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|(1+x,1,1),(1,1+y,1),(1,1,1+z)|=xy+yz+zx...

`|(1+x,1,1),(1,1+y,1),(1,1,1+z)|=xy+yz+zx+xyz`

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    XII BOARDS PREVIOUS YEAR|Exercise Section D 35 B|1 Videos

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

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

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

If Delta=|{:(1,x,x^(2)),(1,y,y^(2)),(1,z,z^(2)):}| , Delta_(1)=|{:(1,1,1),(yz,zx,xy),(x,y,z):}| , then prove that Delta+Delta_(1)=0

If x,y,z are distinct and |(x, x(x^2+1), x+1),(y,y(y^2+1), y+1),(z, z(z^2+1), z+1)|=0 then (A) xyz=0 (B) x+y+z=0 (C) xy+yz+zx=0 (D) x^2+y^2+z^2=1

Prove the following : |(1,x,x^(2)-yz),(1,y,y^(2)-zx),(1,z,z^(2)-xy)|=0 .

Let Delta_(1)=|{:(Ax,x^(2),1),(By,y^(2),1),(Cz,z^(2),1):}| and Delta_(2)=|{:(A,B,C),(x,y,z),(yz,zx,xy):}| , then :

The value of |{:(x,x^2-yz,1),(y,y^2-zy,1),(z,z^2-xy,1):}| is

XII BOARDS PREVIOUS YEAR-XII Boards-All Questions
  1. Find int (dx)/sqrt(3-2x-x^2)

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  2. Determine the product [[-4, 4, 4], [-7, 1, 3],[5, -3, -1]][[1, -1, 1]...

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  3. |(1+x,1,1),(1,1+y,1),(1,1,1+z)|=xy+yz+zx+xyz

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  4. Consider f : R->{-4/3}->R-{4/3} given by f(x) = (4x+3)/(3x+4). Show t...

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  5. The number of irrational roots of the equation (4x)/(x^2+x+3)+(5x)/(...

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  6. Show that the total surface area of a closed cuboid with square bas...

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  7. Using integration, find the area of the triangle ABC, coordinates o...

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  8. Evaluate : int(-1)^2|x^3-x|\ dx

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  9. Show that the differential equation 2y e^(x/y)\ dx+(y-2x e^(x y) ) dy=...

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  10. Find the particular solution of the following differential equation...

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  11. Find the area of a parallelogram ABCD whose side AB and the diagonal A...

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  12. Find the coordinates of the point where the line through the points (...

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  13. 4 कार्ड 1,3,5 और 7 हैं, एक कार्ड पर एक नंबर। दो कार्ड बिना प्रतिस्थापन...

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  14. In a shop X, 30 tins of pure ghee and 40 tins of adulterated ghee whic...

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  15. Let A=R-{3},B=R-{1}, and let f: AvecB be defined by f(x)=(x-2)/(x-3) i...

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  16. A wire of length 36m is to be cut into two pieces. One of the piece...

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  17. Using the method of integration, find the area of the triangle ABC, c...

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  18. Find the equation of the plane through the line of intersection of ...

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  19. If e^y(x+1)=1 , show that (d^2y)/(dx^2)=((dy)/(dx))^2 .

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  20. Let A=[[2,-1],[3,4]],B=[[5,4],[7,4]],C=[[2,5],[3,8]]. Find a matrix D ...

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