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Express abs((a^2,2ab,b^2),(b^2,a^2,2ab),...

Express `abs((a^2,2ab,b^2),(b^2,a^2,2ab),(2ab,b^2,a^2))` in the form of a perfect square.

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If abs((a,b,a-b),(b,c,b-c),(2,1,0))=0 , then prove that a,b,c are in GP.

Without expanding prove abs((bc, a, a^2),(ca, b, b^2),(ab, c, c^2))=abs((1, a^2, a^3),(1, b^2, b^3),(1, c^2, c^3))

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

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)

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) .

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

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

Answer any three questions Using properties of determinants, prove the following 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. Evaluate intfrac[dx][cosx(1+2sinx)]

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  2. Solve the following differential equations (x+tany)dy= sin 2y ""dx

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  3. Express abs((a^2,2ab,b^2),(b^2,a^2,2ab),(2ab,b^2,a^2)) in the form of ...

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  4. If A=[{:(2,1),(-1,3):}],B=[{:(2,3),(1,1):}]andC=[{:(1,0,2),(-2,3,0):}]...

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  5. If f(x)=int0^x e^(2t).sin3tdtthen what is f^1(x)?

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  6. What does the solution set of the inequation 2x+ygt5 represents?

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  7. What is the value of tan(tan^-1""1/2+tan^-1""1/3).

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  8. What is the general solution of tan^-1sqrt(dy/dx)=x?

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  9. Give an example of symmetric matrix.

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  10. If veca and vecb are non-collinear and vecp=xveca+(y+1)vecb,vecq=yveca...

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  11. If y=cos^(-1)((x-1/x)/(x+1/x)),then what is dy/dx?

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  12. What is the restriction on the formula inta^xdx=a^x/(Ina)?

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  13. Write down the symmetric from of the equation of y-axis.

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  14. Solve:"sin"^(-1)2x+"sin"^(-1)x = pi/3.

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  15. Find all possible equivalence relations on X={1,2,3}

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  16. Find the fesible region of the following system:3x-yge0,xge0,yge0

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  17. In a DeltaABC, if mangleA=90^(@), prove that "tan"^(-1)b/(a+c)+"tan"^(...

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  18. If f:XrightarrowY is onto, then prove that f(f^(-1)(B))=B for all Bsub...

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  19. If A is a 3xx3 matrix and absA=2, then which matrix is represented by ...

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  20. [{:(1,-2),(3,2):}][{:(x,2),(1,y):}]=[{:(-3,4),(-1,4):}], find x and y...

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