Previous Year Papers

Download Solved Question Papers Free for Offline Practice and view Solutions Online.

Test Series

Take Zigya Full and Sectional Test Series. Time it out for real assessment and get your results instantly.

Test Yourself

Practice and master your preparation for a specific topic or chapter. Check you scores at the end of the test.

Continuity and Differentiability

Short Answer Type

251. $If space straight x to the power of straight y equals straight y to the power of straight x comma space prove space that space dy over dx equals fraction numerator begin display style straight y over straight x end style minus log space straight y over denominator begin display style straight x over straight y end style minus log space straight x end fraction$

space straight x to the power of straight y equals straight y to the power of straight x rightwards double arrow space log space straight x to the power of straight y equals log space straight y to the power of straight x space space space space space space space rightwards double arrow space straight y space log space straight x equals straight x. log space straight y Differentiating space both space sides space straight w. straight r. straight t. straight x comma straight y.1 over straight x plus log space straight x dy over dx equals straight x.1 over straight y. dy over dx plus log space straight y.1 therefore space open parentheses log space straight x minus straight x over straight y close parentheses dy over dx equals log space straight y minus straight y over straight x space space space rightwards double arrow open parentheses straight x over straight y minus log space straight x close parentheses dy over dx equals straight y over straight x minus log space straight y dy over dx equals fraction numerator begin display style straight y over straight x minus log space straight y end style over denominator begin display style straight x over straight y minus log space straight x end style end fraction

83 Views

252.

If space straight y equals straight x to the power of straight y comma space prove space that space dy over dx equals fraction numerator straight y squared over denominator straight x left parenthesis 1 minus straight y space log space straight x right parenthesis end fraction.

88 Views

253.

Find space dy over dx when space xy equals straight e to the power of straight x minus straight y end exponent.

87 Views

254.

<pre>uncaught exception: <b>file_put_contents(/home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/web/../../../../../../formulas/64/ea/07693cdc340768600ec4c104b639.ini): failed to open stream: Permission denied (errno: 2) in /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/sys/io/File.class.php at line #12file_put_contents(/home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/web/../../../../../../formulas/64/ea/07693cdc340768600ec4c104b639.ini): failed to open stream: Permission denied</b><br /><br />in file: /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/sys/io/File.class.php line 12<br />#0 [internal function]: _hx_error_handler(2, 'file_put_conten...', '/home/config_ad...', 12, Array) #1 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/sys/io/File.class.php(12): file_put_contents('/home/config_ad...', 'mml=<math xmlns...') #2 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php(48): sys_io_File::saveContent('/home/config_ad...', 'mml=<math xmlns...') #3 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/FolderTreeStorageAndCache.class.php(112): com_wiris_util_sys_Store->write('mml=<math xmlns...') #4 /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...') #5 /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) #6 /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) #7 {main}</pre>

89 Views

255.

If space straight y equals square root of fraction numerator 1 minus straight x over denominator 1 plus straight x end fraction end root comma space prove space that space left parenthesis 1 minus straight x squared right parenthesis dy over dx plus straight y equals 0

90 Views

256.

If space straight f left parenthesis straight x right parenthesis equals open parentheses fraction numerator 3 plus straight x over denominator 1 plus straight x end fraction close parentheses to the power of 2 plus 3 straight x end exponent comma space find space straight f apostrophe left parenthesis 0 right parenthesis

83 Views

257.

Differentiate space square root of fraction numerator left parenthesis straight x minus 3 right parenthesis left parenthesis straight x squared plus 4 right parenthesis over denominator 3 straight x squared plus 4 straight x plus 5 end fraction end root straight w. straight r. straight t. straight x

79 Views

258.

Differentiate space square root of fraction numerator left parenthesis straight x minus 1 right parenthesis left parenthesis straight x minus 2 right parenthesis over denominator left parenthesis straight x minus 3 right parenthesis left parenthesis straight x minus 4 right parenthesis left parenthesis straight x minus 5 right parenthesis end fraction end root straight w. straight r. straight t. straight x

91 Views

259. Differentiate : (x + 3)² (x + 4)³ (x + 5)^4.w.r.t.x.

81 Views

260.

Find the derivative of the function given by

f(x)=(1 + x)(1 + x²)(1 + x⁴)(1 + x⁸)and hence find f'(1).

73 Views