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Prove by vector method that in any trian...

Prove by vector method that in any triangle ABC, `a/sinA=b/sinB=c/sinC`.

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USHA PUBLICATION-MODEL QUESTION SET-MODEL QUESTION SET
  1. Integrate intdx/(x^4+1)

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  2. Solve x^2ydx-(x^3+y^3)dy=0.

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  3. Prove by vector method that in any triangle ABC, a/sinA=b/sinB=c/sinC.

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  4. If a line in the space makes angles alpha, beta  and gamma  with the c...

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  5. If the mapping f and g are given by f= {(1,2), (3, 4), (5, 6), (7, 8)}...

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  6. Prove that cos^(-1)(frac[b+acosx][a+bcosx])=2tan^(-1)(sqrt(frac[a-b][a...

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  7. Show that the line y=mx+c touches the curve x^2/a^2-y^2/b^2 = 1 if c^2...

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  8. Show that the shrtest distance of the point (0, 8a) from the curve ax^...

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  9. Show that the curves y = 2^(x) and y = 5^(x) intersect at an angle tan...

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  10. Prove the following: [[(b+c)^2,a^2,bc],[(c+a)^2,b^2,ca],[(a+b)^2,c^2...

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  11. Find the inverse of the following matrix using elementary transformati...

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  12. If A is a singular matrix, then what is A(adjA)?

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  13. Give example of a function which is increasing in (-oo,2) and (3,oo) a...

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  14. If the direction angles of a line are alpha=30^@ and beta=60^@, find t...

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  15. Give an example of a relation which is not a function.

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  16. Write the integrating factor of the differential equation dy/dx(x+y+1)...

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  17. tan{(1/2)sin^(-1)((2x)/(1+x^(2)))+1/2cos^(-1)((1-y^(2))/(1+y^(2)))}.

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  18. What is the angle between vecaand vecb if abs(veca+vecb)=abs(veca-vecb...

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  19. If M=[(1,1,1),(1,1,1),(1,1,1)],then what is M^50 ?

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  20. Write the value x for which d/dxsin(sin^-1x)=1

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