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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 BOARD PREVIOUS YEAR PAPER ENGLISH|Exercise Section D|2 Videos

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

Value of the determinant |(x,1,1),(0,1+x, 1),(-y, 1+x, 1+y)| is (A) xy (B) xy(x+2) (C) x(x+1)(y+1) (D) xy(x+1)

if x ne 0 , y ne 0 ,z ne 0 " and " |{:(1+x,,1,,1),(1+y,,1+2y,,1),(1+z,,1+z,,1+3z):}|=0 then x^(-1) +y^(-1) +z^(-1) is equal to

Prove that : |{:(1,x,yz),(1,y,zx),(1,z,xy):}|=(x-y)(y-z)(z-x)

If x!=0,y!=0,z!=0 and |[1+x,1,1],[1+y,1+2y,1],[1+z,1+z,1+3z]|=0 , then x^(-1)+y^(-1)+z^(-1) is equal to a.1 b.-1 c.-3 d. none of these

If x , y , z are different from zero and |[1+x,1 ,1], [1, 1+y,1], [1, 1, 1+z]|=0 then the value of x^(-1)+y^(-1)+z^(-1) is (a) x y z (b) x^(-1)y^(-1)z^(-1) (c) -x-y-z (d) -1

If x , y , z are different from zero and |[1+x,1, 1],[1 , 1+y ,1],[ 1 ,1, 1+z]|=0 then the value of x^(-1)+y^(-1)+z^(-1) is (a) x y z (b) x^(-1)y^(-1)z^(-1) (c) -x-y-z (d) -1

If "Delta"=|(1,x,x^2),( 1,y, y^2),( 1,z, z^2)| , "Delta"_1=|(1, 1, 1),(yz, z x,x y), (x, y, z)| , then prove that "Delta"+"Delta"_1=0 .

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

If 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

XII BOARD PREVIOUS YEAR PAPER ENGLISH-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)/(x...

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

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

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

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  17. Find the equation of the plane through the line of intersection of t...

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

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

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  20. If x^my^n = (x + y)^(m+n), prove that (d^2y)/(dx^2)=0.

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