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Prove that abs((a,b,c),(a^2,b^2,c^2),(bc...

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

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MODERN PUBLICATION-TEST PAPER 4-PROBLEM
  1. (Allocation Problem.)A farmer has 5 acres of land on which he wishes t...

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  2. Without expanding prove that |[1,a,a^(2),-bc],[1,b,b^(2),-ca],[1,c,c^(...

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

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  4. If A=[[1,2,3],[3,-2,1],[4,2,1]]"show that"A^3-23A-40I=0

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  5. If A =[[1,-2,2],[3,1,-1]] B[[2,4],[1,2],[3,-1]] "verify" "that" (AB)^...

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  6. If f(x)={(ax^2+b if x lt1),(1 if x=1),(2ax-b if xgt1):} is continuous...

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

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  8. Prove that the curves x = y^(2) and xy = k cut at right angles, if 8k^...

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  9. Evaluate the following integrals int(dx)/(sinx(3+2cosx) put cosx=z

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  10. int0^(pi//2)(sqrttanx+sqrtcotx)dx

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  11. Determine the area of the region bounded by y^2=x^3 and the double ord...

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

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  13. If l(1), m(1), n(1) and l(2), m(2), n(2)  are the direction cosines of...

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  14. Find the equation of the plane Which contains the line of intersection...

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  15. Find the distance of the point (-1,-5,-10) from the point of intersect...

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  16. Let R be the relation on the set R of real numbers such that aRb iff a...

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  17. Prove that the following. [[a-b-c,2a,2a],[2b,b-c-a,2b],[2c,2c,c-a-b]]=...

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  18. Find the minimum distance of a point on the curve 2/x^2+1/y^2= 1 from...

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  19. A variable plane meets the coordinate axes at A, B, C and is at a cons...

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  20. Find x and y if [[1,3],[2,-1]][[x],[y]] = [[4],[1]].

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