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Show that |{:(1,x, x ^(3)),(1,y,y ^(3)),...

Show that `|{:(1,x, x ^(3)),(1,y,y ^(3)),(1,z,z^(3)):}| = (x-y) (y-z) (z-x) (x + y + z)`

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using the properties of determinants prove that |{:(1,x+y,x^2+y^2),(1,y+z,y^2+z^2),(1,z+x,z^2+x^2):}|=(x-y)(y-z)(z-x)

Prove that |{:(x,y,z),(x^2,y^2,z^2),(yz,zx,xy):}|=|{:(1,1,1),(x^2,y^2,z^2),(x^3,y^3,z^3):}|=(x-y) (y-z) (z-x) (xy+yz+zx)

Prove that |[x, y, z],[x^2, y^2, z^2], [x^3, y^3, z^3]|=xyz(x-y)(y-z)(z-x)

Show that: |[x, y ,z],[x^2, y^2, z^2], [yz, zx, xy ]|=(x-y)(y-z)(z-x).(xy+yz+zx)

If x,y and z are different and Delta=|{:(x,x^2,1+x^3),(y,y^2,1+y^3),(z,z^2,1+z^3):}|=0 then show that 1+xyz=0

If x+y+z=xyz , prove that (3x-x^3)/(1-3x^2)+(3y-y^3)/(1-3y^2)+(3z-z^3)/(1-3z^2) = (3x-x^3)/(1-3x^2) cdot(3y-y^3)/(1-3y^2)cdot(3z-z^3)/(1-3z^2)

ARIHANT PUBLICATION-SAMPLE PAPER 3 -SHORT ANSWER TYPE QUESTIONS
  1. Answer the question : Evaluate int(2x^(3) + 3x^(2) +5) dx

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  2. If A = [{:(0,2),(3,-4):}] and KA = [{:(0, 3a),(2b, 24):}], then find v...

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  3. Show that |{:(1,x, x ^(3)),(1,y,y ^(3)),(1,z,z^(3)):}| = (x-y) (y-z) (...

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  4. Find the inverse of the following matrix [{:(1,3,-2),(-3,0,-1),(2,1,...

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  5. A card from a pack of 52 playing cards is lost. From the remaining car...

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  6. How many times must a man toss a fair coin so that the probability of ...

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  7. If f(x+y) = f(x) f(y) for all x,y and if f(5) = 2 and f(0) = 3, then w...

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  8. Show that the function f(x) given by f(x)={:{(x" sin "(1)/(x)", if ...

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  9. Show that the line (x)/(a) + (y)/(b) = 1, touches the curve y = be^(-x...

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  10. If f(x) = a In x + bx^2 + x has extreme values at x= - 1 and x = 2 the...

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  11. If x = 3 sin t - sin 3t, y = 3 cos t - cos 3t, find (dy)/(dx) at t = (...

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  12. Evaluate int(2x^(3) + 3x^(2) +5x+2) dx

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  13. Solve the following differerntial equation x (dy)/(dx) + y = x cos x +...

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  14. Evaluate int (x ^(2) +1)/( (x +1) ^(2)) dx

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  15. Evaluateint (cosxtan x )/((sec x + tan x )) dx

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  16. Find the area of region included between the parabola 4y = 3x^(2) and ...

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  17. Find the direction consines of the perpendicular from the origin to th...

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  18. If veca and vecb are unit vectors such that vecaxxvecb is a unit vecto...

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  19. Using vectors, find the area of the Delta ABC, whose vertices are A(1,...

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  20. Prove that the lines x = ay + b, z = cy + d and x = a'y + b' , z= c'y ...

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