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Show that |{:((b+c)^2,a^2,a^2),(b^2,(c...

Show that
`|{:((b+c)^2,a^2,a^2),(b^2,(c+a)^2,b^2),(c^2,c^2,(a+b)^2):}|=2abc(a+b+c)^3`

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Show that: abs((a,a^2,a^3),(b,b^2,b^3),(c,c^2,c^3))=abc(a-b)(b-c)(c-a)

Show that: abs((1,a,a^2),(1,b,b^2),(1,c,c^2))=(a-b)(b-c)(c-a)

Show that |{:(a,b,c),(a+2x,b+2y,c+2z),(x,y,z):}|=0

If 2s=a+b+c show that [[a^2,(s-a)^2,(s-a)^2],[(s-b)^2,b^2,(s-b)^2],[(s-c)^2,(s-c)^2,c^2]] = 2s^3(s-a)(s-b)(s-c)

Without expanding the determinants prove that |{:(a,a^2,bc),(b,b^2,ca),(c,c^2,ab):}| = |{:(1,a^2,a^3),(1,b^2,b^3),(1,c^2,c^3):}|

Show that abs((2(a+b+c),a,b),(2(a+b+c),b+c+2a,b),(2(a+b+c),a,c+a+2b))=2(a+b+c)^3

Prove that abs((a,b,c),(a^2,b^2,c^2),(bc,ca,ab))=(a-b)(b-c)(c-a)(ab+bc+ca)

MODERN PUBLICATION-TEST PAPER 3-PROBLEM
  1. Differentiate with respect to x: y=3^(x^2)+tan^-1((cosx+sinx)/(cosx-si...

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  2. Find the dy/dx when cos x = sqrt ((1)/(1+t^2)), sin y = (2t)/(1+t^2)

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  3. Show that the line y = mx + c touches the parabola y^(2) = 4ax if c = ...

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  4. Show that 2sinx+tanxge3x for all x epsilon(0,(pi)/(2)).

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  5. Evaluate : int (xe^x)/(x+1)^(2) dx

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  6. Evaluate the following integrals int(x^2)dx/((x^2+3)(x^2+2))

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  7. Solve : dy/dx + 1 = e^(x+y)

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  8. Solve : (x + 2y^3)dy/dx = y.

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  9. Find the equation of the plane passing through the points (2,1,3), (3,...

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  10. Find the image of the point (3,-2,1) in the plane x-y+3z=2.

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  11. Determine k such that a vector vec(r) is at right angles to each of th...

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

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  13. Let f:XrightarrowY and g:YrightarrowZ. Prove that gof is bijective if ...

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  14. Find the product of matrices A and B, where A = [[-5,1,3],[7,1,-5],[1,...

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  15. Show that |{:((b+c)^2,a^2,a^2),(b^2,(c+a)^2,b^2),(c^2,c^2,(a+b)^2):}...

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  16. Find the inverse of the following matrices using elementary transforma...

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  17. If x=acos theta+bsin theta and y=a sin theta-bcos theta, then show tha...

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  18. Find the equation of the normal at a point on the curve x^(2) = 4y, wh...

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  19. Find the area of the smaller region bounded by the ellipse frac[x^2][a...

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  20. Prove analytically : The perpendicular bisector of the sides of a tria...

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