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

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`|{:((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)

SHARAM PUBLICATION-QUESTION PAPER 2011-EXERCISE
  1. Find the image of the point (-2,0,3) with respect to the plane y = 3.

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  2. Shade the feasible region for the inequations 2x+3yle6,xge0,yge0 in a ...

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  3. Find n and x, given that: (1+x)^n =1+3/4+((3)(5))/((4)(8))+((3)(5)(7...

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  4. Prove that: A = ([3,1],[-1,2]) impliesA^2-5A+7I =0.

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  5. Test whether the following system of equations have non zero solution....

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  6. Two dice are rolled in succession. Find the probability that the first...

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  7. A and B are two events. If P(A)=3/8,P(B) =1/2 and P(AnnB)=1/4 then fin...

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  8. Prove that y=tan^(-1)sqrt((1+sinx)/(1-sinx))rArr(dy)/(dx)=1/2

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  9. x^py^q= (x+y)^(p+q)implies(dy)/(dx)=y/x

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  10. Find the following limits:lim(xrarr1)(1/(x-1)-1/(lnx))

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  11. Find the following limits:lim(xrarr1)(2-x)^("cosec"pix)

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  12. Discuss the extreme value of the function y=(x+2)^4(x-1)^5

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  13. Find intx^2(sin^4x+cos^4x)dx

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  14. Evaluate the following integrals : int(dx)/((x-2)sqrt(x^(2)-16x+64))

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  15. Solve (x-y+1)dx-(x+y+5)dy=0

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  16. Prove that [vec(p) - vec(q) vec(q) - vec(r) vec(r) - vec(p)] = 0

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  17. Prove that vecaxx(vecbxxvecc)+ vecbxx(veccxxveca)+veccxx(vecaxxvecb) =...

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  18. Solve the following LPP graphically : Maximize : Z=5x1+3x2 subject to ...

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  19. 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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  20. Solve by matrix inversion method. x-2y=3 3x+4y-z=-2 5x-3z=-1

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