Let `A=((2,-2),(1,-1))andB=((-1,2),(-1,2))` Then the number of elements in the set {(n, m): n, m `in` {1, 2....,10} and `nA^(n) + mB^(n) =I` } is

The number of elements in the set {n in {1, 2, 3,…, 100} | (11)^(n) gt (10)^(n) + (9)^(n)} is ________ .

For each positive integer n, let A_(n)=max{(C(n,r)0<=r<=n} then the number of elements n in {1,2...20} for 1.9<=(A_(n))/(A_(n-1))<=2 is

Let X={1,2,-,10}, if set A and B are formed from elements of X the probability that n(A nn B)=2, is

Find the value of the products: (3m-2n)(2m-3n) at m=1,n=-1

A set contains (2n+1) elements.If the number of subsets of this set which contain atmost n elements is 4096, then n is

Statement-1 : nm is not same as m N Statement -2 : 1 nm = 10^(-9) m and 1 m N =10^(-3)N

If the direction cosines of two lines are (l_(1), m_(1), n_(1)) and (l_(2), m_(2), n_(2)) and the angle between them is theta then l_(1)^(2)+m_(1)^(2)+n_(1)^(2)=1=l_(2)^(2)+m_(2)^(2)+n_(2)^(2) and costheta = l_(1)l_(2)+m_(1)m_(2)+n_(1)n_(2) If the angle between the lines is 60^(@) then the value of l_(1)(l_(1)+l_(2))+m_(1)(m_(1)+m_(2))+n_(1)(n_(1)+n_(2)) is

If A=[(1,1),(1,0)] and n epsilon N then A^n is equal to (A) 2^(n-1)A (B) 2^nA (C) nA (D) none of these

I: m is any composite number that divides (m-1)! II: n is a natural number that n^3 + 2n^2 + n divides n!