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.

Application of Derivatives

Name: Zigya - For The Curious Learner
Rating: 4.4 (740 reviews)

Long Answer Type

261.

Find the maximum and minimum value of x + sin 2 x on $left square bracket 0 comma space 2 straight pi right square bracket$ .

75 Views

Short Answer Type

262.

Find both the maximum value and the minimum value of
3x⁴ – 8x³ + 12x² – 48x + 25

90 Views

263. It is given that at x = 1, function x⁴ – 62x² + ax + 9 attains its maximum value, on the interval [0, 2], Find the value of a.

88 Views

Long Answer Type

264.

straight y space equals space fraction numerator ax minus straight b over denominator left parenthesis straight x minus 1 right parenthesis thin space left parenthesis straight x minus 4 right parenthesis end fraction

has a turning point at P(2, -1). Find the values of a and b and show that y is maximum at P.

74 Views

265. If y = a log | x | + bx² + x has its extremum values at x = – 1 and x = 2, find the values of a and b. Prove that these extrema are maximum.

74 Views

Short Answer Type

266.

Find the maximum and minimum values of $fraction numerator log space straight x over denominator straight x end fraction space in space 0 less than straight x less than infinity$ .

74 Views

Long Answer Type

267.
Find the shortest distance of the point (0, c) from the parabola y = x² , where 0 ≤ c ≤ 5.

Let x be the distance between (0, c) and any point (x, y) on the parabola y =x^2. $therefore space space space space space straight s space equals space square root of left parenthesis straight x minus 0 right parenthesis squared plus left parenthesis straight y minus straight c right parenthesis squared end root space equals space square root of straight x squared plus left parenthesis straight y minus straight c right parenthesis squared end root rightwards double arrow space space space straight s space equals space square root of straight y plus left parenthesis straight y minus straight c right parenthesis squared end root 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 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 space space space space space space space space space space space space space space space space space space space space space space open square brackets because space space straight y space equals straight x squared close square brackets rightwards double arrow space space space space ds over dy space equals space fraction numerator 1 over denominator 2 square root of straight y plus left parenthesis straight y minus straight c right parenthesis squared end root end fraction left square bracket 1 plus 2 space left parenthesis straight y minus straight c right parenthesis right square bracket space equals space fraction numerator 2 straight y plus left parenthesis 1 minus 2 straight c right parenthesis over denominator 2 square root of straight y plus left parenthesis straight y minus straight c right parenthesis squared end root end fraction space space space space space space space ds over dy space equals space 0 space space space space space space space rightwards double arrow space space space space space 2 straight y left parenthesis 1 minus 2 straight c right parenthesis space equals space 0 space space space space space space space space space rightwards double arrow space straight y space equals space straight c minus 1 half space space space space space$

$When space straight y thin space less than space straight c minus 1 half space slightly comma space ds over dy space equals space minus ve and space when space straight y greater than straight c space minus 1 half space space slightly comma space space space space ds over dy space equals space plus ve therefore space space space space space space at space space straight y space equals space straight c minus 1 half comma space space ds over dy space changes space from space minus ve space to space ve therefore space space space space space straight s space is space minimum space at space straight y space equals space straight c minus 1 half.$

$and space minimum space value space of space straight s space equals space square root of open parentheses straight c minus 1 half close parentheses space plus space open parentheses straight c minus 1 half minus straight c close parentheses squared end root space equals space square root of straight c minus 1 half plus 1 fourth end root$
$equals square root of straight c minus 1 fourth end root space equals space square root of fraction numerator 4 straight c minus 1 over denominator 4 end fraction end root space equals fraction numerator space square root of 4 straight c minus 1 end root over denominator 2 end fraction.$

160 Views

Short Answer Type

268. An Apache helicopter of enemy is flying along the curve given by y = x² + 7. A soldier, placed at (3. 7), wants to shoot down the helicopter when it is nearest to him. Find the nearest distance.

139 Views

Multiple Choice Questions

269.

For all real values of x, the minimum value of $fraction numerator 1 minus straight x plus straight x squared over denominator 1 plus straight x plus straight x squared end fraction$ is

85 Views

270.

The maximum value of $open square brackets straight x left parenthesis straight x minus 1 right parenthesis space plus space 1 close square brackets to the power of 1 third end exponent comma space space space 0 space less or equal than space straight x space less or equal than space 1$ is

$<pre>uncaught exception: Http Error #404 in file: /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/HttpImpl.class.php line 61 #0 [internal function]: com_wiris_plugin_impl_HttpImpl_0(Object(com_wiris_plugin_impl_HttpImpl), NULL, 'http://www.wiri...', 'Http Error #404') #1 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/php/Boot.class.php(769): call_user_func_array('com_wiris_plugi...', Array) #2 [internal function]: _hx_lambda->execute('Http Error #404') #3 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/haxe/Http.class.php(532): call_user_func_array(Array, Array) #4 [internal function]: haxe_Http_5(true, Object(com_wiris_plugin_impl_HttpImpl), Object(com_wiris_plugin_impl_HttpImpl), Array, Object(haxe_io_BytesOutput), true, 'Http Error #404') #5 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/php/Boot.class.php(769): call_user_func_array('haxe_Http_5', Array) #6 [internal function]: _hx_lambda->execute('Http Error #404') #7 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/HttpImpl.class.php(27): call_user_func_array(Array, Array) #8 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/haxe/Http.class.php(444): com_wiris_plugin_impl_HttpImpl->onError('Http Error #404') #9 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/haxe/Http.class.php(458): haxe_Http->customRequest(true, Object(haxe_io_BytesOutput), NULL, NULL) #10 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/HttpImpl.class.php(40): haxe_Http->request(true) #11 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/TextServiceImpl.class.php(80): com_wiris_plugin_impl_HttpImpl->request(true) #12 /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) #13 {main}</pre>$
$1 half$
1
1