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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)`

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Prove that : Det[[x,x^2,x^3],[y,y^2,y^3],[z,z^2,z^3]]=xyz(x-y)(y-z)(z-x)

For any scalar p prove that =|[x,x^2, 1+p x^3],[y, y^2, 1+p y^3],[z, z^2 ,1+p z^3]|=(1+p x y z)(x-y)(y-z)(z-x) .

Using properties of determinant prove that: |[1,x+y, x^2+y^2],[1, y+z, y^2+z^2],[1, z+x, z^2+x^2]|= (x-y)(y-z)(z-x)

By using properties of determinants. Show that: |[x,x^2,y z],[ y, y^2,z x],[ z, z^2,x y]|=(x-y)(y-z)(z-x)(x y+y z+z x)

Using properties of determinats prove that : |(x,x(x^(2)+1),x+1),(y,y(y^(2)+1),y+1),(z,z(z^(2)+1),z +1)|=(x-y)(y-z)(z-x)(x+y+z)

Using properties of determinants, prove that |[a+x,y,z],[x,a+y,z],[x,y,a+z]|=a^2(a+x+y+z)

Using properties of determinants, prove that |(a+x, y, z),(x, a+y, z),(x, y,a+z)|=a^2(a+x+y+z)

Show that : |[x, y, z ],[x^2,y^2,z^2],[x^3,y^3,z^3]|=x y z(x-y)(y-z)(z-x)dot

Using properties of determinants, prove that |{:(x,y,z),(x^(2),y^(2),z^(2)),(y+z,z+x,x+y):}|=(x-y)(y-z)(z-x)(x+y+z)

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

XII BOARD PREVIOUS YEAR PAPER ENGLISH-BOARD PAPER SOLUTIONS-All Questions
  1. A factory has two machines A and B. Past record shows that machine A...

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  2. Find the inverse of the following matrix using elementary operations: ...

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  3. Using properties of determinants, prove the following: |[x,x^2,1+px^3]...

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  4. Prove the following: tan^(-1)(1/4)+tan^(-1)(2/9)=1/2cos^(-1)(3/5)

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  5. Solve the following for x : cos^(-1)((x^2 - 1)/(x^2 + 1))+t a n^(-1...

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  6. Using matrices, solve the following system of equations: x\ -\ y+z...

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  7. If A^(-1) =[(3,-1,1),(-15,6,-5),(5,-2,2)] and B = [(1,2,-2), (-1,3,0),...

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  8. A merchant plans to sell two types of personal computers - a deskto...

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  9. Given three identical boxes I, II and III each containing two coins...

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  10. Prove that: int0^(pi/4)(sqrt(tanx)+sqrt(cotx))\ dx=sqrt(2)pi/2

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  11. Find the shortest distance between the following pairs of line whose ...

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  12. Using vectors, find the area of the triangle with vertices A (1, 1,...

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  13. Using matrices, solve the following system of equations: 4x+3y+2z=60...

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  14. A random variable X has the following probability distribution: ...

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  15. A window has the shape of a rectangle surmounted by an equilateral ...

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  16. Find the distance of the point (-1,\ -5,\ -10) , from the point of int...

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  17. Show that the right-circular cone of least curved surface and given...

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  18. How many times must a man toss a fair coin, so that the probability...

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  19. Using elementary transformations, find the inverse of the matrix [[-1,...

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  20. Find the equation of the tangent to the curve y=sqrt(3x-2) which is...

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