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.

Limits and Derivatives

Short Answer Type

71.

Find the derivatives of the following functions :

5 sec x + 4 cos x

274 Views

72.

Find the derivatives of the following functions :

sin x cos x

123 Views

73.

Find the derivatives of the following functions :

2 tan x - 7 sec x

114 Views

74. Find the derivatives of the following functions :

$space space space space space space space space fraction numerator sec space straight x space minus 1 over denominator sec space straight x space plus 1 end fraction$

Let $space space space space space space space space space space space space space space space straight y space equals space fraction numerator sec space straight x space minus 1 over denominator sec space straight x plus 1 end fraction$

Differentiating both sides w.r.t. s, we get

$space space space space space space space space space space space space space dy over dx equals straight d over dx open parentheses fraction numerator sec space straight x minus 1 over denominator sec space straight x space plus 1 end fraction close parentheses equals fraction numerator left parenthesis sec space straight x plus 1 right parenthesis begin display style straight d over dx end style left parenthesis sec space straight x minus 1 right parenthesis space minus space left parenthesis sec space straight x minus 1 right parenthesis begin display style straight d over dx end style left parenthesis sec space straight x plus 1 right parenthesis over denominator left parenthesis sec space straight x space plus 1 right parenthesis squared end fraction$

$space space space space space space space space space space space space space space space space equals space fraction numerator left parenthesis sec space straight x plus 1 right parenthesis left parenthesis sec space straight x space tan space straight x minus 0 right parenthesis minus left parenthesis sec space straight x minus 1 right parenthesis left parenthesis sec space straight x space tan space straight x plus 0 right parenthesis over denominator left parenthesis sec space straight x plus 1 right parenthesis squared end fraction$

$space space space space space space space space space space space space space space space space space space space space space equals space fraction numerator sec squared straight x space tan space straight x space plus sec space straight x space tan space straight x minus sec squared space xtan space straight x space plus space sec space straight x space tan space straight x over denominator left parenthesis sec space straight x space plus 1 right parenthesis squared end fraction equals fraction numerator 2 space sec space straight x space tan space straight x over denominator left parenthesis sec space straight x space plus 1 right parenthesis squared end fraction$

104 Views

75. Find the derivatives of the following functions :

space space space space fraction numerator sin left parenthesis straight x plus straight a right parenthesis over denominator cos space straight x end fraction

101 Views

76. Find the derivatives of the following functions :

(ax²+sin x) (p + q cos x)

131 Views

77. Find the derivatives of the following functions :

"<pre

120 Views

78. Find the derivatives of the following functions :

(x + sec x)(x - tan x)

104 Views

79. Find the derivatives of the following functions :

space space space space space space space space space space space space space space space space space space fraction numerator straight x over denominator 1 plus tan space straight x end fraction

96 Views

80.

Evaluate the following limits :

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

105 Views