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Find the equation of the plane which contains the line of intersection of the planes ` vec r` . `( hat i+2 hat j+3 hat k)-4=0,\ vec r`.`(2 hat i+ hat j- hat k)+5=0` and which is perpendicular to the plane ` vec r`.`(5 hat i+3 hat j-6 hat k)+8=0.`

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Find the vector equation of the plane which contains the line of intersection of the plane vec rdot( hat i+2 hat j+3 hat k)-\ 4=0 and vec rdot(2 hat i+ hat j- hat k)+5=0 and which is perpendicular to the plane vec rdot(5 hat i+3 hat j-\ 6 hat k)+8=0.

Find the equation the plane which contain the line of intersection of the planes vec rdot( hat i+2 hat j+3 hat k)-4=0a n d vec rdot(2 hat i+ hat j- hat k)+5=0 and which is perpendicular to the plane vec r(5 hat i+3 hat j-6 hat k)+8=0 .

Find the equation of the plane passing through the intersection of the planes vec r .(2 hat i+ hat j+3 hat k)=7, vec r.(2 hat i+5 hat j+3 hat k)=9 the point (2,1,3)dot

Find the unit vector perpendicular to the plane vec rdot(2 hat i+ hat j+2 hat k)=5.

Find the equation of the plane passing through the intersection of the planes vec rdot( hat i+ hat j+ hat k)=\ 6,\ vec rdot\ \ (2 hat i+3 hat j+4 hat k)=\ -5 and the point (1,1,1).

Find the equation of the plane passing through the intersection of the planes vec rdot( (hat i+ hat j+ hat k)=1\ a n d\ vec rdot((2 hat i+3 hat j- hat k)+4=0 and parallel to x-axis.

Find the equation of the plane through the line of intersection of the planes vec rdot(( hat i+3 hat j)+6=0\ a n d\ vec rdot((3 hat i- hat j-4 hat k)=0, which is at a unit distance from the origin.

Find the distance between the parallel planes vec r.( hat i+2 hat j+3 hat k)+7=0a n d vec r.(2 hat i+4 hat j+6 hat k)+7=0.

Find the equation of a plane through the intersection of the planes vec rdot( hat i+3 hat j- hat k)=5a n d vec rdot(2 hat i- hat j+ hat k)=3 and passing through the point (2,1,-2)dot

Find the distance between the parallel planes, vec r.(2 hat i-3 hat j+6 hat k)=5 a n d vec r.(6 hat i-9 hat j+18 hat k)+20=0.

XII BOARD PREVIOUS YEAR PAPER ENGLISH-BOARD PAPER SOLUTIONS-All Questions
  1. Show that of all the rectangles inscribed in a given fixed circle, ...

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  2. Using integration find the area of the triangular region whose side...

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  3. Find the equation of the plane which contains the line of intersecti...

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  4. Find a unit vector perpendicular to each of the vector vec a+ vec ...

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  5. Find the angle between the following pair of lines: (-x+2)/(-2)=(y-...

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  6. Probabilities of solving a specific problem independently by A and ...

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  7. If x=a^(sin^-1 t) ,\ y=a^(cos^-1t) ,\ show that (dy)/(dx)=-y/x

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  8. Find the point on the curve y=x^2 where the slope of the tangent is eq...

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  9. Find the intervals in which the function f given by f(x)=sinx+cosx ,\...

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  10. A factory makes tennis rackets and cricket bats. A tennis racket ta...

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  11. Suppose 5% of men and 0.25% of women have grey hair. A grey haired ...

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  12. 2 tan^(-1) (cos x) = tan^(-1) (2 cosec x)

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  13. Prove that: cot^(-1)((sqrt(1+sinx)+sqrt(1-sinx))/(sqrt(1+sinx)-sqrt(1-...

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  14. Write the value of the following determinant: |[102, 18, 36],[ 1, 3,...

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  15. If x[[2],[ 3]]+y[[-1],[ 1]]=[[10],[ 5]], write the value of x.

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  16. If int0^a3x^2dx=8,\ write the value of a.

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  17. If int((x-1)/(x^2))e^x dx=f(x)e^x+c , then write the value of f(x).

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  18. If the binary operation * on the set Z of integers is defined ...

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  19. If I is the identity matrix and A is a square matrix such that A...

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  20. Write the value of "cot"(tan^(-1)a+cot^(-1)a).

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