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Prove that cos (sinx) > sin (cos x) for ...

Prove that cos (sinx) > sin (cos x) for all x in `0 le x le pi//2`

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UNITED BOOK HOUSE-MISCELLANEOUS EXERCISE-EXERCISE
  1. Solve(cos y + y cos x ) dx + sin (x - x sin y) dy = 0

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  2. Solve(d^2y)/(dt^2) = tan y sec ^2 y, given dy/dt = 0 when y = 0

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  3. Prove that cos (sinx) > sin (cos x) for all x in 0 le x le pi//2

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  4. If the line ax+by+c=0 is a normal to the curve xy=1 then

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  5. Prove that all points of the curve y^2=4a[x+asinx/a] at which the lang...

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  6. Find the point on the curve 4x^2 + a2y^2 = 4a^2, 4 < a^2 < 8 that is f...

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  7. The area bounded by the parabola y = x - x^2 and the line y = mx equal...

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  8. Prove that f(x)= sin x+sqrt 3 cosx has maximum value at x=pi/6

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  9. The length of the hypotenuse of a right angled triangle is 3 ft. Find ...

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  10. The angle between the tangents to the curves y=sin x and y = cos x at ...

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  11. Show that f(x) = (x-2)e^x + x + 2 is positive for all positive values ...

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  12. Vectors vecm, vecn, vecr are such that vecm + vecn + vecr = 0, prove t...

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  13. If vecp xx vecq = vecm xx vec n and vecp xx vec m = vecq xx vecn, sho...

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  14. If veca xx vecb + vecb xx vecc + vecc xx veca = 0. Show that the vecto...

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  15. The vector vecr is collinear with vector vecn = 2hati + hatj + 3hatk ...

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  16. If veca,vecb and vecc are three mutually perpendicular vectors of equa...

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  17. Find the equation of the plane passing through the point(1,2,1) and pe...

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  18. Find the vector equation of the following plane in scalar product from...

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  19. two numbers are selected at random from 1,2,3,….., 100 and are multipl...

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  20. In a class, 5% of the boys and 10% of the girls have an IQ more than 1...

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