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Using properties of determinants, prove the following: `|xx+y x+2y\ x+2y xx+y x+y x+2y x|=9y^2(x+y)`

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Using properties of determinants, prove the following |[x,x+y,x+2y],[x+2y,x,x+y],[x+y,x+2y,x]|=9y^2(x+y)

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)

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

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 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 |[a+x,y,z],[x,a+y,z],[x,y,a+z]|=a^2(a+x+y+z)

By using properties of determinants. Show that: (i) |x+4 2x2x2xx+4 2x2x2xx+4|=(5x-4)(4-x)^2 (ii) |y+k y y y y+k y y y y+k|=k^2(2ydotk)^2

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)

By using properties of determinants. Show that: (i) |(x+4,2x,2x),(2x,x+4,2x),(2x,2x,x+4)|=(5x-4)(4-x)^2 (ii) |(y+k,y,y),(y,y+k,y),(y,y,y+k)|=k^2(3y+k)

XII BOARD PREVIOUS YEAR PAPER ENGLISH-XII Boards-All Questions
  1. int1/(x^2-4x+8)dx

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  2. Prove that tan(pi/4+1/2 cos^-1(a/b))+tan(pi/4-1/2 cos^-1(a/b))=(2b)/a

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  3. Using properties of determinants, prove the following: |xx+y x+2y\...

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  4. Find the value of c in Rolle’s theorem for the function f(x) = x^3– 3...

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  5. Differentiate the function (sin x)^x+ sin^(-1) sqrtx with respect to...

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  6. The volume of a cube is increasing at the rate of 9cm3/sec. How fas...

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  7. Evaluate: int(2x)/((x^2+1)(x^2+2))dx

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  8. Evaluate: int0^pi(xsinx)/(1+cos^2x)\ dx

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  9. Prove that x^2-y^2=c(x^2+y^2)^2 is the general solution of differe...

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  10. Show that the function f(x) = x^3– 3x^2 + 6x – 100 is increasing on R

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  11. The x-coordinates of a point on t line joining the points Q(2,2,1)a...

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  12. The random variable X can the values 0, 1, 2, 3, Give P(X = 0) = P(X =...

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  13. A die marked 1, 2, 3 in red and 4, 5, 6 in green is tossed. Let A be ...

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  14. Often it is taken that a truthful person commands, more respect in ...

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  15. Two tailors, A and B, earn 300 and 400 per day respectively. A can st...

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  16. Find : int (dx)/(5-8x-x^2)

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  17. Discuss the commutativity and associativity of binary operation * d...

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  18. If the sum of lengths of hypotenuse and a side of a right angled tri...

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  19. Using integration, find the area of region bounded by the triangle who...

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  20. If tan^-1 ((x-3)/(x-4))+tan^-1((x+3)/(x+4))=pi/4, find x

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