{"meta": {"penalty": 1.0, "totalm": 40.0, "correct": 2.0, "totalq": 20, "time": 1800, "sections": []}, "ENGLISH": {"ques": {"list": [{"opt": [{"t": " <em>\u03c0</em>/3\t<br/>", "ty": 5, "co": 1}, {"t": " <em>\u03c0</em>/4\t<br/>", "ty": 5}, {"t": " <em>\u03c0</em>/6\t<br/>", "ty": 5}, {"t": " None of the above", "ty": 1}], "q": {"t": " If  6cos 2<em> +</em>2cos<sup>2 </sup>(<em>/</em>2) + 2sin<sup>2</sup> = 0, 0 &lt;  &lt; /2<em> </em>then the value of <a id=\"MTBlankEqn\"></a><img src=\"http://13b1077a-caf5-4312-93e0-45f8411b9172.png\"/> is equal to\t<br/>", "ty": 5}, "so": {"t": "<p>Sol.</p><p><img alt=\"1\" src=\"http://0374ee29-21ab-48a6-8518-388c5233515a.png\"/><br/> <strong>Note: This question can be solved quickly by using SHORT TRICKS.</strong></p>", "ty": 5}, "qMapId": 7993, "id": 7993, "position": 1, "link": null, "neg": 1.0, "pos": 2.0}, {"opt": [{"t": "<img alt=\"Eqn1\" src=\"http://280c525c-ce24-40d7-affc-f632338fa769.png\"/> <br/>", "ty": 5}, {"t": "<img alt=\"Eqn2\" src=\"http://770e7407-a3e4-45f2-9688-da01eb5d2c26.png\"/> <br/>", "ty": 5}, {"t": " <img alt=\"Eqn3\" src=\"http://2997ec51-43dc-4e6d-b51f-0950c11ec68b.png\"/> <br/>", "ty": 5, "co": 1}, {"t": " <img alt=\"Eqn4\" src=\"http://83221ee1-fbcd-4c71-bc49-574d5698ed71.png\"/>", "ty": 5}], "q": {"t": " If<img alt=\"1\" src=\"http://3ec33d1b-f9ea-4a77-9758-cd2a1966175d.png\"/>, with  and  both in the fourth quadrant, the value of cos (<em> + </em>) is\t<p><br/></p>", "ty": 5}, "so": {"t": "<p>Sol.</p><p> <img alt=\"2\" src=\"http://92239874-2964-466b-bd59-9a0d4ef9553a.png\"/></p>", "ty": 5}, "qMapId": 7994, "id": 7994, "position": 2, "link": null, "neg": 1.0, "pos": 2.0}, {"opt": [{"t": " <img alt=\"Eqn5\" src=\"http://9007f53b-c241-4095-b565-db92e802163f.png\"/> <br/>", "ty": 5}, {"t": " <img alt=\"Eqn6\" src=\"http://3ed733a0-c0f9-4c1f-9291-26d876860843.png\"/><br/>", "ty": 5, "co": 1}, {"t": " <img alt=\"Eqn7\" src=\"http://9f087afa-2ea1-4b63-814b-142271a1c912.png\"/> <br/>", "ty": 5}, {"t": " <img alt=\"Eqn8\" src=\"http://596fe958-1eae-450a-bbe7-c5f83cf7887f.png\"/>", "ty": 5}], "q": {"t": " The value of sin 36 is \t<br/>", "ty": 5}, "so": {"t": "<p>Sol.</p><p><img alt=\"3\" src=\"http://78642b99-b8e6-4ae4-8550-104d9cbac648.png\"/></p>", "ty": 5}, "qMapId": 7995, "id": 7995, "position": 3, "link": null, "neg": 1.0, "pos": 2.0}, {"opt": [{"t": " 2cos 4<em>x</em> cos <em>x</em> <br/>", "ty": 5}, {"t": " 2sin 4<em>x</em> sin <em>x</em> <br/>", "ty": 5}, {"t": " 2sin 6<em>x</em> sin <em>x</em> <br/>", "ty": 5, "co": 1}, {"t": " 2cos 6<em>x</em> cos <em>x</em> ", "ty": 5}], "q": {"t": " Express (cos 5<em>x </em> cos7<em>x</em>) as a product of sines or cosines :\t<br/>", "ty": 5}, "so": {"t": "<p>Sol.