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Find the position vector of a point `R` which divides the line joining two points `P` and `Q` whose position vectors are `(2\ vec a+ vec b)` and (` vec a-\ 3 vec b)` respectively, externally in the ratio 1:2.Also, show that `P` is the mid-point of the line segment `R Qdot`

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XII BOARD PREVIOUS YEAR PAPER ENGLISH-BOARD PAPER SOLUTIONS-All Questions
  1. Find a unit vector in the direction of vec a=2 hat i-\ 3 hat j+6 hat ...

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  2. If [[y+2x,5],[-x,3]]=[[7, 5],[-2 ,3]], find the value of y

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  3. Find the position vector of a point R which divides the line joinin...

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  4. Find the Cartesian equation of the plane passing through the points...

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  5. What is the cosine of the angle which the vector sqrt(2) hat i+ hat j+...

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  6. On a multiple choice examination with three possible answers (out o...

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  7. If A=(a(i j))= [[2, 3,-5],[1, 4, 9],[ 0, 7,-2]] and B=(b(i j))=[[2, 1,...

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  8. Using elementary row operations, find the inverse of the following m...

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  9. Let Z be the set of all integers and R be the relation on Z defined as...

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  10. Evaluate : int(pi//6)^(pi//3)(sinx+cosx)/(sqrt(sin2x))\ dxdot

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  11. If siny=xsin(a+y), prove that (dy)/(dx)=(sin^2(a+y))/(sina)

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  12. If (cosx)^y=(cosy)^x , find (dy)/(dx)

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  13. Evaluate: intx^2log(1+x)dx\

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  14. Differentiate tan^(-1)[(sqrt(1+x^2)-1)/x] with respect to x

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  15. Prove that the volume of the largest cone, that can be inscribed in...

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  16. Show that the normal at any point theta to the curve x=acostheta+at...

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  17. Evaluate : int0^2sqrt(4-x^2)\ dx

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  18. Given inte^x\ (tanx+1)secx\ dx=e^xf(x)+c, write f(x) satisfying the a...

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  19. If A^T=[3 4-1 2 0 1]\ and B=[-1 2 1 1 2 3], then find A^T-\ B^T

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  20. Let A be a square matrix of order 3\ xx\ 3 . Write the value of |2A|...

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