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

521. Find the second order derivatives of the following functions :x³ log x

89 Views

522. Find the second order derivatives of the following functions : e^x sin 5x

84 Views

523. Find the second order derivatives of the following functions : e^{6 x} cos 3x

Let space space space space space straight y equals straight e to the power of 6 straight x end exponent space cos space 3 straight x therefore space dy over dx equals 6 straight e to the power of 6 straight x end exponent space cos 3 straight x minus 3 straight e to the power of 6 straight x end exponent space sin 3 straight x space space space space fraction numerator straight d squared straight y over denominator dx squared end fraction equals 36 straight e to the power of 6 straight x end exponent space cos 3 straight x minus 18 straight e to the power of 6 straight x end exponent space sin 3 straight x minus 18 straight e to the power of 6 straight x end exponent sin space 3 straight x minus 9 straight e to the power of 6 straight x end exponent space cos 3 straight x space space space space space space space space space space space space space space equals 27 straight e to the power of 6 straight x end exponent space cos 3 straight x minus 36 straight e to the power of 6 straight x end exponent space sin 3 straight x equals 9 straight e to the power of 6 straight x end exponent space left parenthesis 3 cos space straight x minus 4 space sin space 3 straight x right parenthesis

89 Views

524. Find the second order derivatives of the following functions : tan^-1 x

91 Views

525. Find the second order derivatives of the following functions : log (log x)

88 Views

526. Find the second order derivatives of the following functions : sin (log x)

81 Views

527.

If space straight x equals square root of straight a to the power of sin to the power of negative 1 end exponent straight t end exponent end root comma space straight y equals square root of straight a to the power of cos to the power of negative 1 end exponent straight t end exponent end root comma space show space that dy over dx equals negative straight y over straight x.

73 Views

528.

Find space fraction numerator straight d cubed straight y over denominator dx cubed end fraction space when space straight y equals fraction numerator log space straight x over denominator straight x end fraction.

85 Views

529.

Find space fraction numerator straight d squared straight y over denominator dx squared end fraction comma space if space space straight y equals straight x cubed plus tan space straight x

92 Views

530.

<pre>uncaught exception: <b>Http Error #502</b><br /><br />in file: /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/HttpImpl.class.php line 61<br />#0 [internal function]: com_wiris_plugin_impl_HttpImpl_0(Object(com_wiris_plugin_impl_HttpImpl), NULL, 'http://www.wiri...', 'Http Error #502') #1 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/php/Boot.class.php(769): call_user_func_array('com_wiris_plugi...', Array) #2 [internal function]: _hx_lambda->execute('Http Error #502') #3 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/haxe/Http.class.php(532): call_user_func_array(Array, Array) #4 [internal function]: haxe_Http_5(true, Object(com_wiris_plugin_impl_HttpImpl), Object(com_wiris_plugin_impl_HttpImpl), Array, Object(haxe_io_BytesOutput), true, 'Http Error #502') #5 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/php/Boot.class.php(769): call_user_func_array('haxe_Http_5', Array) #6 [internal function]: _hx_lambda->execute('Http Error #502') #7 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/HttpImpl.class.php(27): call_user_func_array(Array, Array) #8 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/haxe/Http.class.php(444): com_wiris_plugin_impl_HttpImpl->onError('Http Error #502') #9 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/haxe/Http.class.php(458): haxe_Http->customRequest(true, Object(haxe_io_BytesOutput), NULL, NULL) #10 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/HttpImpl.class.php(40): haxe_Http->request(true) #11 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/TextServiceImpl.class.php(80): com_wiris_plugin_impl_HttpImpl->request(true) #12 /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) #13 {main}</pre>