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Using properties of determinants prove t...

Using properties of determinants prove that `|(1,1, 1+3x),(1+3y,1,1),(1, 1+3z,1)| =9(3xyz+xy+yz+zx) `

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1,1,1+3x1+3y,1,11,1+3z,1]|=9(3xyz+xy+yz+zx)

Using properties of determinants, prove that : |{:((x+y)^(2),zx,xy),(zx,(z+y)^(2),xy),(zy,xy,(z+x)^(2)):}|=2xyz(x+y+z)^(3) .

Using properties of determinants, prove the following: |[x,x^2,1+px^3],[y,y^2,1+py^3],[z,z^2,1+pz^3]|=(1+pxyz)(x-y)(y-z)(z-x)

1+x,1,11,1+y,11,1,1+z]|=xy+yz+zx+xyz

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XII BOARDS PREVIOUS YEAR-XII Boards-All Questions
  1. Find the magnitude of each of the two vectors veca and vec b having th...

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  2. A black and a red dice are rolled. (a)   Find the conditional proba...

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  3. Using properties of determinants prove that |(1,1, 1+3x),(1+3y,1,1),(1...

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  4. Find (dy)/dx, if (x^2+y^2)^2=xy

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  5. If a * b, denoted the larger of 'a' and 'b' and if a o b = a*b + 3 , ...

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  6. If x=a(2theta-sin2theta) and y=a(1-cos2theta) find (dy)/(dx) when thet...

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  7. If y="sin"(sinx),"p r o v et h a t" (d^2y)/(dx^2)+tanx(dy)/(dx)cos^...

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  8. Prove that: 3sin^(-1)x=sin^(-1)(3x-4x^3), x in [-1/2,1/2]

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  9. Find the area of the region in the first quadrant enclosed by the x...

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  10. Find the equations of the tangent and the normal to the curve 16x^2+9y...

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  11. Find the intervals in which the function f(x)=x^4/4-x^3-5x^2+24x+12 is...

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  12. Evaluate : int(0)^(pi/4) (sinx+ cos x)/( 16 + 9sin2x)

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  13. Evaluate : int1^3 (x^2 + 3x + e^x) dx as the limit of the sum.

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  14. An open tank with a square base and vertical sides is to be constructe...

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  15. Find int (2cosx)/((1-sinx)(1+sin^2x)) dx

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  16. Find the particular solution of the differential equation e^xtanydx+(2...

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  17. Find the distance of the point (-1,-5,-10) from the point of inters...

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  18. The differential equations, find a particular solution satisfying t...

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  19. A factory manufactures two types of screws, A and B. Each type of scre...

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  20. Let vec a=4hati+5hatj-hatk, vecb = hati -4hatj+5hatk and vec c=3hati+h...

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