{"meta": {"penalty": 1.0, "totalm": 20.0, "correct": 1.0, "totalq": 20, "time": 600, "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://0bcb78b1-0337-4a09-ba44-5b7cb116be21.png\"/> is equal to\t<br/>", "ty": 5}, "so": {"t": "<p>Sol.</p><p><img alt=\"1\" src=\"http://a3b10b37-948a-4cb7-8ba4-f1322888f045.png\"/><br/> <strong>Note: This question can be solved quickly by using SHORT TRICKS.</strong></p>", "ty": 5}, "qMapId": 7933, "id": 7933, "position": 1, "link": null, "neg": 1.0, "pos": 1.0}, {"opt": [{"t": "<img alt=\"Eqn1\" src=\"http://57231792-7925-4a35-b2ef-a41b0001b6b9.png\"/> <br/>", "ty": 5}, {"t": "<img alt=\"Eqn2\" src=\"http://42688f7e-a4d8-4106-a7bc-01ba747993e2.png\"/> <br/>", "ty": 5}, {"t": " <img alt=\"Eqn3\" src=\"http://3f36fc44-7580-45bf-a7e4-d4bda9fcf30f.png\"/> <br/>", "ty": 5, "co": 1}, {"t": " <img alt=\"Eqn4\" src=\"http://8033fa79-34ea-4c1c-b05e-5a2a7f428e5c.png\"/>", "ty": 5}], "q": {"t": " If<img alt=\"1\" src=\"http://b51dba59-0e62-4ae6-a558-e171811d87bf.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://09784e4e-9f1d-4b9b-8ffe-7e155333484e.png\"/></p>", "ty": 5}, "qMapId": 7934, "id": 7934, "position": 2, "link": null, "neg": 1.0, "pos": 1.0}, {"opt": [{"t": " <img alt=\"Eqn5\" src=\"http://2b407add-4f30-4e3b-8f26-03e9666e7c6f.png\"/> <br/>", "ty": 5}, {"t": " <img alt=\"Eqn6\" src=\"http://990e90bb-dcda-4a3a-be03-8a9c0c85b160.png\"/><br/>", "ty": 5, "co": 1}, {"t": " <img alt=\"Eqn7\" src=\"http://4721eb79-6178-4119-aa12-b1d82196f55a.png\"/> <br/>", "ty": 5}, {"t": " <img alt=\"Eqn8\" src=\"http://1e6c5160-d69d-4531-b0b6-919a15d1c995.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://25744b6d-da13-4927-ba2e-c1776abf88de.png\"/></p>", "ty": 5}, "qMapId": 7935, "id": 7935, "position": 3, "link": null, "neg": 1.0, "pos": 1.0}, {"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://132654cb-67f3-4871-9877-392705934eba.png\"/></p>", "ty": 5}, "qMapId": 7936, "id": 7936, "position": 4, "link": null, "neg": 1.0, "pos": 1.0}, {"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://f3e2edc1-8761-43a1-a499-cbce147e3261.png\"/></p>", "ty": 5}, "qMapId": 7937, "id": 7937, "position": 5, "link": null, "neg": 1.0, "pos": 1.0}, {"opt": [{"t": "    0\t\t<br/>", "ty": 5}, {"t": "    1\t<br/>", "ty": 5, "co": 1}, {"t": " <img src=\"http://b08eb04c-f6e5-43d1-bd46-1d254df709e0.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://73d95296-2625-4169-b5ae-656809822535.png\"/></p>", "ty": 5}, "qMapId": 7938, "id": 7938, "position": 6, "link": null, "neg": 1.0, "pos": 1.0}, {"opt": [{"t": " <img alt=\"Eqn9\" src=\"http://41887ab1-42ab-4064-a6fd-4691e4ff652e.png\"/><br/>", "ty": 5, "co": 1}, {"t": " <img alt=\"Eqn10\" src=\"http://1e89da43-c5b1-450c-b989-8f74e1551ac1.png\"/><br/>", "ty": 5}, {"t": " <img alt=\"Eqn11\" src=\"http://c5804c13-0710-40e3-9da7-6d421167ac73.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://759e18b7-b9ba-4c65-bbe6-479e120dc449.png\"/><br/><strong> \t\tNote: This question can be solved quickly by using SHORT TRICKS.