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Find the minimum value of abs[[a^2,bc,ac...

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

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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) .

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

Evaluate [[a,a^2-bc,1],[b,b^2-ac,1],[c,c^2-ab,1]]

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

Evaluate abs[[1,a,bc],[1,b,ca],[1,c,ab]]-abs[[1,a,b^2],[1,b,b^2],[1,c,c^2]]

Find the value of x if abs[[2,3],[4,5]]=abs[[x,3],[2x,5]]

Prove that [[b^2c^2, bc,b+c],[c^2a^2,ca,c+a],[a^2b^2,ab,a+b]] = 0

Evaluate [[1,a,bc],[1,b,ca],[1,c,ab]]-[[1,a,a^2],[1,b,b^2],[1,c,c^2]]

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

Using the properties of determinants, show that abs[[1+a^2-b^2,2ab,-2b],[2ab,1-a^2+b^2,2a],[2b,-2a,1-a^2-b^2]]=(1+a^2+b^2)^3

USHA PUBLICATION-MODEL QUESTION SET-MODEL QUESTION SET
  1. Using the properties of determinants, show that abs[[1+a^2-b^2,2ab,-2b...

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  2. If A=[{:(costheta,sintheta),(-sintheta,costheta):}], then prove that ...

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

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  4. Find the values of x and y such that [{:(3x+7,5),(y+1, 2-3x):}]=[{:(0,...

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  5. Discuss the continuity of the function defined by f(x)={[x+1, if xle1]...

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  6. Differentiate the functions w.r.t x x^(xcosx)+frac[x^2+1][x^2-1]

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  7. Find the tangent to the curve y = cos (x + y), 0 le x le 2pi which is ...

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  8. Find the intervals in which the function f given by f(x)=sinx+cosx, 0l...

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  9. If x=(sin^(3)t)/(sqrt(cos2t)) and y=(cos^(3)t)/(sqrt(cos2t)), then fin...

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  10. Find the integral intfrac[x^3sin(tan^(-1)x^4)][1+x^8]dx

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  11. Find the integral intfrac[x+3][(5-4x+x^2)]dx

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  12. Evaluate int(0)^(pi//2)logsinxdx.

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  13. Form the differential equation of the family of all circles of radius ...

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  14. Solve the differential equation frac[dy][dx]=log(x+1)

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  15. The two adjacent sides of a parallelogram are 2hati-4hatj+5hatk and ha...

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  16. Prove the following by vector method. In a triangle AOB, mangleAOB = 9...

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  17. Find the distance of the point (2,3,4) from the plane 3x+2y+2z+5=0 mea...

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  18. Prove by vector method that in a parallelogram, the line joining a ve...

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  19. If "sin"^(-1)x + "sin"^(-1)y +"sin"^(-1)z = pi "prove that" x^4+y^4+z^...

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  20. Maximize Z=6x1+10x2subject to x1+2x2gt10,2x1+2x2gt12,3x1+x2gt8,x1,x2gt...

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