator 4 to the power of 6 minus straight r end exponent times space straight x to the power of 6 minus straight r end exponent over denominator 5 to the power of 6 minus straight r end exponent end fraction cross times fraction numerator 5 to the power of straight r over denominator 2 to the power of straight r. space straight x to the power of straight r end fraction

equals space left parenthesis negative 1 right parenthesis to the power of straight r. space straight C presuperscript 6 subscript straight r fraction numerator 2 to the power of 12 minus 2 straight r end exponent. straight x to the power of 6 minus straight r end exponent over denominator 5 to the power of 6 minus straight r end exponent end fraction. fraction numerator 5 to the power of straight r over denominator 2 to the power of straight r. end exponent space straight x to the power of straight r end fraction equals left parenthesis negative 1 right parenthesis to the power of straight r space straight C presuperscript 6 subscript straight r fraction numerator 2 to the power of 12 minus 3 straight r end exponent times straight x to the power of 6 minus 2 straight r end exponent over denominator 5 to the power of 6 minus 2 straight r end exponent end fraction

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 $open parentheses 9 straight x minus fraction numerator 1 over denominator 3 square root of straight x end fraction close parentheses to the power of 18 comma space straight x not equal to 0$

160 Views

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