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Show that 2 sin x + than x ge 3x all x i...

Show that `2 sin x + than x ge 3x all x in (0, pi/20).

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MODERN PUBLICATION-TEST PAPER 1-PROBLEM
  1. If y =(sin^(-1) x)^2, prove that (1-x^2)y2 - xy1 - 2 = 0

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  2. Find the dy/dx when x = a[cos t + log tan (t//2)], y = a sin t

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  3. Show that 2 sin x + than x ge 3x all x in (0, pi/20).

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  4. Show that the line y = mx + c touchees y = 4ax if c = a/m.

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  5. Evaluate int(4x^2/((x-3) (x+1)) dx

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  6. int(pi/5)^(3pi/10) (sinxdx)/(sinx+cosx)

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  7. Solve : (dy/dx)= (x + y)^2

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  8. Find the particular solution of the following differential equation: (...

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  9. Find the area of the region bounded by the line y = 3x + 2, x-axis and...

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  10. Vectors vec(a), vec(b) and vec(c) are such that vec(a) + vec(b) + vec(...

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  11. Find the equation of a plane biscting the line segment joining (-1,4,3...

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  12. Find the foot of the perpendicular drawn from the point (5,7,3) to the...

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  13. Congruence modulo 3 relation partitions the set Z into how many equiva...

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  14. Maximise Z=5x(1)+7x(2) Subject to x(1)+x(2)le4, 5x(1)+8x(2)le24 ...

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  15. If [[x,x^2,x^3-1],[y,y^2,y^3-1],[z,z^2,z^3-1]]=0 then prove that xyz...

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  16. Exaniming consistency and solvability, solve the following equations b...

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  17. If A=((cosx,sinx),(-sinx,cosx)) then prove that A^n=((cosnx,sin nx),(-...

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  18. Find dy/dx x=cos^(3)t/sqrtcos2t, y=sin^(3)t/sqrt cos2t

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

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  20. Integrate : int(ln (x+√(x^2 + a^2))dx.

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