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Binomial Theorem

Short Answer Type

71.

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

227 Views

72.

Find the 11^th term from the end in the expansion of $open parentheses 2 straight x minus 1 over straight x squared close parentheses to the power of 25$

181 Views

73. Prove that in the expansion of (a + b)ⁿ, the co-efficients of terms equidistant from the beginning and end are the same.

107 Views

Long Answer Type

74.

Find n, if the ratio of the fifth term from the beginning to the fifth term from the end in the expansion of $open parentheses fourth root of 2 plus fraction numerator 1 over denominator fourth root of 3 end fraction close parentheses to the power of straight n$ is $square root of 6 colon 1.$

251 Views

Short Answer Type

75. Find the co-efficient of

straight x to the power of 5 space in space left parenthesis straight x plus 3 right parenthesis to the power of 8

120 Views

76. Find the co-efficient of:

straight a to the power of 5 straight b to the power of 7 space in space left parenthesis straight a minus 2 straight b right parenthesis to the power of 12

118 Views

77. Find the positive value of m for which the co-efficient of x² in the expansion of (1 + x)^m is 6.

115 Views

78. In the expansion of (1 + x)ⁿ, the co-efficients of x^p-1 and of x^q-1 are equal. Show that p + q = n + 2, p ≠ q.

115 Views

79. In the expansion of (1 + a)^m+n , prove that co-efficient of a^m and aⁿ are equal.

112 Views

80. Find a, if the co-efficients of x² and x³ in the expansion of (3 + ax)⁹ are equal.

Term containing $straight x squared comma$ in the expansion of $left parenthesis 3 plus ax right parenthesis to the power of 9 space equals space straight C presuperscript 9 subscript 2 space 3 to the power of 7 space left parenthesis ax right parenthesis squared$
Co-efficient of $straight x squared space equals space straight C presuperscript 9 subscript 2 times space 3 to the power of 7 space straight a squared$
Term containing $<pre>uncaught exception: mkdir(): Permission denied (errno: 2) in /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php at line #56mkdir(): Permission denied in file: /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php line 56 #0 [internal function]: _hx_error_handler(2, 'mkdir(): Permis...', '/home/config_ad...', 56, Array) #1 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php(56): mkdir('/home/config_ad...', 493) #2 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/FolderTreeStorageAndCache.class.php(110): com_wiris_util_sys_Store->mkdirs() #3 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/RenderImpl.class.php(231): com_wiris_plugin_impl_FolderTreeStorageAndCache->codeDigest('mml=<math xmlns...') #4 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/TextServiceImpl.class.php(59): com_wiris_plugin_impl_RenderImpl->computeDigest(NULL, Array) #5 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/service.php(19): com_wiris_plugin_impl_TextServiceImpl->service('mathml2accessib...', Array) #6 {main}</pre>$ in the expansion of $left parenthesis 3 plus ax right parenthesis to the power of 9 space equals space straight C presuperscript 9 subscript 3 space 3 to the power of 6 space left parenthesis ax right parenthesis cubed$
Co-efficient of $straight x cubed space equals space straight C presuperscript 9 subscript 3. space 3 to the power of 6. space straight a cubed$

From the condition of the question,

 $straight C presuperscript 9 subscript 2 times 3 to the power of 7 times straight a squared space equals space straight C presuperscript 9 subscript 3 times space 3 to the power of 6 times space straight a cubed$

$rightwards double arrow$ $36 times 3 to the power of 7 times straight a squared space equals space straight C presuperscript 9 subscript 3 times 3 to the power of 6 times straight a cubed$

$rightwards double arrow$ $108 straight a squared equals 84 straight a cubed$

$rightwards double arrow$ 108 = 84a

$rightwards double arrow$ $straight a equals 108 over 84 equals 18 over 14 equals 9 over 7$