</strong></p>", "ty": 5}, "qMapId": 7939, "id": 7939, "position": 7, "link": null, "neg": 1.0, "pos": 1.0}, {"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://d5a782f4-0525-48f7-995e-9b918aef0f43.png\"/><br/> <strong>Note: This question can be solved quickly by using SHORT TRICKS.</strong></p>", "ty": 5}, "qMapId": 7940, "id": 7940, "position": 8, "link": null, "neg": 1.0, "pos": 1.0}, {"opt": [{"t": "\t1/2\t\t<br/>", "ty": 5}, {"t": " <img alt=\"Eqn13\" src=\"http://19f4d914-ce91-45ab-85ed-ee9613dc16cf.png\"/> <br/>", "ty": 5}, {"t": "\t1/8\t\t<br/>", "ty": 5, "co": 1}, {"t": " <img alt=\"Eqn14\" src=\"http://3cab1927-eaf3-4fb3-9f05-921fe64f4fa6.png\"/> ", "ty": 5}], "q": {"t": "<p> <img alt=\"Eqn12\" src=\"http://0ee6dde8-d2cd-4ee6-9b35-19c92dbeffd2.png\"/>is equal to \t<br/></p>", "ty": 5}, "so": {"t": "<p>Sol.</p><p> <img alt=\"9\" src=\"http://2dbfa4a5-2f6f-4318-af53-327b483fe320.png\"/><br/> <br/> <strong>Note: This question can be solved quickly by using SHORT TRICKS.</strong></p>", "ty": 5}, "qMapId": 7941, "id": 7941, "position": 9, "link": null, "neg": 1.0, "pos": 1.0}, {"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://184d0d76-5310-4c64-967c-0d6ef7f672a2.png\"/>is equal to \t<br/>", "ty": 5}, "so": {"t": "<p>Sol.</p><p><strong><img alt=\"10\" src=\"http://db345a29-57e5-405a-bfc8-38edddcc0cbe.png\"/></strong></p><p><strong>\tNote: This question can be solved quickly by using SHORT TRICKS.</strong></p>", "ty": 5}, "qMapId": 7942, "id": 7942, "position": 10, "link": null, "neg": 1.0, "pos": 1.0}, {"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://9e3bbdf4-bd94-4677-bf89-25b0ff7a2a99.png\"/>is equal to \t<br/>", "ty": 5}, "so": {"t": "<p>Sol.</p><p><img alt=\"11\" src=\"http://421a89e9-25e1-40f9-a37c-83142dbd39d0.png\"/></p>", "ty": 5}, "qMapId": 7943, "id": 7943, "position": 11, "link": null, "neg": 1.0, "pos": 1.0}, {"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://ac50c02c-77ac-4791-b20a-8b5d45b97adf.png\"/><br/><strong>Note: This question can be solved quickly by using SHORT TRICKS.</strong></p>", "ty": 5}, "qMapId": 7944, "id": 7944, "position": 12, "link": null, "neg": 1.0, "pos": 1.0}, {"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://e8dec8fb-a968-4eae-b390-8c1b2b8dea5e.png\"/></p>", "ty": 5}, "qMapId": 7945, "id": 7945, "position": 13, "link": null, "neg": 1.0, "pos": 1.0}, {"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://bffa61a4-45b0-4acc-b6ec-32902e1df792.png\"/> and <em> +  = </em>, then tan  equals \t<br/>", "ty": 5}, "so": {"t": "<p>Sol.