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.

Complex Numbers and Quadratic Equations

Short Answer Type

71.

Find the modulus of the following complex numbers :

$space space space space fraction numerator 3 minus 4 straight i over denominator 4 minus 3 straight i end fraction$

107 Views

72.

Find the modulus of the following complex numbers :

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

111 Views

73.

Solve x²+ 3 = 0

127 Views

74.

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

135 Views

75.

Conver $straight pi over 12$ to degrees.

115 Views

76.

Write the complex number $space space space space space space space space fraction numerator straight i minus 1 over denominator cos begin display style straight pi over 3 end style plus space straight i space sin begin display style straight pi over 3 end style end fraction$ in the polar form.

119 Views

77.

Write the conjugate of z = – 3 – 21

129 Views

78.

Find the value of the following : $space space space space open parentheses 1 plus straight i close parentheses to the power of 4 open parentheses 1 plus 1 over straight i close parentheses to the power of 4$

133 Views

Multiple Choice Questions

79.
The sum of all real values of x satisfying the equation
$left parenthesis straight x squared minus 5 straight x space plus 5 right parenthesis to the power of straight x squared plus 4 straight x minus 60 space equals space 1 end exponent$ is:

3

-4

6

6

Given,

$left parenthesis straight x squared minus 5 straight x space plus 5 right parenthesis to the power of straight x squared plus 4 straight x minus 60 end exponent space equals space 1 clearly comma space this space is space possible space when straight I. space straight x squared space plus space 4 straight x minus 60 space equals space 0 space and space straight x squared minus 5 straight x space plus 5 space not equal to space 0 II. space straight x squared minus 5 straight x plus 5 space equals space 1 III. space straight x squared minus 5 straight x space plus 5 space equals space minus 1 space and space straight x squared plus 4 straight x minus 60 space equals space Even Case space straight I space when space straight x squared space plus space 4 space straight x minus 60 space equals space 0 comma space then straight x squared space plus space 10 space straight x space minus 6 straight x space minus 60 equals 0 rightwards double arrow space straight x left parenthesis straight x plus 10 right parenthesis minus 6 left parenthesis straight x plus 10 right parenthesis space equals space 0 rightwards double arrow left parenthesis straight x plus 10 right parenthesis left parenthesis straight x plus 6 right parenthesis space equals space 0 rightwards double arrow straight x space equals space minus space 10 space or space straight x equals space 6 Note space that comma space for space these space two space vaues space of space straight x comma space straight x squared minus 5 straight x space plus space 5 space not equal to 0 Case space II space when space straight x squared space minus 5 straight x space plus 5 space equals space 1 straight x squared space minus 5 straight x space plus 4 space equals space 0 straight x squared minus 4 straight x minus straight x space plus 4 equals 0 straight x left parenthesis straight x minus 4 right parenthesis minus 1 left parenthesis straight x minus 4 right parenthesis space equals 0 left parenthesis straight x minus 4 right parenthesis left parenthesis straight x minus 1 right parenthesis space equals 0 straight x equals space 4 space or space straight x space equals 1 Case space III space when space straight x squared minus 5 straight x space plus 5 space equals space minus 1 straight x squared minus 5 straight x space plus 5 space equals space minus 1 straight x squared minus 5 straight x space plus space 6 space equals space 0 rightwards double arrow space straight x squared minus 2 straight x minus 3 straight x space plus 6 space equals space 0 straight x left parenthesis straight x minus 2 right parenthesis minus 3 left parenthesis straight x minus 2 right parenthesis space equals space 0 left parenthesis straight x minus 2 right parenthesis left parenthesis straight x minus 3 right parenthesis space equals 0 straight x equals 2 space or space straight x space equals space 3 Now comma space when space straight x space equals space 2 comma space straight x to the power of 2 space end exponent plus 4 straight x minus 60 space equals space 4 plus 8 minus 60 equals negative 48 comma space which space is space an space interger when space straight x space equals space 3 comma space straight x squared plus space 4 straight x space minus 60 space equals space 9 space plus 12 minus 60 space equals space minus 39 which space is space not space an space even space interger. Thus comma space in space this space case comma space we space get space straight x space equals space 2 Hence comma space the space sum space of space all space real space values space of space straight x space equals space minus 10 plus 6 plus 4 plus 1 plus 2 space equals 3$

654 Views

80.

A complex number z is said to be unimodular, if |z|= 1. suppose z₁ and z₂ are complex numbers such that $fraction numerator straight z subscript 1 minus 2 straight z subscript 2 over denominator 2 minus straight z subscript 1 begin display style stack straight z subscript 2 with minus on top end style end fraction$ is unimodular and z₂ is not unimodular. Then, the point z₁ lies on a