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Prove that ((i-sqrt(3))/(i+sqrt(3)))^(10...

Prove that `((i-sqrt(3))/(i+sqrt(3)))^(100)+((i+sqrt(3))/(i-sqrt(3)))^(100)=-1`

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ICSE-MODEL TEST PAPER - 10 -SECTION - A
  1. Find the domain and range of f(x)=(x+2)/(|x+2|).

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  2. List all the proper subsets of {0,{1},3}.

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  3. If a cosA=b cos B, then prove that either the triangle is isosceles or...

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  4. If secx=sqrt(2) and x does not lie in the 1^(st) quadrant, find the va...

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  5. Solve 4cos^(2)x=3,0lexle2pi

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  6. For the quadratic equation (k-1)x^(2)-kx+1=0, find k so that the roots...

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  7. Find the greatest value of 3+5x-2x^(2).

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  8. A function f is defined on the set of real numbers as follows : f(x)...

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  9. If "tan"(x-y)/(2)," tan z, tan"(x+y)/(2) are in G.P., then show that c...

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  10. If alpha and beta are two different values of theta lying between 0 an...

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  11. Using principle of mathematical induction, prove that 5^(n+1)+4.6^(n) ...

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  12. Given that y=(3x-1)^(2)+(2x-1)^(3), find (dy)/(dx) and points on the c...

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  13. Differentiate using 1^(st) principle : f(x)=(1)/(sqrt(2x+3))

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  14. If "tan"(x-y)/(2),tanz,"tan"(x+y)/(2) are in G.P., then show that cosx...

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  15. If the A.M. and G.M. between two numbers are in the ratio x:y, then pr...

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  16. Prove that ((i-sqrt(3))/(i+sqrt(3)))^(100)+((i+sqrt(3))/(i-sqrt(3)))^(...

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  17. The point P(-1,0) lies on the circle x^(2)+y^(2)-4x+8y+k=0. Find the r...

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  18. A line is drawn through the point A(4,-1) and parallel to the line 3x-...

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  19. Lives of LG and Samsung Microwaves that are currently popular were obs...

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