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

61.

Find the domain of the function $space space space space space space space space space straight f left parenthesis straight x right parenthesis space equals space fraction numerator straight x squared plus 3 straight x plus 5 over denominator straight x squared plus straight x minus 6 end fraction$

116 Views

62.

space space space space space space space space Let space straight f space equals space open curly brackets open parentheses straight x comma fraction numerator straight x squared over denominator 1 plus straight x squared end fraction close parentheses space colon space straight x space bold R close curly brackets

be a function from R into Detemine the range of f.

110 Views

63. Find the range of the following functions :

(i) f(x) = x²-4x + 6,

space space space straight x element of straight R

<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>

124 Views

64. Find the range of the following functions :

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 f left parenthesis straight x right parenthesis space equals space 1 half straight x comma space space straight x element of straight R

116 Views

65.

If the following f : R $rightwards arrow$ f is defined by :

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

(i) f(2) (ii) f(4) (iii) f(-1) (iv) f (-3)

131 Views

66.

Let f(x) = 5x +3 and g(x) = $space space space space space space space square root of straight x minus 1 end root comma space straight x element of straight R comma space straight x greater or equal than 1.$ Find (i) (f+g)(x) (ii) (f-g)(x) (iii)

(fg) (x) $space space space space space space space space space space space space space space left parenthesis iv right parenthesis space space space open parentheses straight f over straight g close parentheses left parenthesis straight x right parenthesis space space space space space space space space space space space space space space left parenthesis straight v right parenthesis space open parentheses straight g over straight f close parentheses left parenthesis straight x right parenthesis$

142 Views

67.

Let f and g be two functions defined by f(x) = $space space space space space space space space square root of straight x minus 1 end root space and space straight g left parenthesis straight x right parenthesis space equals space square root of 4 minus straight x squared end root$

find (i) f +g (ii) g + f (iii) f - g (iv) g - f (v) gg (vi) gf

106 Views

68.

The relation f is defined by $space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space straight f left parenthesis straight x right parenthesis equals space open curly brackets table attributes columnalign left columnspacing 1.4ex end attributes row cell straight x cubed comma end cell cell 0 less or equal than straight x less or equal than 3 end cell row cell 9 straight x comma end cell cell 3 less or equal than straight x less or equal than 7 end cell end table close$

and relation g is defined by $space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space straight g left parenthesis straight x right parenthesis equals space open curly brackets table attributes columnalign left columnspacing 1.4ex end attributes row cell straight x cubed comma end cell cell 0 less or equal than straight x less or equal than 3 end cell row cell 9 straight x comma end cell cell 3 less or equal than straight x less or equal than 7 end cell end table close$

Explain, why f is a function and g is not.

131 Views

Multiple Choice Questions

69.
If the function g(x) = $open curly brackets table attributes columnalign left end attributes row cell straight k square root of straight x plus 1 end root comma space space 0 space less or equal than straight x space less or equal than 3 end cell row cell mx plus 2 space comma space 3 space less than straight x less or equal than 5 end cell end table close$ is differntiable, then the value of k+m is

2

16/5

10/3

10/3

Since, g(x) is differentiable ⇒ g(x) must be continuous.
therefore, $straight g space left parenthesis straight x right parenthesis space equals space open curly brackets table attributes columnalign left end attributes row cell straight k square root of straight x plus 1 end root comma space space space 0 less or equal than straight x less or equal than 3 end cell row cell mx plus 2 comma space space space space space space 3 less than space straight x less or equal than 5 end cell end table close$
At x =3, RHL = 3m+2
and at x = 3, LHL= 2k
therefore, 2k = 3m + 2 ... (i)
Also, g'(x) = $open curly brackets table attributes columnalign left end attributes row cell fraction numerator straight k over denominator 2 square root of straight x plus 1 end root end fraction space comma space 0 less or equal than straight x less or equal than 3 end cell row cell straight m space space space space space space space space space space space space space space comma space 3 less than straight x less or equal than 5 end cell end table close$
therefore, L{g'(3)} = k/4 and R{g'(3)} = m
⇒ k/4 = m i.e, k = 4m ..... (ii)
On solving eqs (i) and (ii), we get
k = 8/5, m =2/5
⇒ k+m =2

379 Views

70.

If a ε R and the equation - 3(x-[x]2 + 2(x-[x] +a² = 0(where,[x] denotes the greatest integer ≤ x) has no integral solution, then all possible value of lie in the interval

(-1,0) ∪ (0,1)
(1,2)
(-2,-1)
(-∞,-2) ∪ (2, ∞)

182 Views

Previous Year Papers

Test Series

Test Yourself

Short Answer Type

Multiple Choice Questions

69. If the function g(x) = is differntiable, then the value of k+m is 2 16/5 10/3 10/3