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If a, b and c are all positive real, the...

If a, b and c are all positive real, then prove that minimum value of determinant
`|{:(a^2+1,ab,ac),(ab,b^2+1,bc),(ac,bc,c^2+1):}|` = `1+a^2+b^2+c^2`

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Prove the following: [[a^2+1,ab,ac],[ab,b^2+1,bc],[ac,bc,c^2+1]] =1+a^2+b^2+c^2

Find the minimum value of abs[[a^2,bc,ac+c^2],[a^2+ab,b^2,ac],[ab,b^2+bc,c^2]]

Prove the following: [[-a^2,ab,ac],[ab,-b^2,bc],[ac,bc,-c^2]]=4a^2b^2c^2

Show that without expanding at any stage |{:(1/a,a^2,bc),(1/b,b^2,ca),(1/c,c^2,ab):}|=0

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Using properties of determinants, prove the following abs{:(a^2, bc, ac +c^2 ),(a^(2) + ab, b^(2),ac ),(ab, b^(2) + bc,c^(2) ):}=4a^(2) b^(2) c^(2) .

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MODERN PUBLICATION-TEST PAPER 2-PROBLEM
  1. Answer the following: What is the value of [[o,-h,-g],[h,o,-f],[g,f,...

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  2. Show that no two normals to a parabola are parallel.

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  3. Find the intervals where the following functions are (a) increasing an...

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  4. Find int (cos x /sin^(2) x + sin x ) dx

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  5. Evaluate : int(0) ^(pi/4) dx/cos x (cos x + sin x).

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  6. Find the differential equation whose general soltution is c1x^2+c2y=1 ...

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  7. Find the area of the region bounded by the curve y=6x-x^(2), the X-axi...

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  8. Prove the following by vector method. The parallelogram whose diagonal...

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  9. Prove that the two lines whose direction cosines are connected by the ...

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

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  11. Find the equation of the line through the point (3, -1, 2) and paralle...

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  12. If N denotes the set of all natural numbers and R be the relation on N...

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  13. If a, b and c are all positive real, then prove that minimum value of ...

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  14. Solve the following system of equations by the matrix inversion method...

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  15. Find the inverse of [(1,1,2),(0,1,2),(1,2,1)] using elementary operati...

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  16. Show that of all the rectangles inscribed in a given fixed circle, the...

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  17. Evaluate : int dx /cosx (5+3 cos x).

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  18. Find the area of the parallelogram whose diagonals are the vectors 3ha...

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  19. For an vector vec(r) = x hat(i) + y hat(j) + z hat(k), prove that vec(...

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  20. Find the equation of plane through the point (2,0,-3) and containing t...

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