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Using properties of determinants, prove that `|2yy-z-x2y2z2z z-x-y x-y-z z x2x|=(x+y+z)^3`

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Prove: |(2y, y-z-x,2y),(2z,2z, z-x-y),( x-y-z,2x,2x)|=(x+y+z)^3

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 |{:(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)

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 |{:(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 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 the properties of determinants, show that: [[x, x^2, yz],[y, y^2, zx],[z, z^2, xy]]=(x-y)(y-z)(z-x)(xy+yz+zx)

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 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)

XII BOARD PREVIOUS YEAR PAPER ENGLISH-BOARD PAPER SOLUTIONS-All Questions
  1. Find the particular solution of the differential equation x(dy)/(dx)-y...

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  2. Differentiate tan^(-1)((sqrt(1-x^2))/x) with respect to cos^(-1)(2xsqr...

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  3. Using properties of determinants, prove that |2yy-z-x2y2z2z z-x-y x-y...

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  4. Write the vector equation of the plane, passing through the point (...

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  5. Let A={1,\ 2,\ 3,\ ,\ 9} and R be the relation on AxxA defined by (a ...

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  6. Evaluate: int(x-3)sqrt(x^2+3x-18)\ dx

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  7. Evaluate : int(sin^6x+cos^6x)/(sin^2xdotcos^2x)dx

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  8. Find the particular solution of the differential equation e^xsqrt(1-y^...

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  9. A dealer in rural area wishes to purchase a number of sewing machin...

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  10. From a lot of 15 bulbs which include 5 defectives, a sample of 4 bu...

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  11. A card from a pack of 52 playing cards is lost. From the remaining car...

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  12. Find the distance between the point (7,2,4) and the plane determined b...

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  13. Find the distance of the point (-1,-5,-10) from the point of intersect...

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

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  15. Assume that each born child is equally likely to be a boy or ...

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  16. Let * be a binary operation, on the set of all-zero real numbers, give...

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  17. If 2[3 4 5x]+[1y0 1]=[7 0 10 5], find (x-y)dot

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  18. If sin(sin^(-1)""(1)/(5)+cos^(-1)x)=1, then find the value of x.

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  19. If |(2x,5),(8,x)|=|(6,-2),(7,3)| then the value of x is

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  20. Solve the following matrix equation for x : ,[x1][1 0-2 0]-Odot

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