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If vec a= hat i+ hat j+ hat k ,\ \ vec...

If ` vec a= hat i+ hat j+ hat k ,\ \ vec b=4 hat i-\ 2 hat j+3 hat k` and ` vec c= hat i-\ 2 hat j+ hat k ,` find a vector of magnitude 6 units which is parallel to the vector `2 vec a-\ vec b+3 vec c` .

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XII BOARD PREVIOUS YEAR PAPER ENGLISH-BOARD PAPER SOLUTIONS-All Questions
  1. Find the particular solution of the differential equation: (1+e^(2x))d...

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  2. Let vec a= hat i+4 hat j+2 hat k ,\ \ vec b=3 hat i-\ 2 hat j+7 hat ...

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  3. If vec a= hat i+ hat j+ hat k ,\ \ vec b=4 hat i-\ 2 hat j+3 hat k a...

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  4. Prove, using properties of determinants: |[y+k, y, y],[ y, y+k, y],[...

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  5. Consider f: R^+ rarr [4, oo] given by f(x)=x^2+4. Show that f is inver...

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  6. What are the direction cosines of a line, which makes equal angles ...

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  7. Evaluate: int(dx)/(x(x^5+3))

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  8. Find the value of k so that the function f defined by f(x)={(kcosx)/(...

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  9. Prove that : tan^(-1)(1/2)+tan^(-1)(1/5)+tan^(-1)(1/8)=pi/4dot

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  10. Find the vector and cartesian equations of the line passing through...

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  11. Evaluate: |(cos15^0,sin15^0),(sin75^0,cos75^0)|

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  12. What is the principal value of cos^(-1)cos((2pi)/3)+sin^(-1)sin((2p...

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  13. Let A = {1, 2, 3}, B = {4, 5, 6, 7}and let f = {(1, 4), (2, 5), (3, 6)...

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  14. Evaluate: int(dx)/(sqrt(1-x^2))

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  15. Evaluate: int(a x+b)^3dx

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  16. If a matrix has 5 elements, write all possible orders it can have.

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  17. If A=[[2, 3],[ 5,-2]], write A^(-1) in terms of A

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

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  19. Write the projection of the vector hat i- hat j on the vector ha...

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  20. Write the direction-cosines of the line joining the points (1, 0, 0...

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