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AAKASH SERIES-BINOMIAL THEOREM-EXERCISE - 1.4 (Level-2)
- Find the remainder when 3^(37) is divided with 80 ?
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- Find the remainder when 2^(60) is divided with 7.
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- Find the number of distinct terms in the expansion (x + 2y + 3z + ...
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- Find the number of distinct terms in the following expansions. (x^(2...
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- Find the number of distinct terms in the following expansions. (p+q)...
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- Find the number of distinct terms in the expansion (x+ y + z)^10+ ...
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- Prove that, C(0) *""^(2n)C(n)-C(1)*""^((2n-2))C(n)+C(2) *""^((2n-4))C(...
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- If (1+x)^(n)=sum(r=0)^(n)""^(n)C(r )x^(r ) and if sum(r=0)^(n) (1)/(""...
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- Prove that C(0)-(1)/(3)*C(1)+(1)/(5)*C(2) - …+(-1)^(n)*(1)/(2n+1)C(n) ...
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- If a, b, c, d be 3^(rd), 4^(th), 5^(th) and 6^(th) terms of the expans...
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- Show that sum(r=0)^(n) (-1)^(r ). ""^(n)C(r ) {(1)/(2^(r )) +(3^(r ))/...
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- If sum(r = 0)^(2n) a(r ) (x-2)^(r ) = sum(r = 0)^(2n) b(r ) (x-3)^(r )...
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- Show that the coefficient of x^(n)y^(n) in the expansion of {(1+x)(1+...
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- If (1)/(1!(n-1)!) + (1)/(3!(n-3)!) + (1)/(5!(n-5)!) +…. =
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- If sum(r =0)^(n) ((r+2)/(r+1)) *""^(n)C(r ) =(255)/(6). Find n.
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- Show that 1sum(r =0)^(50) (""^(100)C( r))*(""^(200)C(150+r ))=""^(300)...
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- Prove that sum(k=1)^(n-r ) ""^(n-k)C(r )= ""^(n)C( r+1) .
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- Show that C(0) +(C(0) +C(1))+(C(0)+C(1)+C(2)) +…+(C(0) +C(1)+…+C(n)) =...
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- If x > 0 , write the first negative term in the expansion of (1 + 2x)^...
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- If x is small and the expansion of (a)/((1-x)^(2)) +(b)/((2+3x)^(2)) ...
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