</p><p><img alt=\"14\" src=\"http://d9e979ef-ee5c-45a5-b81a-1cea7d0a3dc0.png\"/></p>", "ty": 5}, "qMapId": 7946, "id": 7946, "position": 14, "link": null, "neg": 1.0, "pos": 1.0}, {"opt": [{"t": " <img alt=\"Eqn17\" src=\"http://952b3246-159b-4bc2-8305-81d5e7f78f3b.png\"/> <br/>", "ty": 5}, {"t": " <img alt=\"Eqn18\" src=\"http://a0709b56-bb37-491d-a252-1854d432b44d.png\"/> <br/>", "ty": 5, "co": 1}, {"t": " <img alt=\"Eqn19\" src=\"http://e7defd54-2697-4698-833f-9313603268e4.png\"/> <br/>", "ty": 5}, {"t": " <img alt=\"Eqn20\" src=\"http://6f40a938-e914-4919-aa92-926286816107.png\"/> ", "ty": 5}], "q": {"t": " Given both <em> </em>and  are acute angles <img alt=\"Eqn16\" src=\"http://8e0ee3f2-245c-46a8-9327-eb8b35959cd0.png\"/>then the value of <em> + </em> belongs to \t<br/>", "ty": 5}, "so": {"t": "<p>Sol.</p><p><img alt=\"15\" src=\"http://4510ff40-e33d-41eb-8066-b79662c778e8.png\"/><br/><strong> \tNote: This question can be solved quickly by using SHORT TRICKS.</strong></p>", "ty": 5}, "qMapId": 7947, "id": 7947, "position": 15, "link": null, "neg": 1.0, "pos": 1.0}, {"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://e0c14c52-4e2e-43c0-917d-679c4e668c48.png\"/>then <em> +  =</em> <br/>", "ty": 5}, "so": {"t": "<p>Sol.</p><p><img alt=\"16\" src=\"http://88342099-3cff-49cc-9daa-3d5752e213f1.png\"/> <br/> <strong>Note: This question can be solved quickly by using SHORT TRICKS.</strong></p>", "ty": 5}, "qMapId": 7948, "id": 7948, "position": 16, "link": null, "neg": 1.0, "pos": 1.0}, {"opt": [{"t": "\t\u2013<img alt=\"23\" src=\"http://68ab8b7d-ebd9-49b6-9695-a0df8a5a832b.png\"/> <br/>", "ty": 5, "co": 1}, {"t": " <img alt=\"24\" src=\"http://4f40462a-61be-4953-afe0-d690482de0dd.png\"/> <br/>", "ty": 5}, {"t": " <img alt=\"25\" src=\"http://5d2f9364-a505-4e99-bb61-85434a609520.png\"/> <br/>", "ty": 5}, {"t": "\t\u2013.<img alt=\"26\" src=\"http://af8b2784-0ad4-4a01-b279-921bac61f163.png\"/>", "ty": 5}], "q": {"t": " Let ,   be such that  &lt;     &lt; 3. If  <img alt=\"4\" src=\"http://6a800013-11a6-451a-a51c-f1d13b70e239.png\"/>, then the value of <img alt=\"Eqn22\" src=\"http://824a41cb-61f6-45b7-ab9b-904622b434b2.png\"/>is: \t<br/>", "ty": 5}, "so": {"t": "<p>Sol.</p><p><img alt=\"17\" src=\"http://ad1c45cf-6538-4cb6-bde9-8a97b78c134e.png\"/></p>", "ty": 5}, "qMapId": 7949, "id": 7949, "position": 17, "link": null, "neg": 1.0, "pos": 1.0}, {"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://f557d7fa-8fc4-43a3-bf66-0d2786ddddbc.png\"/> <br/><strong>Note: This question can be solved quickly by using SHORT TRICKS.</strong></p>", "ty": 5}, "qMapId": 7950, "id": 7950, "position": 18, "link": null, "neg": 1.0, "pos": 1.0}, {"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://8b558e18-c90f-452f-a117-933f6d5df715.png\"/><br/> <strong>Note: This question can be solved quickly by using SHORT TRICKS.</strong></p>", "ty": 5}, "qMapId": 7951, "id": 7951, "position": 19, "link": null, "neg": 1.0, "pos": 1.0}, {"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://01871742-82be-462e-b4a3-51ec9ec037bb.png\"/><br/> <strong>Note: This question can be solved quickly by using SHORT TRICKS.</strong></p>", "ty": 5}, "qMapId": 7952, "id": 7952, "position": 20, "link": null, "neg": 1.0, "pos": 1.0}]}, "desc": ""}}