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Check if the relation R on set of real n...

Check if the relation R on set of real numbers, defined as `R = {(a,b) : aleb^3}` is reflexsive, symmetric or transitive.

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Show that the relation R in the set of real numbers, defined as R = {(a,b): a le b^(2) } is neither reflexive nor symmetric nor transitive.

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MODERN PUBLICATION-TEST PAPER 1-PROBLEM
  1. Write the distance between the plane x-2y+z=6 and 2x-4y+2z=8

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  2. What is the image of the point (6, 3, -4) with respect to yz- plane ...

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  3. Check if the relation R on set of real numbers, defined as R = {(a,b) ...

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  4. Examine f:(-1,1) rarr R,f(x) = x/(1-x^2functions if it is (i) injecti...

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  5. Solve the following LPP graphically Maximize, Z=20x+30y Subject to...

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  6. Let A and B are symmetric matrices of the same order. Prove that AB is...

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  7. Express abs((a^2,2ab,b^2),(b^2,a^2,2ab),(2ab,b^2,a^2)) in the form of ...

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  8. Verify that [AB]^T = B^T A^T whereA=[[1,2,3],[3,-2,1]],B=[[1,2],[2,0],...

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  9. Discuss the continuity and differentiability of function f(x)=|x|+|x-1...

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  10. If sin (x + y) = y cos (x + y) then prove that dy/dx =-(1 + y^2)/y^2

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  11. Find dy/dx for (x+y)^(cosx) = e^(x+y).

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  12. Prove that , if y=logtan((pi)/(4)+(x)/(2)) , then (dy)/(dx)=secx

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  13. Evaluate : int (cos px + cos qx)/(sin px + sin qx) dx.

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  14. Evaluate int (4x-5)/(x^2-x-2)dx

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  15. FInd the area of the region bounded by y^2 = x and y = x.

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  16. Solve : dy/dx (x^2 - 1) + 2xy = 1.

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  17. Form the differential equation for : y = a sin^-1 x + b cos^-1 x.

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  18. Find the point of intersection of the line 2x - 4= 3y = z with plane x...

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  19. Find the equation of the plane parallel to x - 5y + z + 1 =0 and at a ...

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  20. If 2s=a+b+c show that [[a^2,(s-a)^2,(s-a)^2],[(s-b)^2,b^2,(s-b)^2],[...

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