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Express in the form A+iB,(A,B are real),...

Express in the form A+iB,(A,B are real),`i/(1+i)+(1+i)/i`

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UNITED BOOK HOUSE-TECHNO INDIA GROUP ACADEMIA,SOUTH KOLKATA.-EXERCISE
  1. In /\ABC,a=2,b=3 and sin A=2/3.Find |B

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  2. Prove that ,(sin2x)/(1+cos2x)=tanx

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  3. Express in the form A+iB,(A,B are real),i/(1+i)+(1+i)/i

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  4. If (2n)C3:nC3=11:1find n.

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  5. The n term of an A.P is 7n-5,find the sum of first 20 terms of the se...

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  6. Find the 4the term from the end in the expansion of (x^3/2-2/x^2)^9

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  7. Find the equation of the perpendicular bisect or of the line joining t...

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  8. Find the ratio in which the line segment joining A(2,4,5) and B(3,5,4)...

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  9. Evaluate :lim(hrarr0)(e^h h)/h-1

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  10. If f(x)=x|x|,prove that f'(x)=2|x|.

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  11. In a lottery there are 10 prizes and 25 blanks.Find the probability of...

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  12. Find mean and variance for the following data 5,9,8,12,6,10,6,8.

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  13. For any three sets A, B, C. show thatAxx(B-C)=(AxxB)-(AxxC)

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  14. In any /\ABC,prove that sin(B-C)/(sin(B+C))=(b^2-c^2)/(a^2)

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  15. Prove that,cosx/(1-sinx)=tan(pi/4+x/2)

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  16. Prove by mathematical induction that1/1.3+1/3.5+1/5.7+...+1/((2n-1)(2n...

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  17. If x+iy=2/(3+costheta+isintheta),show that 2x^2+2y^2=3x-1

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  18. find the co-efficient of (2r+4)th and (r-2)th terms in the expansion o...

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  19. If p, q, r are in G.P and the equation px^2+2qx+r=0 and dx^2+2ex+f=0 h...

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  20. Show that the points (a,0),(0,b)and (3a,-2b)are collinear.Also find th...

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