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

111. If a, b, c, d are in GP., show that (a² + b² + c²) (b² + c² + d²) = (ab + bc + cd)²

135 Views

Long Answer Type

112.

If a, b, c are in G.P. and x, y are the arithmetic means of a, b and b, c respectively,

then prove that $straight a over straight x plus straight c over straight y equals 2$ and $space space 1 over straight x plus 1 over straight y equals 2 over straight b$

171 Views

Short Answer Type

113.

If a, b, c are in A.P. and x,y,z are in G.P., show that

$straight x to the power of straight b minus straight c end exponent. space straight y to the power of straight c minus straight a end exponent. space straight z to the power of straight a minus straight b end exponent space equals space 1$

138 Views

114. Find a GP. for which sum of first two terms is –4 and fifth term is 4 times the 3rd term.

146 Views

115. If A.M. and G.M. of roots of a quadratic equation are 8 and 5 respectively, then obtain the quadratic equation.

153 Views

Long Answer Type

116. If a and b are roots of x² – 3x+p = 0 and c, d are roots of x² – 12x + q = 0 where a, b, c, d form a GP., prove that (q + p) : (q – p) = 17 : 15

265 Views

117. Find four numbers in GP. whose sum is 85 and product is 4096.

477 Views

Short Answer Type

118. Find the sum of n terms of the series whose nth term is given by

straight n squared plus 2 to the power of straight n

136 Views

Long Answer Type

119.
Insert 5 G.M.'s between $32 over 9 space and space 81 over 2$

Let $<pre>uncaught exception: mkdir(): Permission denied (errno: 2) in /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php at line #56mkdir(): Permission denied in file: /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php line 56 #0 [internal function]: _hx_error_handler(2, 'mkdir(): Permis...', '/home/config_ad...', 56, Array) #1 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php(56): mkdir('/home/config_ad...', 493) #2 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/FolderTreeStorageAndCache.class.php(110): com_wiris_util_sys_Store->mkdirs() #3 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/RenderImpl.class.php(231): com_wiris_plugin_impl_FolderTreeStorageAndCache->codeDigest('mml=<math xmlns...') #4 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/TextServiceImpl.class.php(59): com_wiris_plugin_impl_RenderImpl->computeDigest(NULL, Array) #5 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/service.php(19): com_wiris_plugin_impl_TextServiceImpl->service('mathml2accessib...', Array) #6 {main}</pre>$ be five G.M.'s between $32 over 9$ and $81 over 2$

∴ $32 over 9 comma space straight G subscript 1 comma space straight G subscript 2 comma space straight G subscript 3 comma space straight G subscript 4 comma space straight G subscript 5 comma space 81 over 2$ are in G.P.

Here, $straight a space equals space 32 over 9 comma$ Let r be the common ratio

Now, $straight t subscript 7 space equals space 81 over 2 space rightwards double arrow space ar to the power of 7 minus 1 end exponent space equals space 81 over 2 space rightwards double arrow space 32 over 9 straight r to the power of 6 space equals space 81 over 2 space rightwards double arrow space straight r to the power of 6 space equals space 729 over 64 space rightwards double arrow space straight r to the power of 6 space equals space open parentheses 3 over 2 close parentheses to the power of 6 space rightwards double arrow space straight r space equals space plus-or-minus 3 over 2$

When r = $3 over 2 comma$ $straight a space equals space 32 over 9 comma$ then

$straight G subscript 1 space equals space straight t subscript 2 space equals space ar space equals space 32 over 9.3 over 2 space equals space 16 over 3$

 $straight G subscript 2 space equals space straight t subscript 3 space equals space ar squared space equals space 32 over 9 open parentheses 3 over 2 close parentheses squared space equals space 32 over 9.9 over 4 space equals space 8$

 $straight G subscript 3 space equals space straight t subscript 4 equals ar cubed space equals space 32 over 9 open parentheses 3 over 2 close parentheses cubed space equals space 32 over 9.27 over 8 equals 12$

$straight G subscript 4 space equals space straight t subscript 5 space equals ar to the power of 4 space equals space 32 over 9 open parentheses 3 over 2 close parentheses to the power of 4 space equals space 32 over 9.81 over 16 space equals space 18$

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

When $straight r equals fraction numerator negative 3 over denominator 2 end fraction comma space space space straight a space equals space 32 over 9 comma$ then

 $straight G subscript 1 space equals space straight t subscript 2 space equals space ar space equals space 32 over 9 open parentheses fraction numerator negative 3 over denominator 2 end fraction close parentheses space equals space fraction numerator negative 16 over denominator 3 end fraction$

$straight G subscript 2 space equals space straight t subscript 3 space equals space ar squared space equals space 32 over 9 open parentheses 3 over 2 close parentheses squared space equals space 32 over 9. space 9 over 4 space equals space 8$

$straight G subscript 3 space equals space straight t subscript 4 space equals space ar cubed space equals space 32 over 9 open parentheses fraction numerator negative 3 over denominator 2 end fraction close parentheses cubed space equals space 32 over 9 open parentheses fraction numerator negative 27 over denominator 8 end fraction close parentheses space equals space minus 12$

$straight G subscript 4 space equals space straight t subscript 5 space equals space ar to the power of 4 space equals space 32 over 9 open parentheses fraction numerator negative 3 over denominator 2 end fraction close parentheses to the power of 4 space equals space 32 over 9 open parentheses 81 over 16 close parentheses space equals space 18$

 $space space space straight G subscript 5 space equals space straight t subscript 6 space equals space ar to the power of 5 space equals space 32 over 9 open parentheses fraction numerator negative 3 over denominator 2 end fraction close parentheses to the power of 5 space equals space 32 over 9 open parentheses fraction numerator negative 243 over denominator 32 end fraction close parentheses space equals space minus 27$