</p><p><img alt=\"4\" src=\"http://689cb7b0-b47d-413f-ac4d-767e286f2607.png\"/></p>", "ty": 5}, "qMapId": 7996, "id": 7996, "position": 4, "link": null, "neg": 1.0, "pos": 2.0}, {"opt": [{"t": "\t\u2013 4/5 but not 4/5\t\t<br/>", "ty": 5}, {"t": "\t\u2013 4/5 or 4/5\t<br/>", "ty": 5, "co": 1}, {"t": "\t  4/5 but not \u2013 4/5 \t\t<br/>", "ty": 5}, {"t": "   None of the above\t", "ty": 1}], "q": {"t": " If  tan <em>\u03b8</em> = \u2013 4/3 , then sin <em>\u03b8</em> is\t<br/>", "ty": 5}, "so": {"t": "<p>Sol.</p><p><img alt=\"5\" src=\"http://77c84847-df38-4eea-ba5e-7eb9084f0c94.png\"/></p>", "ty": 5}, "qMapId": 7997, "id": 7997, "position": 5, "link": null, "neg": 1.0, "pos": 2.0}, {"opt": [{"t": "    0\t\t<br/>", "ty": 5}, {"t": "    1\t<br/>", "ty": 5, "co": 1}, {"t": " <img src=\"http://15f81dc8-89c2-44a2-94bd-81fdf83dfbc3.png\"/>1\t\t<br/>", "ty": 5}, {"t": "    2", "ty": 1}], "q": {"t": " If sin <em>x</em> + sin<sup>2 </sup><em>x</em> =1, then cos<sup>2 </sup><em>x</em> + cos<sup>4 </sup><em>x</em> is equal to   ", "ty": 5}, "so": {"t": "<p>Sol.</p><p><img alt=\"6\" src=\"http://6f38fbf3-7e6d-418b-a3d5-cdcd058557d4.png\"/></p>", "ty": 5}, "qMapId": 7998, "id": 7998, "position": 6, "link": null, "neg": 1.0, "pos": 2.0}, {"opt": [{"t": " <img alt=\"Eqn9\" src=\"http://90ed2fbb-e34f-4ed3-aa4c-5cd1ac4f994c.png\"/><br/>", "ty": 5, "co": 1}, {"t": " <img alt=\"Eqn10\" src=\"http://fc246fff-d9a6-4a33-a343-048d55d2e6cc.png\"/><br/>", "ty": 5}, {"t": " <img alt=\"Eqn11\" src=\"http://f210b441-7909-4703-a52d-faf42ff6a276.png\"/><br/>", "ty": 5}, {"t": "\tNone of the above", "ty": 1}], "q": {"t": " If <em> +  +  =</em> 2,  then<p><br/></p>", "ty": 5}, "so": {"t": "<p>Sol.</p><p><img alt=\"7\" src=\"http://cdfa2337-797a-460f-8c87-62afac366af7.png\"/><br/><strong> \t\tNote: This question can be solved quickly by using SHORT TRICKS.</strong></p>", "ty": 5}, "qMapId": 7999, "id": 7999, "position": 7, "link": null, "neg": 1.0, "pos": 2.0}, {"opt": [{"t": "\t1  <em>A </em> 2\t\t<br/>", "ty": 5}, {"t": "\t3/4  <em>A </em> 1\t<br/>", "ty": 5, "co": 1}, {"t": "\t13/16  <em>A </em> 1\t<br/>", "ty": 5}, {"t": "\t3/4  <em>A </em> 13/16<p> </p>", "ty": 5}], "q": {"t": " Given <em>A</em> = sin<sup>2</sup> + cos<sup>4</sup> , then for real value of <br/>", "ty": 5}, "so": {"t": "<p>Sol.</p><p><img alt=\"8\" src=\"http://2945abc5-4a36-4e90-a777-da3e72756f7b.png\"/><br/> <strong>Note: This question can be solved quickly by using SHORT TRICKS.