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Factorize the following. [[x+a,b,c],[b,x...

Factorize the following. `[[x+a,b,c],[b,x+c,a],[c,a,x+b]]`

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Factorize the following. [[a,b,c],[b+c,c+a,a+b],[a^2,b^2,c^2]]

Prove the following: [[a,b,c],[b,c,a],[c,a,b]]=3abc-a^3-b^3-c^3

Prove that the following. [[a,b,c],[a^2,b^2,c^2],[bc,ca,ab]] =(b-c)(c-a)(a-b)(bc+ca+ab)

Prove that the following. [[b+c,a,a],[b,c+a,b],[c,c,a+b]] =4ab

Prove that the following. [[a,b,c],[x,y,z],[p,q,r]]=[[y,b,q],[x,a,p],[z,c,r]]=[[x,y,z],[p,q,r],[a,b,c]]

Prove the following: [[a+b+c,-c,-b],[-c,a+b+c,-a],[-b,-a,a+b+c]] =2(b+c)(c+a)(a+b)

Prove that the following. [[a,a^2,a^3],[b,b^2,b^3],[c,c^2,c^3]] = abc(a-b)(b-c)(c-a)

Prove that the following. [[1,1,1],[b+c,c+a,c+a],[b^2+c^2,c^2+a^2,a^2+b^2]] =(b-c)(c-a)(a-b)

Prove the following: [[b+c,a+b,a],[c+a,b+c,b],[a+b,c+a,c]] = a^3+b^3+c^3-3abc

Prove that the following. [[a-b-c,2a,2a],[2b,b-c-a,2b],[2c,2c,c-a-b]]=(a+b+c)^3

SHARAM PUBLICATION-MODEL QUESTION PAPER -15-EXERCISE
  1. Solve the following equation: "cos"("tan"^(-1)x)="sin"("cot"^(-1)3/(...

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

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  3. Factorize the following. [[x+a,b,c],[b,x+c,a],[c,a,x+b]]

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  4. Solve the following : [[1+x,1,1],[1,1+x,1],[1,1,1+x]]=0

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  5. Eliminate x,y,z from a=x/y-z, b=y/z-x, c=z/x-y

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  6. For what value of lambda,is the function f(x)={(lambdax^2-2x,if xle0),...

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  7. If cos y = x cos(a+y) then prove that dy/dx = (cos^2(a+y))/sin a

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  8. If y^2cot x = x^2 coty then find (dy)/(dx)

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  9. Find the equation of the normal to the curve y=(logx)^2 at x=frac[1][e...

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  10. Find two positive numbers whose product is 256 and whose sum is least.

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  11. Integrate:inta/(b+ce^x)dx

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  12. Integrate:int sec(sqrtx)/(sqrtx)dx

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  13. Prove that int0^(pi/2)(sin^nx)/(sin^nx+cos^nx)dx=pi/4

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  14. Find the area bounded by y=sinx,y=0,x=pi/2

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

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  16. If hati +hatj+hatk and 2hati -alphahatj+3hatk are orthogonal to each o...

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  17. If the magnitude of the difference of two unit vectors is sqrt3 then f...

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  18. Find the equation of the plane Paralel to the plane 2x-y+3z+1=0 and at...

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  19. If veca=2vecb and vecc=-3vecb, then what is the angle between veca and...

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  20. If l1,m1,n1andl2,m2,n2 are the direction cosines of two mutually perpe...

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