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Express [[1 2 3] [4 0 1] [-1 5 -2]] as a...

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

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MODERN PUBLICATION-TEST PAPER 1-PROBLEM
  1. Show that the operation * given by x*y=x+y+ -xy is a binary oeration o...

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

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

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

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  5. 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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  6. Find x if '||a b c| |b a b| |x b c|| = 0

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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