Statement 1: `"Delta"=|m y+n z m q+n r m b+n c k z-m x k r-m p k c-m a-n x-k y-n p-k q-n a-k b|` is equal to 0. Statement 2: The value of skew symmetric matrix of order 3 is zero.

Statements : P gt M gt Q, Q gt Z gt N Conclusions : I. M gt Z II. N lt P

If P(n) is a statement (n in N) such that if P(k) is true,P(k+1) is true for k in N, then P(k) is true.

Let A = { n in N | n^(2) le n + 10,000 } B = { 3k + 1 | k in N } and C = { 2 k |k in K } , then the sum of all the elements of the set A cap (B - C) is equal to ______

If p is nearly equal to q and n gt 1 , such that ((n+1) p+(n-1)q)/((n-1)p+(n +1)q) = ((p)/(q))^(k) , then the value of k, is

P @ Q means P is greater than Q. P underline"@" Q means P is either greater than or equal to Q. P = Q means P is equal to Q. P © Q means P is smaller than Q. P underline"©" Q means P is either smaller than or equal to Q. Statements: L underline"©" K, M © N, K = M Conclusions: I. N @ L II. K underline"©" N

Let m=(a)/(2)-b ,such that a^(2)-b^(4)=19 where a,b in N and n is the number of values of k for which sum of roots of equation x^(2)-2kx+2k-1=0 is equal to sum of square of its roots,then value of (3|m|+n) equals

If m and n are roots of the equation (x+p)(x+q)-k=0 then find the roots of the equation (x-m)(x-n)+k=0

If A =[(a,b,c),(x,y,z),(l,m,n)] is a skew-symmetric matrix,m nthen which of the following is equal to x+ y+ z?