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Find the direction cosines of the line passing through the following points: `(-2,\ 4,\ -5),\ \ (1,2,3)dot`

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XII BOARDS PREVIOUS YEAR-BOARD PAPER SOLUTIONS-All Questions
  1. If 'f' is an invertible function, defined as f(x)=(3x-4)/5, write f...

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  2. Write a square matrix of order 2, which is both symmetric and skew ...

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  3. Find the direction cosines of the line passing through the followin...

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  4. If A=[[1, 2],[ 4, 2]], then find the value of k if |2A|=k\ |A|

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  5. If | vec a|=sqrt(3)\ | vec b|=2\ \ and vec a.vec b=sqrt(3,)\ find t...

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  6. A pair of dice is thrown 4 times. If getting a doublet is considere...

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  7. Evaluate: int0^1 1/(1+x^2)\ dx

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  8. Write the principal value of cos^(-1)(1/2)-2sin^(-1)(-1/2)

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  9. Simplify : cos theta[[costheta,si ntheta],[-si ntheta,costheta]]+si nt...

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  10. Evaluate int1^4(x^2-\ x)\ dx as a limit of sums.

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  11. If Delta=|[5, 3 ,8],[ 2, 0 ,1],[ 1 ,2 ,3]| , write the minor of the el...

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  12. Evaluate : int(1-x)sqrt(x)\ dxdot

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  13. Evaluate: int0^(pi/4)(sinx+cosx)/(9+16sin2x)dx

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  14. Find lambda where projection of vec (a) = lambda hat (i) + hat (j) ...

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  15. If a line has direction ratios 2, –1, –2, then what are its directi...

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  16. Write the vector equation of the line given by (x-5)/3=(y+4)/7=(z-6...

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  17. Prove that: tan^(-1)[(sqrt(1+x)-sqrt(1-x))/(sqrt(1+x)+sqrt(1-x))]=pi/4...

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  18. Using properties of determinants, solve the following for x: |[x-2, ...

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  19. If x=tan(1/alogy)\ , show that (1-x^2)(d^2\ y)/(dx^2)+(2x-a)(dy)/(dx)=...

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  20. Evaluate: int0^(pi/2)(x+sinx)/(1+cosx)

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