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Find the angle between the lines ` vec r=2 hat i-5 hat j+ hat k+lambda(3 hat i+2 hat j+6 hat k)` and ` vec r=7 hat i-6 hat k+mu( hat i+2 hat j+2 hat k)dot`

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Find the angle between the lines vec r=(2 hat i-5 hat j+ hat k)+lambda(3 hat i+2 hat j+6 hat k)a n d\ vec r=7 hat i-6 hat k+mu( hat i+2 hat j+2 hat k)dot

Find the angle between the lines vec r=3 hat i+2 hat j-4 hat k+lambda( hat i+2 hat j+2 hat k) a n d vec r=(5 hat j-2 hat k)+mu(3 hat i+2 hat j+6 hat k)dot

Find the shortest distance between the following lines: vec r=2 hat i-5 hat j+ hat k+lambda(3 hat i+2 hat j+6 hat k) and vec r=7 hat i-6 hat k+mu( hat i+2 hat j+2 hat k)

Find the angel between the following pair of lines: vec r=2 hat i-5 hat j+ hat k+lambda(3 hat i+2 hat j+6 hat k)a n d vec r=7 hat i-6 hat k+mu( hat i+2 hat j+2 hat k) x/2=y/2=z/1a n d(x-5)/4=(y-2)/1=(z-3)/8

Find the shortest distance between the lines: vec r=6 hat i+2 hat j+2 hat k+lambda( hat i-2 hat j+2 hat k)a n d\ vec r=-4 hat i- hat k+mu(3 hat i-2 hat j-2 hat k)dot

Find the shortest distance between the lines: vec r=6 hat i+2 hat j+2 hat k+lambda\ ( hat i-2 hat j+2 hat k) and vec r=-4 hat i- hat k+mu\ (3 hat i-\ 2 hat j-\ 2 hat k)

Find the shortest distance between the lines vec r=( hat i+2 hat j+ hat k)+lambda( hat i- hat j+ hat k) and vec r=2 hat i- hat j- hat k+mu(2 hat i+ hat j+2 hat k)

Find the shortest distance between the lines vec r=( hat i+2 hat j+ hat k)+lambda( hat i- hat j+ hat k) and vec r=(2 hat i- hat j- hat k)+mu(2 hat i+ hat j+2 hat k)

Find the angle between the following pairs of lines:(i) -> r=2 hat i-5 hat j+ hat k+lambda(3 hat i+2 hat j+6 hat k) and -> r=7 hat i-6 hat k+mu( hat i+2 hat j+2 hat k) (ii) -> r=3 hat i+ hat j-2 hat k+lambda( hat i- hat j-2 hat k) and -

Find the shortest distance between the lines: vec r= hat i+2 hat j+3 hat k+lambda( hat i-3 hat j+2 hat k)a n d\ vec r=4 hat i+5 hat j+6 hat k+mu(2 hat i+3 hat j+ hat k)dot

XII BOARD PREVIOUS YEAR PAPER ENGLISH-BOARD PAPER SOLUTIONS-All Questions
  1. Solve the differential equation (x^2-y)dy+(y^2+x^2y^2)dx=0, given t...

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  2. Solve the differential equation (dy)/(dx)+ycotx=2cosx , given that ...

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  3. Find the angle between the lines vec r=2 hat i-5 hat j+ hat k+lambda(...

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  4. Let f:W->W , be defined as f(x)=x-1 , if x is odd and f(x)=x+1 , if x ...

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  5. Using properties of determinants, prove that |[a+x,y,z],[x,a+y,z],[x,y...

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  6. x=acostheta+bsintheta and y=asintheta-bcostheta, show that y^2(d^2y)/(...

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  7. If x^my^n=(x+y)^(m+n) prove that (dy)/(dx)=y/x

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  8. Two schools P and Q want to award their selected students on the va...

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  9. An insurance company insured 2000 scooter drivers, 4000 car drivers...

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  10. Three cards are drawn at random (without replacement) from a well shuf...

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  11. Evaluate : int(xcos^(-1)x)/(1-x^2)dx

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  12. Evaluate :int(3x-2)sqrt(x^2+x+1) dx

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  13. In answering a question on a multiple choice test, a student either kn...

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  14. A manufacturer produces nuts and bolts. It takes 2 hours work on machi...

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  15. Solve the differential equation : (xsin^2(y/x)-y)dx+xdy=0 given y=pi/4...

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  16. The sum of surface areas of a sphere and a cuboid with sides x/3,x and...

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  17. Show that the relation R in the set A = {1, 2, 3, 4, 5} given by R = {...

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  18. Using properties of determinants, solve for x:|[a+x, a-x, a-x],[ a-...

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  19. A trust fund has Rs. 35,000 is to be invested in two different types o...

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  20. Find the solution f the differential equation (dy)/(dx)=x^3e^(-2y)dot

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