JEE Advanced 2013 Paper 2 Mathematics Q18

Mathematics

Problem

Match List I with List II and select the correct answer using the code given below the lists. Column I — P: (1y2[cos⁡(tan⁡−1y)+ysin⁡(tan⁡−1y)]2[cot⁡(sin⁡−1y)+tan⁡(sin⁡−1y)]2+y4)1/2\left(\dfrac{1}{y^2}\dfrac{[\cos(\tan^{-1}y)+y\sin(\tan^{-1}y)]^2}{[\cot(\sin^{-1}y)+\tan(\sin^{-1}y)]^2}+y^4\right)^{1/2} takes value; Q: If cos⁡x+cos⁡y+cos⁡z=0=sin⁡x+sin⁡y+sin⁡z\cos x+\cos y+\cos z=0=\sin x+\sin y+\sin z, a possible value of cos⁡((x−y)/2)\cos((x-y)/2) is; R: If cos⁡(π/4−x)cos⁡2x+sin⁡xsin⁡2xsec⁡x=cos⁡xsin⁡2xsec⁡x+cos⁡(π/4+x)cos⁡2x\cos(\pi/4-x)\cos2x+\sin x\sin2x\sec x=\cos x\sin2x\sec x+\cos(\pi/4+x)\cos2x, a possible value of sec⁡x\sec x is; S: If cot⁡(sin⁡−11−x2)=sin⁡(tan⁡−1(x6))\cot(\sin^{-1}\sqrt{1-x^2})=\sin(\tan^{-1}(x\sqrt6)), x≠0x\ne0, a possible value of xx is Column Ii — 1: 125/3\tfrac12\sqrt{5/3}; 2: 2\sqrt2; 3: 1/21/2; 4: 11

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