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

61.

The fourth term of a GP. is 27 and the 7th term is 729, find the GP.

389 Views

62.

The seventh term of a GP. is 8 times the fourth term and 5th term is 48. Find the GP.

208 Views

63.

If the GP.’s 5,10, 20, .......and 1280, 640, 320, ......have their nth terms equal, find the value of n.

387 Views

64.

The third term of a GP. is 4. Find the product of its first five terms.

812 Views

65.
The 5th, 8th and 11th terms of a GP. are p, q and s respectively. Show that q² = ps.

Let a be the first term and r be the common ratio

 $straight t subscript 5 space equals space straight p space rightwards double arrow space ar to the power of 5 minus 1 end exponent space equals space straight p space rightwards double arrow space ar to the power of 4 space equals space straight p$

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

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

Now, $space space straight q squared space equals space left parenthesis ar to the power of 7 right parenthesis squared space equals space straight a squared straight r to the power of 14$ ...(i)

 $ps space equals space left parenthesis ar to the power of 4 right parenthesis space left parenthesis ar to the power of 10 right parenthesis space equals straight a squared straight r to the power of 14$ ...(ii)

From (i) and (ii), we have

 $straight q squared space equals space ps$

115 Views

66.

Find all the sequences which are simultaneously in A.P. and GP.

343 Views

67.

In a finite GP. the product of the terms equidistant from the beginning and the end is always same and equal to the product of first and last term.

140 Views

68.

If the first and the nth terms of a GP. are a and b respectively and if P is the product of first n terms, prove that P² = (ab)ⁿ.

107 Views

Long Answer Type

69.

If $fraction numerator straight a plus bx over denominator straight a minus bx end fraction space equals space fraction numerator straight b plus cx over denominator straight b minus cx end fraction space equals space fraction numerator straight c plus dx over denominator straight c minus dx end fraction$ $left parenthesis straight x not equal to 0 right parenthesis comma space$ show that a, b, c, d are in G.P.