</strong></p>", "ty": 5}, "qMapId": 8000, "id": 8000, "position": 8, "link": null, "neg": 1.0, "pos": 2.0}, {"opt": [{"t": "\t1/2\t\t<br/>", "ty": 5}, {"t": " <img alt=\"Eqn13\" src=\"http://284e64a9-94d7-460e-ba9f-ed947e17f9cc.png\"/> <br/>", "ty": 5}, {"t": "\t1/8\t\t<br/>", "ty": 5, "co": 1}, {"t": " <img alt=\"Eqn14\" src=\"http://acf22962-7961-4fbc-8e81-38c58be84acd.png\"/> ", "ty": 5}], "q": {"t": "<p> <img alt=\"Eqn12\" src=\"http://b2f8259e-54dd-4070-adbb-f364866aab88.png\"/>is equal to \t<br/></p>", "ty": 5}, "so": {"t": "<p>Sol.</p><p> <img alt=\"9\" src=\"http://a4088e5c-caea-4cc5-b93c-a8900f4389ad.png\"/><br/> <br/> <strong>Note: This question can be solved quickly by using SHORT TRICKS.</strong></p>", "ty": 5}, "qMapId": 8001, "id": 8001, "position": 9, "link": null, "neg": 1.0, "pos": 2.0}, {"opt": [{"t": "\t0\t\t<br/>", "ty": 5}, {"t": "\t1\t<br/>", "ty": 5, "co": 1}, {"t": "\t3\t\t<br/>", "ty": 5}, {"t": "\tSin 4 + cos 6\t", "ty": 1}], "q": {"t": " The expression <img alt=\"temp\" src=\"http://c4e754dd-4751-4d83-b327-067fa96319c3.png\"/>is equal to \t<br/>", "ty": 5}, "so": {"t": "<p>Sol.</p><p><strong><img alt=\"10\" src=\"http://ff61c484-65db-4fec-8b8b-e7ae4d4904dd.png\"/></strong></p><p><strong>\tNote: This question can be solved quickly by using SHORT TRICKS.</strong></p>", "ty": 5}, "qMapId": 8002, "id": 8002, "position": 10, "link": null, "neg": 1.0, "pos": 2.0}, {"opt": [{"t": "\t2\t\t<br/>", "ty": 5, "co": 1}, {"t": "\t2 sin 20/sin40<br/>", "ty": 5}, {"t": "\t4\t\t<br/>", "ty": 5}, {"t": "\t4 sin 20/sin40\t", "ty": 1}], "q": {"t": " The value of the expression <img alt=\"3\" src=\"http://43c05cb3-af4f-4724-b547-cef6f0b19339.png\"/>is equal to \t<br/>", "ty": 5}, "so": {"t": "<p>Sol.</p><p><img alt=\"11\" src=\"http://18370d73-8180-488f-b57e-a482da51b491.png\"/></p>", "ty": 5}, "qMapId": 8003, "id": 8003, "position": 11, "link": null, "neg": 1.0, "pos": 2.0}, {"opt": [{"t": "\t11\t\t<br/>", "ty": 5}, {"t": "\t12\t<br/>", "ty": 5}, {"t": "\t13\t\t<br/>", "ty": 5, "co": 1}, {"t": "\t14\t", "ty": 1}], "q": {"t": " 3(sin <em>x</em>  cos <em>x</em>)<sup>4</sup> + 6(sin <em>x</em> + cos <em>x</em>)<sup>2 </sup>+ 4(sin<sup>6</sup> <em>x</em> + cos<sup>6</sup> <em>x</em>) is equal to <br/>", "ty": 5}, "so": {"t": "<p>Sol.</p><p><img alt=\"12\" src=\"http://8809f210-d849-4922-8fad-963d9cb9e59d.png\"/><br/><strong>Note: This question can be solved quickly by using SHORT TRICKS.</strong></p>", "ty": 5}, "qMapId": 8004, "id": 8004, "position": 12, "link": null, "neg": 1.0, "pos": 2.0}, {"opt": [{"t": "\tsin 15\t\t<br/>", "ty": 5}, {"t": "\tcos 15\t<br/>", "ty": 5}, {"t": "\tsin 15 cos 15\t\t<br/>", "ty": 5}, {"t": "\tsin 15cos 75\t", "ty": 1, "co": 1}], "q": {"t": " Which of the following numbers is rational? \t<br/>", "ty": 5}, "so": {"t": "<p>Sol.