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The tangent to the curve х = е^tcos t, у...

The tangent to the curve `х = е^tcos t`, `у = е^tsin t` and `t=π/4` makes what angle with x-axis.•

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MODERN PUBLICATION-TEST PAPER 1-PROBLEM
  1. Determine the maximum value of |[cosx sinx], [-sinx cosx-1]|.

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  2. f(x) = xlxl differentiable at х = 0.

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  3. The tangent to the curve х = е^tcos t, у = е^tsin t and t=π/4 makes wh...

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  4. If |vec(a)| = 8, |vec(b)| = 3 and |vec(a) xx vec(b)| = 12, then find t...

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  5. Write the equation of X-axis in space.

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  6. Evaluate inte^x(cosx-sinx)dx.

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  7. What is the order of the differential equation of all circles of given...

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  8. An animal feed company must produce 200kg of a mixture consisting of i...

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  9. Test whether the relations are reflexive, symmetric or transitive on t...

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  10. Show that the operation * given by x*y=x+y+ -xy is a binary oeration o...

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  11. "Let" f(x) =sqrtx "and" g(x) = 1 -x^2. Compute fog and gof and find th...

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  12. Express [[1 2 3] [4 0 1] [-1 5 -2]] as a sum of a symmetric and a skew...

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  13. If ax+hy+g=0, hx+by+f=0 and gx+fy+c=lamda, find the value of lamda in ...

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  14. If[[x,y],[x,x/2+t]]+[[y,x+t],[x+2,x/2]]=[[1,4],[2,3]] find x,y,z and t...

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  15. Find x if '||a b c| |b a b| |x b c|| = 0

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  16. Test differentiability and continuity of the following functions. f(...

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  17. If y =(sin^(-1) x)^2, prove that (1-x^2)y2 - xy1 - 2 = 0

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

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

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

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