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Show that the four points with position vectors `4hati+8hatj+12hatk,2hati+4hatj+6hatk,3hati+5hatj+4hatk` and `5hati+8hatj+5hatk` are coplanar.

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Find 'lambda' so that the four points with position vectors -hati+3hatj+2hatk,3hati+lambda hatj+4hatk,5hati+7hatj+3hatk and -13hati+17hatj-hatk are coplanar.

Using scalar triple product, show that the four points given by position vectors : 2hati+3hatj+2hatk,4hati-5hatk,3hati+hatj-2hatk and 5hati+3hatj-4hatk are coplanar.

Using scalar triple product, show that the four points given by position vectors 4hati+5hatj+hatk , -hatj-hatk , 3hati+9hatj+4hatk and -4hati+4hatj+4hatk are coplanar.

Using scalar triple product, show that the four points given by position vectors hati+hatj+10hatk , 2hati+3hatj+11hatk , 3hati+2hatj+6hatk and hati-2hatj+4hatk are coplanar.

Show that the four points A,B,C and D with position vectors 4hati+5hatj+hatk,-(hatj+hatk),(3hati+9hatj+4hatk) and 4(-hati+hatj+hatk) respectively are coplanar.

Using scalar triple product prove that the four points whose position vectors are given by the vectors -hatj+hatk , 2hati-hatj-hatk , hati+hatj+hatk and 3hatj+3hatk are coplanar.

Show that the three points with position vectors -2hati+3hatj+5hatk , hati+2hatj+3hatk and 7hati-hatk are collinear.

Show that the three points with position vectors 2hati+6hatj+3hatk , hati+2hatj+7hatk and 3hati+10hatj-hatk are collinear.

Show that the vectors hati-hatj-hatk,2hati+3hatj+hatk and 7hati+3hatj-4hatk are coplanar.

Show that the four points having position vectors 6hati-7hatj,16hati-19hatj-4hatk,3hatj-6hatk,2hati+5hatj+10hatk are not coplanar.

OMEGA PUBLICATION-HP BOARD MARCH 2017-SERIES -C
  1. Find (dy)/(dx) if xy^2 + y^2 = tan x + y

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  2. If y = 500e^(7x), show that (d^2y)/(dx^2) = 49 y

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  3. Evaluate int(x+3)sqrt(3-4x-x^(2))dx

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  4. Evaluate int e^(x)(1/x-1/(x^(2)))dx.

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  5. Evaluate : int0^(pi/2) (sin^(3/2)x)/(sin^(3/2)x+cos^(3/2)x)dx.

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  6. Solve the differntial equation (dy)/(dx)+y/x=x^(2)

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  7. Solve the differential equation (dy)/(dx)=(x+1)/(2-y),(y!=2)

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  8. Show that the four points with position vectors 4hati+8hatj+12hatk,2ha...

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  9. Find the angle between the pair of lines (x-5)/7=(y+2)/(-5)=z/1 and x...

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  10. A couple has two children, find the probability that both children are...

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  11. Find the probability distribution of number of heads in four tosses of...

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  12. If is known that 10% of certain articles manufactured are defective. W...

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  13. Solve the following system of linear equations by matrix method : 3x -...

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  14. Find the equations of the tangent and normal to the hyperbola x^2/a^2 ...

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  15. Find two positive numbers x and y such that x+y = 60 and xy^3 is maxim...

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  16. Find the area of the region bounded by (y^2=4ax) and its latus rectum ...

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  17. Area lying between the curve y^2 = 4x and the line y = 2x is :

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  18. Find the shortest distance between the lines vecr=hati+2hatj+3hatk+lam...

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  19. Find the coordinates of the point where the line through (5,1,6) and (...

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  20. Solve the following linear programming problem graphically : Maximize ...

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