</p><p> <img alt=\"13\" src=\"http://cb098739-ac1d-4d1b-896f-212f36c04ce5.png\"/></p>", "ty": 5}, "qMapId": 8005, "id": 8005, "position": 13, "link": null, "neg": 1.0, "pos": 2.0}, {"opt": [{"t": "\t2 (tan  + tan )\t\t<br/>", "ty": 5}, {"t": "\ttan  + tan \t<br/>", "ty": 5}, {"t": "\ttan  + 2tan \t\t<br/>", "ty": 5, "co": 1}, {"t": "\t2 tan  + tan \t", "ty": 1}], "q": {"t": " If  <img alt=\"Eqn15\" src=\"http://6853721d-d164-42d6-8ada-037b52a1e627.png\"/> and <em> +  = </em>, then tan  equals \t<br/>", "ty": 5}, "so": {"t": "<p>Sol.</p><p><img alt=\"14\" src=\"http://bdf9c48a-29f6-42f6-a683-107e4e969c23.png\"/></p>", "ty": 5}, "qMapId": 8006, "id": 8006, "position": 14, "link": null, "neg": 1.0, "pos": 2.0}, {"opt": [{"t": " <img alt=\"Eqn17\" src=\"http://55163e47-cc2f-4a45-bff7-16843f8c2a73.png\"/> <br/>", "ty": 5}, {"t": " <img alt=\"Eqn18\" src=\"http://6db39cba-9708-4b7d-a323-05f1267b8cdc.png\"/> <br/>", "ty": 5, "co": 1}, {"t": " <img alt=\"Eqn19\" src=\"http://aa5757a3-2c3d-4915-8532-7281df20a4cf.png\"/> <br/>", "ty": 5}, {"t": " <img alt=\"Eqn20\" src=\"http://097b6ceb-52da-4798-bf61-18895fb58f57.png\"/> ", "ty": 5}], "q": {"t": " Given both <em> </em>and  are acute angles <img alt=\"Eqn16\" src=\"http://b230cf8f-3829-4046-b9aa-e062e335dfd9.png\"/>then the value of <em> + </em> belongs to \t<br/>", "ty": 5}, "so": {"t": "<p>Sol.</p><p><img alt=\"15\" src=\"http://0c7fdee1-c6b9-4f52-8b4a-764d9b17c918.png\"/><br/><strong> \tNote: This question can be solved quickly by using SHORT TRICKS.</strong></p>", "ty": 5}, "qMapId": 8007, "id": 8007, "position": 15, "link": null, "neg": 1.0, "pos": 2.0}, {"opt": [{"t": "\t/3\t\t<br/>", "ty": 5}, {"t": "\t/4\t<br/>", "ty": 5, "co": 1}, {"t": "\t/6\t\t<br/>", "ty": 5}, {"t": "\tNone of the above ", "ty": 1}], "q": {"t": " If <img alt=\"Eqn21\" src=\"http://c3fae4e0-c5f1-43ae-9731-0c37f5f2c970.png\"/>then <em> +  =</em> <br/>", "ty": 5}, "so": {"t": "<p>Sol.</p><p><img alt=\"16\" src=\"http://b97946bf-c239-4c49-8701-a33a420388b1.png\"/> <br/> <strong>Note: This question can be solved quickly by using SHORT TRICKS.</strong></p>", "ty": 5}, "qMapId": 8008, "id": 8008, "position": 16, "link": null, "neg": 1.0, "pos": 2.0}, {"opt": [{"t": "\t\u2013<img alt=\"23\" src=\"http://7103a979-7ae4-4926-b089-62a967b5a647.png\"/> <br/>", "ty": 5, "co": 1}, {"t": " <img alt=\"24\" src=\"http://5cda8c31-9a36-4d94-b41c-7493d37fdf30.png\"/> <br/>", "ty": 5}, {"t": " <img alt=\"25\" src=\"http://57b7f076-ad5c-43c7-a270-e785a3bf4a49.png\"/> <br/>", "ty": 5}, {"t": "\t\u2013.