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Write the cartesian equation of the following line given in vector form : ` vec r=2 hat i+ hat j-4 hat k+lambda\ ( hat i- hat j- hat k)`

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Find the vector equation of the following planes in non parametric form: -> r=(2 hat i+2 hat j- hat k)+lambda( hat i+2 hat j+3 hat k)+mu(5 hat i-2 hat j+7 hat k)dot

Find the vector equation of the following planes in Cartesian form: vec r= hat i- hat j+lambda( hat i+ hat j+ hat k)+mu( hat i-2 hat j+3 hat k)dot

Find the vector and Cartesian equations of the plane containing the two lines vec r=2 hat i+ hat j-3 hat k+lambda( hat i+2 hat j+5 hat k)a n d , vec r=3 hat i+3 hat j+2 hat k+mu(3 hat i-2 hat j+ 5hat k)

Find the vector equation of the following plane in scalar product form: vec r=( hat i- hat j)+lambda( hat i+ hat j+ hat k)+mu( hat i-2 hat j+3 hat k) .

Find the vector equation of the following plane in scalar product form: vec r=( hat i- hat j)+lambda( hat i+ hat j+ hat k)+mu( hat i-2 hat j+3 hat k)dot

Find the shortest distance between the following pairs of line whose vector equation are: vec r=3 hat i+8 hat j+3 hat k+lambda(3 hat i- hat j+ hat k)a n d\ vec r=-3 hat i-7 hat j+6 hat k+mu(-3 hat i+2 hat j+4 hat k)

Find the shortest distance between the following pairs of line whose vector equation are: vec r=(3 hat i+5 hat j+7 hat k)+lambda( hat i-2 hat j+7 hat k)a n d\ vec r=- hat i- hat j- hat k+mu(7 hat i-2 hat j+ hat k)

Find the vector equation of the following planes in scalar product form ( vecr . vecn =d): r= hat i- hat j+lambda( hat i+ hat j+ hat k)+mu(-4 hat i-2 hat j+3 hat k)dot

Find the shortest distance between the following pairs of line whose vector equation are: vec r=( hat i+2 hat j+3 hat k+lambda(2 hat i+3 hat j+4 hat k)a n d\ vec r=(2 hat i+4 hat j+5 hat k)+mu(3 hat i+4 hat j+5 hat k)

Find the Cartesian form of the equation of the following plane: vec r=( hat i- hat j)+s( hat i+ hat j+2 hat k)+t( hat i+2 hat j+ hat k)dot

XII BOARD PREVIOUS YEAR PAPER ENGLISH-BOARD PAPER SOLUTIONS-All Questions
  1. Find (dy)/(dx), if y=sin^(-1)[xsqrt(\ 1-x)-\ sqrt(x)\ sqrt(1-x^2)\ ]\

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  2. Show that the function f defined as follows, is continuous at x=2 , ...

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  3. Write the cartesian equation of the following line given in vector ...

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  4. Write the position vector of the mid-point of the vector joining th...

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  5. If vec a\ .\ vec a=0 and vec a\ . vec b=0, then what can be conclud...

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  6. If f: R rarr R is defined by f(x)=3x+2,\ define f\ [f(x)]\

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  7. Write the principal value of tan^-1 (-1)

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  8. Write the values of x-y+z from the following equation: [[x+y+z], [x+z ...

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  9. Write the order of the product matrix : [[1], [2], [3]] [[2,3,4]]

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  10. If |[x, x],[ 1, x]|=|[3, 4],[ 1, 2]|, write the positive value of x

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  11. Evaluate: int((1+logx)^2)/x\ dxdot

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  12. Evaluate: int1^(sqrt(3))(dx)/(1+x^2)

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  13. If int(a x+b^2)\ dx=f(x)+c , find f(x)

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  14. For what value of p , is ( hat i+ hat j+ hat k)p a unit vector?

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  15. What is the value of the following determinant? Delta=|[4,a, b+c],[4...

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  16. What is the domain of the function sin^(-1)x ?

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  17. If 'f' is an invertible function, defined as f(x)=(3x-4)/5, write f...

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

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

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

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