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Write A=[[3,5],[1,-1]] as the sum of a s...

Write `A=[[3,5],[1,-1]]` as the sum of a symmetric and a skew symmetric matrix.

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A N EXCEL PUBLICATION-PROBABILITY-QUESTION BANK
  1. Prove that 2 tan^(-1)(1/2) + tan^(-1)(1/7) = tan^(-1)(31/17)

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  2. If A=[[0,1],[0,0]] ,B=[[1,0],[0,0]], then BA=

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  3. Write A=[[3,5],[1,-1]] as the sum of a symmetric and a skew symmetric ...

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  4. Find the inverse of A=[[2,-6],[1,-2]]

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  5. The value of abs((x,x-1) , (x+1,x):} is a)1 b)x c)x^2d)0

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  6. Using properties of determinants prove the following. abs[[1,x,x^2...

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  7. Find all points of discontinuity of f where f is defined by f(x)={(2x+...

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  8. If e^(x-y)=x^y then prove that dy/dx=logx/[logex]^2

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  9. The slope of the tangent to the curve given x=1-costheta,y=theta-sin...

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  10. Find the intervals in which the function f(x)=x^2-4x+6 is strictly dec...

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  11. Find the minimum and maximum value, if any, of the function f(x)=(2x-1...

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  12. Which of the following function has neither local maxima nor local min...

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  13. Find the equation of the tangent to the curve y=3x^2 at (1,1)

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  14. Use differentiation to approximate sqrt36.6.

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  15. The angle between the vectors veca and vecb such that absveca=absvecb=...

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  16. Find the unit vector along veca-vecb where veca=i+3j-k and vecb=3i+2j+...

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  17. If the points A and B are (1,2,-1) and (2,1,-1) respectively, then vec...

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  18. Find the value of lambda for which the vectors 2i-4j+5k, i-lambdaj+k ...

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  19. Find the angle between the vectors veca=hati+hatj-hatk and vecb=hati-h...

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  20. Prove that int cos^2xdx=x/2+(sin2x)/4+c

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