<img alt=\"26\" src=\"http://5f621042-fc6d-4637-9f09-7aa117b9cb2a.png\"/>", "ty": 5}], "q": {"t": " Let ,   be such that  &lt;     &lt; 3. If  <img alt=\"4\" src=\"http://574b9b13-837a-4317-8132-f5f41aa2c063.png\"/>, then the value of <img alt=\"Eqn22\" src=\"http://ef0be274-63e2-4746-9392-d7cd41ceeef3.png\"/>is: \t<br/>", "ty": 5}, "so": {"t": "<p>Sol.</p><p><img alt=\"17\" src=\"http://d5a082cd-53ec-4f95-99ee-c2f7f23ac619.png\"/></p>", "ty": 5}, "qMapId": 8009, "id": 8009, "position": 17, "link": null, "neg": 1.0, "pos": 2.0}, {"opt": [{"t": "\t  1\t\t<br/>", "ty": 5}, {"t": "\t\u20131\t<br/>", "ty": 5}, {"t": "\tzero\t\t<br/>", "ty": 5}, {"t": "\tNone of the above.\t", "ty": 1, "co": 1}], "q": {"t": " If sin (<em> + </em>) = 1, sin (<em> </em>) = 1/2 then, tan (<em> + </em>2)  tan (2<em> + </em>) is equal to\t<br/>", "ty": 5}, "so": {"t": "<p>Sol.</p><p><img alt=\"18\" src=\"http://2587a2e9-31ec-4622-af39-080497385701.png\"/> <br/><strong>Note: This question can be solved quickly by using SHORT TRICKS.</strong></p>", "ty": 5}, "qMapId": 8010, "id": 8010, "position": 18, "link": null, "neg": 1.0, "pos": 2.0}, {"opt": [{"t": " <em>y</em> = 0\t\t<br/>", "ty": 5}, {"t": " <em>y</em>  2\t<br/>", "ty": 5}, {"t": " <em>y</em>   2\t\t<br/>", "ty": 5}, {"t": " <em>y</em>  2.\t", "ty": 5, "co": 1}], "q": {"t": " If <em>y</em> = sin<sup>2 </sup><em> </em>+ cosec<sup>2 </sup>,   0, then \t<br/>", "ty": 5}, "so": {"t": "<p>Sol.</p><p> <img alt=\"19\" src=\"http://1b3d5e91-8b8a-4624-adc7-9bb829e86fd7.png\"/><br/> <strong>Note: This question can be solved quickly by using SHORT TRICKS.</strong></p>", "ty": 5}, "qMapId": 8011, "id": 8011, "position": 19, "link": null, "neg": 1.0, "pos": 2.0}, {"opt": [{"t": "\t5\t\t<br/>", "ty": 5}, {"t": "\t9<br/>", "ty": 5}, {"t": "\t7\t\t<br/>", "ty": 5}, {"t": "\t0\t<br/> <p><strong></strong></p>", "ty": 5, "co": 1}], "q": {"t": " 3cos <em>x</em> + 4sin <em>x</em> + 5 has minimum value :\t<br/>", "ty": 5}, "so": {"t": "<p>Sol.</p><p><img alt=\"20\" src=\"http://0257ae5f-0520-4839-85ee-5eca580ed4b1.png\"/><br/> <strong>Note: This question can be solved quickly by using SHORT TRICKS.</strong></p>", "ty": 5}, "qMapId": 8012, "id": 8012, "position": 20, "link": null, "neg": 1.0, "pos": 2.0}]}, "desc": "<p><img alt=\"\" src=\"https://s3-ap-southeast-1.amazonaws.com/achieverspoint/staging/mca/english/quiz//home/ubuntu/apps/heyman/current/uploads/2017/11/28/synonyms_kX8GGs0.jpg\" style=\"height:800px; width:619px\"/>Triginometry</p>\n"}}