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

show that ``^nC_r+`^(n-1)C_(r-1)+`^(n-1)C_(r-2)=`^(n+1)C_r`

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Show that .^(n)C_(r)+.^(n-1)C_(r-1)+.^(n-1)C_(r-2)=.^(n+1)C_(r) .

.^(n-1)C_(r)+^(n-1)C_(r-1)=

If 2lerlen show that ^nC_r +2 ^nC_(r-1) +^nC_(r-2)=^(n+2)C_r

Show that , (.^(n)C_(r)+^(n)C_(r-1))/(.^(n)C_(r-1)+^(n)C_(r-2))=(.^(n+1)p_(r))/(r.^(n+1)p_(r-1))

Prove that , .^(n)C_(r)+3.^(n)C_(r-1)+3.^(n)C_(r-2)+^(n)C_(r-3)=^(n+3)C_(r)

The roots of the equation |^x C_r^(n-1)C_r^(n-1)C_(r-1)^(x+1)C_r^n C_r^n C_(r-1)^(x+2)C_r^(n+1)C_r^(n+1)C_(r-1)|=0 are a) x=n b) x=n+1 c) x=n-1 d) x=n-2

Show that , .^(n)C_(r)=(n-r+1)/(r).^(n)C_(r-1) .

Prove that .^(n)C_(0) - .^(n)C_(1) + .^(n)C_(2) - .^(n)C_(3) + "……" + (-1)^(r) .^(n)C_(r) + "……" = (-1)^(r ) xx .^(n-1)C_(r ) .

Prove that nC_r+3.nC_(r-1)+3nC_(r-2)+nC_(r-3)=(n+3)C_r

The result of ^(n-1)C_r+^(n-1)C_(r-1)=

UNITED BOOK HOUSE-MODEL QUESTION PAPERS-SET 11-EXERCISE
  1. In /\ABCif1/(a+c)+1/(b+c)=3/(a+b+c),show that angleC=pi/3

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

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

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

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

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

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

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

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

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

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

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  12. Solve :sqrt3sinx+cosx=2

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

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

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

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

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

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

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  19. If the circles x^2+y^2+2ax+c^2=0and x^2+y^2+2by+c^2=0touch each other,...

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  20. Find the co-ordinate of a point equidistance from the points' (0, 0. 0...

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