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Mathematics : Binomial Theorem

Short Answer Type

161.

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

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162.

Find the co-efficient of $straight x to the power of 8$ in the expansion of $<pre>uncaught exception: mkdir(): Permission denied (errno: 2) in /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php at line #56mkdir(): Permission denied in file: /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php line 56 #0 [internal function]: _hx_error_handler(2, 'mkdir(): Permis...', '/home/config_ad...', 56, Array) #1 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php(56): mkdir('/home/config_ad...', 493) #2 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/FolderTreeStorageAndCache.class.php(110): com_wiris_util_sys_Store->mkdirs() #3 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/RenderImpl.class.php(231): com_wiris_plugin_impl_FolderTreeStorageAndCache->codeDigest('mml=<math xmlns...') #4 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/TextServiceImpl.class.php(59): com_wiris_plugin_impl_RenderImpl->computeDigest(NULL, Array) #5 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/service.php(19): com_wiris_plugin_impl_TextServiceImpl->service('mathml2accessib...', Array) #6 {main}</pre>$

118 Views

163.

Find the co-efficient of $space straight x to the power of 18$ in the expansion of $open parentheses ay to the power of 1 half end exponent minus bx cubed close parentheses to the power of 17$

122 Views

164.

Show that there is no term involving $straight x to the power of 6$ in the expansion of $open parentheses 2 straight x squared minus 3 over straight x close parentheses to the power of 11.$

120 Views

165.

If $straight x to the power of straight p$ occurs in the expansion of $open parentheses straight x squared plus 1 over straight x close parentheses to the power of 2 straight n end exponent comma$ prove that its co-efficient is $fraction numerator left parenthesis 2 straight n right parenthesis factorial over denominator open parentheses begin display style fraction numerator 4 straight n minus straight p over denominator 3 end fraction end style close parentheses factorial space open parentheses begin display style fraction numerator 2 straight n plus straight p over denominator 3 end fraction end style close parentheses factorial end fraction.$

108 Views

166.

If $straight x to the power of straight r$ occurs in the expansion of $open parentheses straight x plus 1 over straight x close parentheses to the power of straight n comma$ find the co-efficient of $straight x to the power of straight r.$

117 Views

Long Answer Type

167. Use Binomial Theorem to prove that 11ⁿ- 10n always leaves a remainder 1 when divided by 100.

167 Views

Short Answer Type

168. In the expansion of (1 - x)^2n-1 the co-efficient of x^r is denoted by a_r. Show that a_r-1 + a_2n-r =0.

119 Views

169. Three successive terms in the expansion of (1 + x)ⁿ are 462, 330 and 165. Find n.

128 Views

170. The co-efficients of three consecutive terms in the expansion of (1 + a)ⁿ are in the ratio 1 : 7 : 42. Find n.

121 Views