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Using properties of determinants, prove the following: `|[1,a,a^2],[a^2,1,a],[a,a^2,1]|=(1-a^3)^2`

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Using properties of determinants, prove the following: |[1,x,x^2],[x^2, 1,x],[x,x^2,1]|=(1-x^3)^2

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)

Using properties of determinants, prove the following: |[a^2 + 1,ab, ac], [ab,b^2 + 1,b c],[ca, cb, c^2+1]|=1+a^2+b^2+c^2

Using properties of determinant, prove that |{:( 1,a,a^(2)),(a^(2) , 1,a),( a,a^(2),1):}|=(a^(3) -1)^(2)

Using properties of determinants, prove the following |(a^2+1,ab,ac),(ab,b^2+1,bc),(ca,cb,c^2+1)|=1+a^2+b^2+c^2 .

Using properties of determinants, prove the following |(a^2,ab,ac),(ab,b^2+1,bc),(ca,cb,c^2+1)|=1+a^2+b^2+c^2 .

By using properties of determinants. Show that: |[1,x,x^2],[x^2, 1,x],[x,x^2, 1]|=(1-x^3)^2

Using properties of determinants, prove the following: |[1,1+p,1+p+q],[2,3+2p,1+3p+2q],[3,6+3p,1+6p+3q]|=1

Prove: |(1,a, a^2),(a^2, 1,a),( a, a^2, 1)|=(a^3-1)^2

Using properties of determinants, prove that |[(a+1)(a+2),a+2,1],[(a+2)(a+3),a+3,1],[(a+3)(a+4),a+4,1]|=-2

XII BOARD PREVIOUS YEAR PAPER ENGLISH-BOARD PAPER SOLUTIONS-All Questions
  1. Find the minimum value of (a x+b y), where x y=c^2dot

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  2. Find the coordinates of a point on the parabola y=x^2+7x+2 which is cl...

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

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  4. Solve the following differential equation : (sqrt(1+x^2+y^2+x^2y^2))d...

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  5. If a=[[5,6,-3],[-4,3,2],[-4,-7,3]], then write the cofactor of the e...

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  6. Write the sum of the order and degree of the differential equation ...

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  7. Write the solution of the differential equation (dy)/(dx)=2^(-y)

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  8. Using integration, find the area of the region bounded by the line x...

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  9. Find the probability distribution of the number of doublets in four...

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  10. Find the unit vector in the direction of the sum of the vectors 2 hat ...

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  11. Find the area of a parallelogram whose adjacent sides are represente...

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  12. Find the sum of the intercepts cut off by the plane 2x+y-z=5 , on the ...

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  13. If 2tan^(-1)(costheta)=tan^(-1)(2cos e ctheta),(theta!=0) , then find ...

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  14. If tan^(-1)(1/(1+1. 2))+tan^(-1)(1/(1+2. 3))+.... +tan^(-1)(1/(1+n.(n+...

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  15. Evaluate : int(sin(x-a))/(sin(x+a))dx

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  16. Maximise z = 8x + 9y subject to the constraints given below : 2x+3...

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  17. Evaluate: inte^(2x)sin(3x+1)\ dx

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  18. In a parliament election, a political party hired a public relation...

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  19. Find whether the following function is differentiable at x = 1 and x...

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  20. If y=(x+sqrt(1+x^2))^n , then show that (1+x^2)(d^2y)/(dx^2)+x(dy)/(d...

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