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Prove that cos^(-1)""(12)/(13)+sin^(-1)"...

Prove that `cos^(-1)""(12)/(13)+sin^(-1)""(3)/(5)=sin^(-1)""(56)/(65)`

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OMEGA PUBLICATION-HP BOARD MARCH 2017-SERIES -C
  1. Form a differential equation representing the family of curves y^(2) =...

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  2. Let T be the set of all triangles in a plane with R a relation in T gi...

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  3. Prove that cos^(-1)""(12)/(13)+sin^(-1)""(3)/(5)=sin^(-1)""(56)/(65)

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  4. Write tan^(-1)((sqrt(1+x^(2))-1)/(x)),xne0 simplest form.

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  5. Using the properties of determinants, show that |(1+a,1,1),(1,1+b,1),(...

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  6. Find (dy)/(dx) if xy^2 + y^2 = tan x + y

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  7. If y = 500e^7x + 600e^-7x show that (d^2y/dx^2) = 49y

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  8. Evaluate int(x+3)sqrt(3-4x-x^(2))dx

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  9. Evaluate int e^(x)(1/x-1/(x^(2)))dx.

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  10. Evaluate : int0^(pi/2) (sin^(3/2)x)/(sin^(3/2)x+cos^(3/2)x)dx.

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  11. Solve the differntial equation (dy)/(dx)+y/x=x^(2)

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  12. Solve the differential equation (dy)/(dx)=(x+1)/(2-y),(y!=2)

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  13. Show that the four points with position vectors 4hati+8hatj+12hatk,2ha...

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  14. Find the angle between the pair of lines (x-5)/7=(y+2)/(-5)=z/1 and x...

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  15. A family has two children. What is the probability that both the child...

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  16. Find the probability distribution of number of heads in four tosses of...

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  17. If is known that 10% of certain articles manufactured are defective. W...

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  18. Solve the following system of linear equations by matrix method : 3x -...

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  19. Find the equations of the tangent and normal to the hyperbola x^2/a^2 ...

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  20. Find two positive numbers x and y such that x+y = 60 and xy^3 is maxim...

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