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In /\ABCif1/(a+c)+1/(b+c)=3/(a+b+c),show...

In `/_\ABC`if`1/(a+c)+1/(b+c)=3/(a+b+c)`,show that `angleC=pi/3`

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UNITED BOOK HOUSE-MODEL QUESTION PAPERS-SET 11-EXERCISE
  1. If f:fRrarrR^+defineed as f(x)=x^2,show that f is surjective.

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  2. If cotalphacotbeta=3,show that (cos(alpha-beta))/(cos(alpha+beta))=2

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  3. In /\ABCif1/(a+c)+1/(b+c)=3/(a+b+c),show that angleC=pi/3

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  4. Express(sqrt3-i)/(1-sqrt3i)in modulus amplitude form

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  5. show that ^nCr+^(n-1)C(r-1)+^(n-1)C(r-2)=^(n+1)Cr

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  6. Find the middle term of the expansion of (P^2-1/P)^9

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  7. Show that the sum of 4 + 12 + 20 + 28 + .... up to n the term is a squ...

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  8. If the distance from- origin to- the straight line 3x + 5y + a = 0 is3...

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  9. Find the co-ordinate of the image of (3, 2, -4) on xy plane.

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  10. If f(x)=x^5+x^3-2x+3,Prove that f'(1)+f'(-1)=4f(0).

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  11. Evaluate :lim(xrarroo)(1+2+3+...+n)/n^2

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  12. For any three sets A,B and C ,prove that A-(BcupC)=(A-B)cap(A-C).

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  13. For any two positive acute angles theta and phi if sin(theta+phi)=k s...

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  14. Solve :sqrt3sinx+cosx=2

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  15. Prove by mathematical induction. 1.1! + 2. 2! + 3. 3! + ... +n . n! = ...

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  16. If z = x + iy then l z - 8| + Iz + 8| = 20. represents a ellipse

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  17. If (1+x)^n=c0+c1x+c2x^2+....+cnx^n,then show that c0/1+c2/3+c4/5+...=2...

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  18. If the ath and bth term of an AP are 1/b and 1/a,then show that (ab)th...

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  19. In /\XYZthe co-ordinate of Y and Z are (-a, 0) and (a, 0), andangle XZ...

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  20. If the three straight lines ax + 2y + 1 = 0, 3y + bx + 1 = 0 and cx+ 4...

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