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Prove that all the diagonal elements of ...

Prove that all the diagonal elements of a skew symmetric matrix are zero .

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MODERN PUBLICATION-TEST PAPER 2-PROBLEM
  1. Let ~ be defined by (m,n)~(p,q) if mq=np where m, n, p,qinZ-{0}. Show ...

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  2. If A=[[2,1],[-1,3]], B=[[2,3],[1,1]] "and" C=[[1,0,2],[-2,3,0]],verify...

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  3. Prove that all the diagonal elements of a skew symmetric matrix are ze...

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  4. If x,y,z are positive and are the pth, qth and rth terms of a G.P. the...

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  5. Answer the following: What is the value of [[o,-h,-g],[h,o,-f],[g,f,...

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  6. Show that no two normals to a parabola are parallel.

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  7. Find the intervals where the following functions are (a) increasing an...

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  8. Find int (cos x /sin^(2) x + sin x ) dx

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  9. Evaluate : int(0) ^(pi/4) dx/cos x (cos x + sin x).

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  10. Find the differential equation whose general soltution is c1x^2+c2y=1 ...

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  11. Find the area of the region bounded by the curve y=6x-x^(2), the X-axi...

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  12. Prove the following by vector method. The parallelogram whose diagonal...

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  13. Prove that the two lines whose direction cosines are connected by the ...

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  14. A variable plane meets the coordinate axes at A, B, C and is at a cons...

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  15. Find the equation of the line through the point (3, -1, 2) and paralle...

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  16. If N denotes the set of all natural numbers and R be the relation on N...

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  17. If a, b and c are all positive real, then prove that minimum value of ...

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  18. Solve the following system of equations by the matrix inversion method...

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  19. Find the inverse of [(1,1,2),(0,1,2),(1,2,1)] using elementary operati...

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  20. Show that of all the rectangles inscribed in a given fixed circle, the...

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