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.

Cubes and Cube Roots

Short Answer Type

11.

Is 216 a perfect cube? What is the number whose cube is 216?

919 Views

Long Answer Type

12.

Find the smallest number by which each of the following numbers must be divided to obtain a perfect cube. (i) 81 (ii) 128 (iii) 135 (iv) 192 (v) 704

1360 Views

Short Answer Type

13. Parikshit makes a cuboid of plasticine of sides 5 cm, 2 cm, 5 cm. How many such cuboids will he need to form a cube?

765 Views

14.

Find the cube root of 1728.

2219 Views

15.

Fint the cube root of 27000 by prime factorisation.

593 Views

16. State true or false: for any integer m, m² < m³. Why?

297 Views

17. What is the smallest number by which 288 must be multiplied so that the product is a perfect cube?

1225 Views

18.

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

113 Views

19. Show that 0.001728 is the cube of a rational number. Find that rational number whose cube is 0.0017288.

We have

$space space space space 0.001728 space equals space 1728 over 1000000$

Now,
We haveNow,
∴

∴ $space space space space 1728 over 1000000 space equals space fraction numerator 2 cross times 2 cross times 2 cross times 2 cross times 2 cross times 2 cross times 3 cross times 3 cross times 3 over denominator 2 cross times 2 cross times 2 cross times 2 cross times 2 cross times 2 cross times 5 cross times 5 cross times 5 cross times 5 cross times 5 cross times 5 end fraction$

$space space space space equals space fraction numerator 3 cross times 3 cross times 3 over denominator 5 cross times 5 cross times 5 cross times 5 cross times 5 cross times 5 end fraction$

$space space equals fraction numerator 3 cubed over denominator 5 cubed cross times 5 cubed end fraction$

$space space space space space space space equals open parentheses fraction numerator 3 over denominator 5 cross times 5 end fraction close parentheses cubed$

∴ $space space space space space space space space space space space space space space cube root of 1728 over 1000000 end root equals space open parentheses fraction numerator 3 over denominator 5 cross times 5 end fraction close parentheses cubed$

$space space space space space space space rightwards double arrow space space space space space space space cube root of 1728 over 1000000 end root equals fraction numerator 3 over denominator 5 cross times 5 end fraction$

$rightwards double arrow space space space space space space cube root of 0.001728 end root space equals space 3 over 25$

Thus, 0.001728 is the cube of $space 3 over 25$ .

922 Views

20. The volume of a cubical box is 64 cm³. What is its side?

1037 Views