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Prove that:|[1, a ,a^2],[a^2, 1 ,a],[a, ...

Prove that:`|[1, a ,a^2],[a^2, 1 ,a],[a, a^2, 1]|` is a perfect square.

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USHA PUBLICATION-MODEL QUESTION SET-MODEL QUESTION SET
  1. If A=[{:(1,-2,2),(3,1,-1):}]andB=[{:(2,4),(1,2),(3,-1):}] , then veri...

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  2. Find B if B^(2)=[{:(17,8),(8,17):}]

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  3. Prove that:|[1, a ,a^2],[a^2, 1 ,a],[a, a^2, 1]| is a perfect square.

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  4. If ysqrt(x^2 +1) = log{sqrt(x^2 +1)- x} then prove that (x^2 +1) dy/dx...

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  5. If y=tan^(-1)(cosx/(1+sinx)),then prove that dy/dx=-1

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  6. Let f(x)={(1/(x+[x]),if xlt0),(-1,if xge0):} Examine the continuity of...

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  7. Show that the function e^x/x^p is strictly increasing for x gt p gt 0.

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  8. Find the equation of tangents and normals to the parabola y^2=4ax at t...

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  9. Find the solution of the following differential equations: (4x+6y+5)dx...

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  10. Evaluate inte^x((1+sinx)/(1+cosx))dx.

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  11. Evaluate the integral: int(x^2-4)/(x-2)dx

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  12. Solve the following differential equations (x+tany)dy= sin 2y ""dx

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  13. Evaluate int0^7 [x/3]dx

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  14. Prove that the point (1,2,3),(-1,1,0),(2, 1, 3) and (1, 1, 2) are copl...

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  15. If veca and vecb are unit vectors represented by the adjacent sides of...

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  16. Find the distance of the point (1,-2,3) from the plane x-y+z=5, measur...

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  17. Find the angle which a diagonal of a cube makes with one of its edges.

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  18. Find the value of k for which A (1,0,3), B(-1,2,4), C(1,2,1) and D(k,2...

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  19. Show that (veca-vecb)xx(veca+vecb) = 2(vecaxxvecb). Interpret this res...

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  20. Find the area of the parallelogram whose diagonals are vectors 3hati+h...

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