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using properties of determinants, prove that `abs[[1,a,a^2],[1,b,b^2],[1,c,c^2]]=(a-b)(b-c)(c-a)`.

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MAXIMUM PUBLICATION-MODEL QUESTION-EXAMPLE
  1. Write two non-zero matrices A and B for which AB=0.

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  2. express A=[[1,-1],[2,3]] as the sum of a symmetric matrix and a skew s...

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  3. using properties of determinants, prove that abs[[1,a,a^2],[1,b,b^2],...

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  4. Which among the following is not true

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  5. Find dy/dx, if x^2+y^2+xy=100

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  6. Identify the following function: Is the function differentiable? Why...

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  7. Find derivative of y=sqrttanx

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  8. The slope of the tangent to the curve y=e^(2x) at (0,1) is.....a)1 b)2...

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  9. Find the equation of a line perpendicular to the tangent to the curve ...

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  10. The general solution of a differential equation contains 3 arbitrary c...

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  11. Check whether y=e^(-3x) is a solution of the differential equation fra...

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  12. Let A=R-{3} and B=R-{1} Consider the function f:ArarrB defined by f(x)...

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  13. Let A=R-{3} and B=R-{1} Consider the function f:ArarrB defined by f(x)...

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  14. Let A=R-{3} and B=R-{1} Consider the function f:ArarrB defined by f(x)...

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  15. If xy<1,tan^-1x+tan^-1y=........ a)tan^-1(frac(x-y)(1+xy)) b)tan^-1(f...

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  16. Solve tan^-1 2x+tan^-1 3x=pi/4

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  17. find frac(dy)(dx),if y=x^x+x^sinx

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  18. if y=xcosx, find frac(d^2y)(dx^2)

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  19. intfracf(x)(tanx)dx=logabstanx+c, then f(x) is

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  20. if {df(x)}/dx=4x^2-3/x^4, given f(2)=0. Find f(x)

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