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.

Find $left parenthesis straight a plus straight b right parenthesis to the power of 4 minus left parenthesis straight a minus straight b right parenthesis to the power of 4.$ then evaluate $space space left parenthesis square root of 3 plus square root of 2 right parenthesis to the power of 4 minus left parenthesis square root of 3 minus square root of 2 right parenthesis to the power of 4$

128 Views

12.

Find $left parenthesis straight x plus 1 right parenthesis to the power of 5 plus left parenthesis straight x minus 1 right parenthesis to the power of 5$ and hence evaluate $left parenthesis square root of 2 plus 1 right parenthesis to the power of 5 plus space left parenthesis square root of 2 minus 1 right parenthesis to the power of 5$

209 Views

13.

Simplify: $left parenthesis straight x plus 2 straight y right parenthesis to the power of 10 plus left parenthesis straight x minus 2 straight y right parenthesis to the power of 10$

115 Views

14. Show that 9ⁿ ^{+ 1} - 8n - 9 is divisible by 64, whenever n is a positive integer.

283 Views

15. Using Binomial Theorem, prove that 6ⁿ - 5n always leaves remainder 1 when divided by 25.

394 Views

16.
Find the value of $space space open parentheses straight a squared plus square root of straight a squared minus 1 end root close parentheses to the power of 4 plus open parentheses straight a squared minus square root of straight a squared minus 1 end root close parentheses to the power of 4$

Replace $<pre>uncaught exception: mkdir(): Permission denied (errno: 2) in /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php at line #56mkdir(): Permission denied in file: /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php line 56 #0 [internal function]: _hx_error_handler(2, 'mkdir(): Permis...', '/home/config_ad...', 56, Array) #1 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php(56): mkdir('/home/config_ad...', 493) #2 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/FolderTreeStorageAndCache.class.php(110): com_wiris_util_sys_Store->mkdirs() #3 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/RenderImpl.class.php(231): com_wiris_plugin_impl_FolderTreeStorageAndCache->codeDigest('mml=<math xmlns...') #4 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/TextServiceImpl.class.php(59): com_wiris_plugin_impl_RenderImpl->computeDigest(NULL, Array) #5 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/service.php(19): com_wiris_plugin_impl_TextServiceImpl->service('mathml2accessib...', Array) #6 {main}</pre>$
∴ $left parenthesis straight a squared plus square root of straight a squared minus 1 end root right parenthesis to the power of 4 plus left parenthesis straight a squared minus square root of straight a squared minus 1 right parenthesis end root to the power of 4 equals space left parenthesis straight x plus straight y right parenthesis to the power of 4 plus left parenthesis straight x minus straight y right parenthesis to the power of 4$
 $equals left square bracket straight C presuperscript 4 subscript 0 space straight x to the power of 4 straight y to the power of 0 plus straight C presuperscript 4 subscript 1 space straight x cubed straight y plus straight C presuperscript 4 subscript 2 space straight x squared straight y squared plus straight C presuperscript 4 subscript 3 space xy cubed plus straight C presuperscript 4 subscript 4 space straight x to the power of 0 straight y to the power of 4 right square bracket$
 $plus left square bracket straight C presuperscript 4 subscript 0 space end subscript straight x to the power of 4 straight y to the power of 0 minus straight C presuperscript 4 subscript 1 space straight x cubed straight y plus straight C presuperscript 4 subscript 2 space straight x squared straight y squared plus straight C presuperscript 4 subscript 3 space xy cubed space plus space straight C presuperscript 4 subscript 4 space end subscript straight x to the power of 0 straight y to the power of 4 right square bracket$
 $equals 2 space left square bracket straight C presuperscript 4 subscript 0 space straight x to the power of 4 straight y to the power of 0 plus straight C presuperscript 4 subscript 2 space straight x squared straight y squared plus space straight C presuperscript 4 subscript 4 space straight x to the power of 0 straight y to the power of 4 right square bracket$
 $equals space 2 space open square brackets straight x to the power of 4 plus 6 straight x squared straight y squared plus straight y to the power of 4 close square brackets$

 $equals space 2 open square brackets left parenthesis straight a squared right parenthesis to the power of 4 plus 6 left parenthesis straight a squared right parenthesis squared space left parenthesis square root of straight a squared minus 1 end root right parenthesis squared plus left parenthesis square root of straight a squared minus 1 right parenthesis end root to the power of 4 close square brackets$ [By replacing again x by a² and y by $square root of straight a squared minus 1 end root$ ]
 $<pre>uncaught exception: mkdir(): Permission denied (errno: 2) in /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php at line #56mkdir(): Permission denied in file: /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php line 56 #0 [internal function]: _hx_error_handler(2, 'mkdir(): Permis...', '/home/config_ad...', 56, Array) #1 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php(56): mkdir('/home/config_ad...', 493) #2 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/FolderTreeStorageAndCache.class.php(110): com_wiris_util_sys_Store->mkdirs() #3 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/RenderImpl.class.php(231): com_wiris_plugin_impl_FolderTreeStorageAndCache->codeDigest('mml=<math xmlns...') #4 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/TextServiceImpl.class.php(59): com_wiris_plugin_impl_RenderImpl->computeDigest(NULL, Array) #5 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/service.php(19): com_wiris_plugin_impl_TextServiceImpl->service('mathml2accessib...', Array) #6 {main}</pre>$
 $equals space 2 left square bracket straight a to the power of 8 plus 6 straight a to the power of 6 minus 6 straight a to the power of 4 plus straight a to the power of 4 minus 2 straight a squared plus 1 right square bracket$
 $equals 2 left square bracket straight a to the power of 8 plus 6 straight a to the power of 6 minus 5 straight a to the power of 4 minus 2 straight a squared plus 1 right square bracket$