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Express the matrix A=[[2,4,-6],[ 7,3,5],...

Express the matrix `A=[[2,4,-6],[ 7,3,5],[ 1,-2, 4]]` as the sum of a symmetric and skew symmetric matrix.

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XII BOARD PREVIOUS YEAR PAPER ENGLISH-BOARD PAPER SOLUTIONS-All Questions
  1. In the interval pi/2 lt x lt pi, find the value of x for which the mat...

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  2. Write the vector equation of the line passing through (1,2,3) and pe...

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  3. Express the matrix A=[[2,4,-6],[ 7,3,5],[ 1,-2, 4]] as the sum of a sy...

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  4. Write the direction ratios of the vector 3 vec a+2 vec b where vec a=...

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  5. Find the vector and cartesian equations of the plane passing through t...

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  6. Solve the differential equation (dy)/(dx)-3ycotx=sin2x given y=2 when ...

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  7. Solve for x :tan^(-1)((1-x)/(1+x))=1/2tan^(-1)x ,x >0

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  8. Prove that 2tan^(-1)(1/2)+tan^(-1)(1/7)=sin^(-1)((31)/(25sqrt(2)))

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  9. Find : int0^(1/(sqrt(2)))(sin^(-1)x)/((1-x^2)^(3/2))dx

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  10. Find : intx/((x^2+1)(x-1))dx

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  11. Find the areas of the region {(x , y): y^2lt=4x ,4x^2+4y^2lt=9}, using...

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  12. Find the area enclosed by the parabola 4y=3x^2 and the line 2y=3x+12.

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  13. Find the projection of the vector vec a=2 hat i+3 hat j+2 hat k on th...

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  14. If y=A e^(m x)+B e^(n x), show that (d^2y)/(dx^2)-(m+n)(dy)/(dx)+m n y...

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  15. Find : int(x+3)/(sqrt(5-4x+x^2))dx

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  16. Find the shortest distance between the following lines: vec r=2 hat i...

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  17. For what value of lambda the function defined by f(x)={lambda(x^2+2),i...

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  18. If x=a e^t(sint+cost) and y=a e^t(sint-cost), prove that (dy)/(dx)=(x+...

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  19. Evaluate : int0^(pi/4)log(1+tanx)dxdot

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  20. Find : intx/((x-1)^2(x+2))dx

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