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.

Relations and Functions

Short Answer Type

11. Let A = {–1, 1}, B = {2, 3}, C = {3, 5} be subsets of real numbers.

n(A X A X A)

109 Views

12. Let A = {1,2, 3, 4}

space space space space space space space space space space space straight S space equals space left curly bracket left parenthesis straight a comma space straight b right parenthesis space colon space straight a element of straight A comma space straight b space element of space straight A comma space straight a space divides space straight b right curly bracket

space space space space space space space space straight B space equals space left curly bracket straight x space colon space straight x element of straight A comma space straight x space is space straight a space prime right curly bracket

Write (i) S explicity, (ii) B explicity, (iii) S x B

99 Views

13.

If A × B = {(a, x),(a , y), (b, x), (b, y)}. Find A and B.

189 Views

14.

The Cartesian product A × A has 9 elements among which are found (–1, 0) and (0,1). Find the set A and the remaining elements of A × A.

166 Views

15. Let A = {I, 2, 3}, B = {2, 3, 4} and C = {4, 5}. Verify that :

<pre>uncaught exception: <b>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</b><br /><br />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<br />#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>

100 Views

16. Let A = {I, 2, 3}, B = {2, 3, 4} and C = {4, 5}. Verify that :

$space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space straight A cross times open parentheses straight B union straight C close parentheses equals left parenthesis straight A cross times straight B right parenthesis union left parenthesis straight A cross times straight C right parenthesis$

space space space space space space space space space straight B union straight C space equals space left curly bracket 2 comma space 3 comma space 4 right curly bracket union left curly bracket 4 comma space 5 right curly bracket space equals thin space left curly bracket 2 comma space 3 comma space 4 comma space 5 right curly bracket

space space space space space space space space space space space space space space space space space space space straight A cross times left parenthesis straight B union straight C right parenthesis space equals space left curly bracket 1 comma space 2 comma space 3 right curly bracket comma space left curly bracket 2 comma space 3 comma space 4 comma space 5 right curly bracket

= {(1, 2), (1, 3), |(1, 4), (1, 5), (2, 2), (2, 3), (2, 4), (2, 5), (3, 2), (3, 3), (3, 4), (3, 5)} ...(ii)

From (ii) and (iii), we have

space space space space space left parenthesis straight A cross times straight B right parenthesis union left parenthesis straight A cross times straight C right parenthesis space

= {(1, 2), (1, 3), (1, 4), (1, 5), (2, 2), (2, 3), (2, 4), (2, 5), (3, 2), (3, 3), (3, 4), (3, 5)} .....(ii)

Hence, from (i) and (ii)

space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space straight A cross times left parenthesis straight B union straight C right parenthesis equals left parenthesis straight A cross times straight A right parenthesis union open parentheses AXC close parentheses

117 Views

17. Find the values of x and y when

(2x, x+y) = (6, 2)

94 Views

18.

If A = {a, b, c} and B = {p, q}, then find :

A x B

91 Views

19. Let A = {I, 2, 3}, B = {2, 3, 4} and C = {4, 5}. Verify that :

A x (B - C) = (A x B) - (A x C)

86 Views

20.

Let A = {1, 2}, B = {1, 2, 3, 4}, C={5, 6} and D = {5, 6, 7, 8}. Verify that A x C is a proper subset of B x D.

88 Views