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If m=^nC2show that ^mC2=3^(n+1)C4...

If m=``^nC_2`show that ``^mC_2=3^(n+1)C_4`

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If m=.^(n)C_(2) show that , .^(m)C_(2)=3.^(n+1)C_(4)

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

Find the sum of the series .^(n)C_(0)+2.^(n)C_(1)x+3.^(n)C_(2)x^(2)+....+(n+1).^(n)C_(n)x^(n) and hence show that , .^(n)C_(0)+2.^(n)C_(1)x+3.^(n)C_(2)x^(2)+....+(n+1)^(n)C_(n)=(n+2)2^(n-1)

If (1+x)^n=sum_(r=0)^n^n C_r , show that C_0+(C_1)/2++(C_n)/(n+1)=(2^(n+1)-1)/(n+1) .

If m >1,n in N show that 1^m+2^m+2^(2m)+2^(3m)+...+2^(n m-m)> n^(1-m)(2^n-1)^m

If p+q=1, then show that sum_(r=0)^nr^2^nC_rp^rq^(n-r)=npq+n^2p^2

If (1+x)^(n)=1+""^(n)C_(1)x+""^(n)C_(2)x^(2)+….+""^(n)C_(n) x^(n) show that, n*2^(n-1)=""^(n)C_(1)+2*""^(n)C_(2)+….. +n*""^(n)C_(n) .

If (1+x)^n=C_0+C_1x+C_2x^2+…..+C_nx^n .then show that C_1+2C_2+…. nC_n=n.2^(n-1) .

Using binomial theorem (without using the formula for .^n C_r ) , prove that .^nC_4+^m C_2-^m C_1.^n C_2 = .^m C_4-^(m+n)C_1.^m C_3+^(m+n)C_2.^m C_2-^(m+n)C_3^m.C_1 +^(m+n)C_4dot

If (1+x)^(n)=C_(0)+C_(1)+x+C_(2)x^(2)+...+C_(n) x^(n) Show that C_(1)^(2)+2*C_(2)^(2)+3*C_(3)^(2)....+n*C_(n)^(2)=((2n-1)!)/([(n-1)!]^(2))

UNITED BOOK HOUSE-MODEL QUESTION PAPERS-SET 3-EXERCISE
  1. In /\ABC, if a = 3. b = 5 and c =7, show that the triangle is obtused.

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  2. If | z + 2 | + | z - 2 | le 6, find the maximum value of I z I.

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  3. If m=^nC2show that ^mC2=3^(n+1)C4

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  4. If a+b=3,then show that the minimum value of |a+ib|=is 3/sqrt2

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  5. Find the sum of the following infinite G.P series 0.9+0.81+0.792+….

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  6. Show that the distance between (1,-1) and ((2m^2)/(1+m^2),(1-m)^2/(1+m...

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  7. Find the radius of sphere passing through (2,0,1) and having centre(0,...

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  8. Prove that lim(xrarroo)(1+1/x)^x=e

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  9. For all real values of x and y, if f(x+y)=f(x)f(y), f(5)=4, f'(0)=2, f...

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  10. IfP(A)=1/2,P(B)=1/3)and P(A capB)=1/4find (A 'capB')

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  11. In.an examination. 50%of the condidates have passed in mathematics 50%...

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  12. If A,B,(A - B)are positive acute angles, then prove that geometrically...

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  13. Show thatcos((2pi)/7)+cos((4pi)/7)+cos((6pi)/7)=-1/2

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  14. Show that a^6+a^4+a^2+1=0,when a=1/sqrt2(1+i)

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  15. Prove by mathematical induction:(3^(4n+1)+2^(2n+2))is divisible by 7.

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  16. Show that the co-efficient of the middle term of the expansion of(1+x)...

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  17. If (y/z)^a.(z/x)^b.(x/y)^c=1and a,b,c are in A.P ,show that x,y,z are ...

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  18. In /\XYZthe equation of the perpendicularbisector of XY and XZ arc x-y...

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  19. Find the distance of the point (3. 5) from the line 2x + 3y = 14measur...

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  20. The end’ points of a rod having length l are moving a long with two st...

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