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Consider the binary operation **:R xxR t...

Consider the binary operation `**:R xxR to R and o:R xx R to R` defined as `a**b = |a-b| and a o b = a `. For all `a , b in R`. Show that * is commutative but not associative, .o. is associative but not commutative.

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ARIHANT PRAKASHAN-VERY SIMILAR TEST 2 -SECTION -B
  1. Prove that tan^(-1)((6x-8x^(3))/(1-12x^(2)))-tan^(-1)((4x)/(1-4x^(2)))...

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  2. Find the feasible region of the following system 2x+yge6,x-yle3,xge0...

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  3. Consider the binary operation **:R xxR to R and o:R xx R to R defined ...

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  4. If the function'f : R rarrR is given by f(x) = x^(2) +2 and g:R rarr R...

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  5. Solve for x, 2 tan ^(-1)(cos x) =tan^(-1) (2"cosec"x).

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  6. Factorize the following. [[x,2,3],[1,x+1,3],[1,4,x]]

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  7. If A=[{:(1,2,2),(2,1,-2),(x,2,y):}] is a matrix satisfying AA=9I, then...

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  8. If A=[a(ij)] is a square matrix such that a(ij)=i^(2)-j^(2) , the...

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  9. If A(x(1), y(1)), B(x(2), y(2)), and, C(x(3), y(3)) are vertices of an...

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  10. A random variable X has following probability distribution . Fin...

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  11. A random variable X has following probability distribution . Fin...

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  12. A random variable X has following probability distribution . Fin...

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  13. A random variable X has following probability distribution . Fin...

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  14. If x=sqrt(a^(sin^(-1)t)),y=sqrt(a^(cos^(-1)t)), then show that (dy)/(d...

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  15. Find the extreme points of the function f(x)=x^(2)sqrt(1-x^(2)). Als...

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  16. Verify the LMVT for the function f(x)=(1)/(4x-1),1lexle4.

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  17. Using differentials, find approximate value (255)^(1//4)

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  18. Find the equations of all lines having slope -1, that are tangent to t...

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  19. Evaluate int(1)/(sqrt(8+3x-x^(2)))dx.

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  20. Evaluate int(0)^(pi//4)tan^(5)xdx.

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