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Syllabus

^{2}and has 1200 turns. Calculate self-inductance of the toroid. Assume field to be uniform across the cross section of toroid.let o be a point inside a triangle ABC such that angle OAC=angle OCB= angle OBA= alpha .then prove that

1)cota +cot b + cot c=cot alpha

2) cosec

^{2}a+cosec^{2}b+cosec^{2}c= cosec^{2}alpha^{-1}1/3 = 9/4 sin^{-1}2 root 2/3b-c/a = tan B/2 - tan C/2 / tan B/2 + tan C/2

^{ }a(b

^{2+c2}) cosA+b (c^{2}^{+a2})cosB+c(^{a2+b2})cosC=3abcHow many states in India?^{2}-b^{2}/a^{2}+b^{2}^{2}+ BC^{2 }= AC^{2}^{2}+b^{2}c^{2}=3(OA^{2}+OB^{2}+OC^{2})- 9 OG^{2}where O is any point in plane of triangle ABC....kindly give proof using vector algebra rather than plane geometry (i know all concepts related to vector analysis and vector algebra)quick ans neededthank u

a

^{2}sin(B-C)/sin A + b^{2}sin(C-A)/sin B + c^{2}sin(A-b)/sin C = 0^{2}tanB=b^{2 }tanA, then prove that the triangle is either right triangle or isosceles.$3.\mathrm{If}\frac{\mathrm{sin}\left(\mathrm{\theta}+\mathrm{A}\right)}{\mathrm{sin}\left(\mathrm{\theta}+\mathrm{B}\right)}=\sqrt{\frac{\mathrm{sin}2\mathrm{A}}{\mathrm{sin}2\mathrm{B}}}\mathrm{then}{\mathrm{tan}}^{2}\mathrm{\theta}=\phantom{\rule{0ex}{0ex}}\left(1\right)\mathrm{tan}\mathrm{A}\left(2\right)\mathrm{tan}\mathrm{B}\left(3\right)\mathrm{tan}\mathrm{A}+\mathrm{tan}\mathrm{B}\left(4\right)\mathrm{tan}\mathrm{A}\mathrm{tan}\mathrm{B}\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}4.\mathrm{If}\mathrm{tan}\mathrm{\beta}=2\mathrm{sin}\mathrm{\alpha}\mathrm{sin}\mathrm{\gamma}\mathrm{cos}\mathrm{ec}\left(\mathrm{\alpha}+\mathrm{\gamma}\right),\mathrm{then}\mathrm{cot}\mathrm{\alpha},\mathrm{cot}\mathrm{\beta}\mathrm{and}\mathrm{cot}\mathrm{\gamma}\mathrm{are}\mathrm{in}.\phantom{\rule{0ex}{0ex}}\left(1\right)\mathrm{A}.\mathrm{P}.\left(2\right)\mathrm{G}.\mathrm{P}.\left(3\right)\mathrm{H}.\mathrm{P}.\left(4\right)\mathrm{A}.\mathrm{G}.\mathrm{P}\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}5\mathrm{If}\mathrm{tan}\mathrm{\beta}=\frac{\mathrm{n}\mathrm{tan}\mathrm{\alpha}}{1+\left(1-\mathrm{n}\right){\mathrm{tan}}^{2}\mathrm{\alpha}}\mathrm{tan}\left(\mathrm{\alpha}-\mathrm{\beta}\right)=\phantom{\rule{0ex}{0ex}}\left(1\right)\left(1+\mathrm{n}\right)\mathrm{tan}\mathrm{\alpha}\left(2\right)\left(1-\mathrm{n}\right)\mathrm{tan}\mathrm{\alpha}\phantom{\rule{0ex}{0ex}}\left(3\right)-\left(1+\mathrm{n}\right)\mathrm{tan}\mathrm{\alpha}\left(4\right)-\left(1-\mathrm{n}\right)\mathrm{tan}\mathrm{\alpha}$

Q18. State and explain Biot -Savart's law.

(OR)

A fine insulated wire 15.7 m. long is used to make a coil of radius 5 cm, find the magnitude of magnetic induction in air, at the centre of the coil, when the current of 0.2A is sent through it.

Q19. Define :

(i) Magnetic dipole

(ii) Magnetic length

(iii) Magnetic moment

Q20. State properties of electric lines of force.

Q21. State law of conservation of momentum. Give any two examples.