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check whether the relation R in the set ...

check whether the relation R in the set N of natural numbers given by
R = { (a,b) : a is divisor of b }
is reflexive, symmetric or transitive. Also determine whether R is an equivalence relation

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Check whether the relation R in the set N of natural numbers given by R = { (a,b) : a is a divisor of b } is reflexive, symmetric or transitive. Also determine whether R is an equivalence relation

Determine whether Relation R on the set N of all natural numbers defined as R={(x ,\ y): y=x+5 and x<4} is reflexive, symmetric or transitive.

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

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Determine whether Relation R on the set Z of all integer defined as R={(x ,\ y): (x-y) =i n t e g e r} is reflexive, symmetric or transitive.

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Determine whether Relation R on the set A={1,\ 2,\ 3,\ 4,\ 5,\ 6} defined as R={(x ,\ y): y is divisible by x} is reflexive, symmetric or transitive.

Show that the relation R on the set Z of integers, given by R={(a ,\ b):2 divides a-b} , is an equivalence relation.

XII BOARD PREVIOUS YEAR PAPER ENGLISH-XII Boards-All Questions
  1. If A is a non-singular square matrix of order 3 such that A^2= 3A, the...

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  2. Find the area, lying above the x-axis and included between the circle ...

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  3. check whether the relation R in the set N of natural numbers given by ...

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  4. Given a skew symmetric matrix A = [ (0, a , 1),(-1, b, 1),(-1, c, 0)],...

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  5. Using the method of integration find the area of the triangle ABC, co...

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  6. Find the points of intersection of the line vecr = (2hati - hatj + 2h...

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  7. Prove that tan^(-1) (1/4) + tan^(-1) (2/9) = 1/2 sin^(-1) (4/5)

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  8. The vectors 3 hat i- hat j +2 hat k', 2 hat i+hat j + 3 hat k and hat ...

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  9. Find : int{(x^3 + 1)/(x^3-x)}dx

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  10. If tan^(-1)(Y/X) = log (sqrt(X^2+Y^2)) , prove that (dy/dx) = ((X+Y)/(...

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  11. Find the shortest distance between the lines vecr = 2hati - hatj + hat...

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  12. Find: int((tan^(3)x)/(cos^(3)x)) dx

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  13. Solve the following differential equation: (1+ e ^(y/x)) dy + e^(y...

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  14. Find f'(x) if f(x) = tan x^(tan x)

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  15. If y=e^(acos^(-1)x),-1lt=x<1, show that (1-x^2)(d^2y)/(dx^2)-x(dy)/(d...

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  16. If f(x) = sqrt ((sec x -1)/(sec x + 1)) , find f'( pi /3)

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  17. The area of the triangle formed by the vertices O, A, and B, where vec...

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  18. If A = [(5, -1, 4), (2, 3, 5), (5, -2, 6)] , find A^(-1) and use it t...

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  19. The vectors 3hati - hatj +2hatk, 2hati+hatj+3hatk and hati+lambdahatj-...

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  20. A cottage industry manufactures pedestal lamps and wooden shades.Both ...

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