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.

Sequences and Series

Short Answer Type

51.

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

86 Views

52.

If a, b, c are in A.P., prove that $fraction numerator 1 over denominator square root of straight b plus square root of straight c end fraction comma space fraction numerator 1 over denominator square root of straight c plus square root of straight a end fraction comma space fraction numerator 1 over denominator square root of straight a plus square root of straight b space end root end fraction$ are also in A.P.

90 Views

53.
If $straight a squared comma space straight b squared comma space straight c squared$ are in A.P., then prove that $fraction numerator straight a over denominator straight b plus straight c end fraction comma space fraction numerator straight b over denominator straight c plus straight a end fraction comma space fraction numerator straight c over denominator straight a plus straight b end fraction$ are in A.P.

will be in A.P.

if

will be in A.P. (By adding 1 to each number)

if

will be in A.P.

if

will be in A.P. (By dividing each number a + b + c)

if

if (b - a) (b + a) = (c - b) (c + b)

if

are in A.P. which is true.

Hence,

are in A.P.

83 Views

54.

104 Views

55.

If $space space left parenthesis straight b minus straight c right parenthesis squared comma space left parenthesis straight c minus straight a right parenthesis squared comma space left parenthesis straight a minus straight b right parenthesis squared$ are in A.P., prove that $fraction numerator 1 over denominator straight b minus straight c end fraction comma space fraction numerator 1 over denominator straight c minus straight a end fraction comma space fraction numerator 1 over denominator straight a minus straight b end fraction$ are in A.P.

114 Views

56.

If a, b, c are in A.P. then prove that $left parenthesis straight a minus straight c right parenthesis squared space equals space 4 left parenthesis straight b squared minus ac right parenthesis$

75 Views

57.

If a, b, c are in A.P. then prove that

$straight a cubed plus 4 straight b cubed plus straight c cubed space equals space 3 straight b left parenthesis straight a squared plus straight c squared right parenthesis$

81 Views

58.

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