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In what interval f(x)=log(5) x is decrea...

In what interval `f(x)=log_(5) x` is decreasing (if any) ?

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MODERN PUBLICATION-TEST PAPER 8-EXERCISE
  1. If [{:(3,2),(7,x):}][{:(5,-2),(-7,y):}]=[{:(1,0),(0,1):}] then find th...

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  2. If y=at^2 and x=2at then find (d^2y)/dx^2 at x=1/2.

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  3. In what interval f(x)=log(5) x is decreasing (if any) ?

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  4. Write the value of int(-1)^1 (sin^5 x + 5)dx .

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  5. The degree of the differential equation satisfying sqrt(1-x^2)+sqrt(1+...

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  6. Write the value of y so that the points (1,y,2),(3,2,-1) and (-4,6,3) ...

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  7. Write the equation of the plane passing through (1,2,3) and parllel to...

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  8. Let A = {1, 2, 3). Then, show that the number of relations containing ...

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  9. Test whether the relations are reflexive, symmetric or transitive on t...

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  10. Let * be the binary operation on N given by a*b = LCM of a and b. Fin...

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  11. Show that f:R to R defined as f(x)= 4x+3 is invertible. Find the inver...

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  12. Express A=[[x,a,b],[a,y,c],[b,c,z]] as the sum of a symmetric and a sk...

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

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  14. Prove that |[a-b-c,2a,2a],[2b, b-c-a, 2b],[2c, 2c, c-a-b]|= (a+b+c)^3.

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  15. Find the inverse of the following matrix [{:(1,1,2),(0,1,2),(1,2,1):}]...

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  16. Prove that the following. [[a,b,c],[x,y,z],[p,q,r]]=[[y,b,q],[x,a,p],[...

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  17. Examine the contiunity of the the following functions at indicated poi...

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  18. Differentiate : (sec x+ tan x)^cot x.

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  19. If y=e^(ax)sinbx show that y2-2ay1+(a^2+b^2)y=0.

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  20. Prove the inequality x^2e^(-x^2) le e^(-1),x in R.

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