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Prove that : [(vec a × vec b) (vec b × v...

Prove that : `[(vec a × vec b) (vec b × vec c) (vec c × vec a)] = [vec a vec b vec c]^(2)`.

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MODERN PUBLICATION-SAMPLE PAPER 2015-EXERCISE
  1. Solve the following differential equation : x^(2)(y-1)dx+y^(2)(x-1)dy ...

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  2. Prove that the lines joining the midpoints of consecutive sides of a q...

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  3. Prove that : [(vec a × vec b) (vec b × vec c) (vec c × vec a)] = [vec ...

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  4. If vec a, vec b, vec c are mutually perpendicular vectors of equal mag...

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  5. Prove that the measure of the angle between two main diagonals of a cu...

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  6. Find the equation of the plane through the points (1, 2, -3), (2,3, -4...

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  7. Find the perpendicular distance of the point (-1,3,9) from the line (x...

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  8. Solve the following LPP graphically : Minimize Z = 6x(1)+7x(2) Sub...

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  9. Find the feasible region the the following system of equations 2y-xge0...

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  10. Solve the following equations by cramer's rule : 7x+y+1 = 0, x+13y+5 =...

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  11. If A=[{:(3,-4),(1,-1):}] then show that A^(k)=[{:(1+2k,-4k),(k,1-2k):}...

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  12. If A =[[1,-2,2],[3,1,-1]] B[[2,4],[1,2],[3,-1]] "verify" "that" (AB)^...

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  13. How many four digits even numbers with distict digits can be formed ou...

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  14. In how many ways can 10 boys and 10 girls sit in a row so that no two ...

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  15. Find the fifth term in the expansion of (6x-a^3/x)^10

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  16. Two different digits are selected at random from the digits 1 through ...

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  17. Suppose that the probability that your alarm goes off in the morning i...

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  18. Find the tangent to the curve y = cos (x + y), 0 le x le 2pi which is ...

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  19. Evaluate intfrac[dx][cosx(1+2sinx)]

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  20. If vec a = 2 hat i + hat j, vec b = - hat i + 2 hat k, vec c = 2 hat i...

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