Let A=((1,1,1),(0,1,1),(0,0,1)). Then fo...

Let `A=((1,1,1),(0,1,1),(0,0,1))`. Then for positive integer n. `A^(n)` is

`((1,n,n^(2)),(0,n^(2),n),(0,0,n))`

`((1,n,n((n+1)/(2))),(0,1,n),(0,0,1))`

`((1,n^(2),n),(0,n,n^(2)),(0,0,n^(2)))`

`((1,n,2n-1),(0,(n+1)/(2),n^(2)),(0,0,(n+1)/(2)))`

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If A={:[(1,1,1),(0,1,1),(0,0,1)] , Prove by mathematical induction that, A^(n)={:[(1,n,(n(n+1))/2),(0,1,n),(0,0,1)] for every positive integer n.

If A={:[(a,b),(0,1)]:}, prove by mathematical induction that, A^(n)= [{:(,a^(n), (b(a^(n) -1))/(a-1)),(,0,1)]:} for every positive integer n.

Let, I=({:(1,0,0),(0,1,0),(0,0,1):}) " and " P=({:(1,0,0),(0,-1,0),(0,0,-2):}) . Then the matrix P^(3)+2P^(2) is equal to -

int (dx)/(1+nsqrt(x+1)) , n is a positive integer.

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if A={:[(1,1,1),(1,1,1),(1,1,1)]:}, prove by mathematical induction that, A^(n)={:[(3^(n-1),3^(n-1),3^(n-1)),(3^(n-1),3^(n-1),3^(n-1)),(3^(n-1),3^(n-1),3^(n-1))]:} for every positive integer n.

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Let m be the smallest positive integer such that the coefficient of x^2 in the expansion of (1+x)^2 + (1 +x)^3 + (1 + x)^4 +........+ (1+x)^49 + (1 + mx)^50 is (3n + 1) .^51C_3 for some positive integer n. Then find the value of n.

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WB JEE PREVIOUS YEAR PAPER-QUESTION PAPER 2017-Multiple Choice Questions

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