If the 11 letters A, B, ..., K denote an arbitrary permutation of he integers `(1,2,ddot,11),` then `(A-1)(B-2)(C-3)...(K-11)` will be a. necessarily zero b. always odd c. always even d. none of these

If the 11 letters A,B,.....K denote an arbitrary permutation of the integers (1,2....11), then (A-1)(B-2)(C-3)....(K-11) will be

If nth-order square matrix A is a orthogonal, then |adj(adjA)| is (a)always -1 if n is even (b) always 1 if n is odd (c) always 1 (d) none of these

Four non –zero vectors will always be a. linearly dependent b. linearly independent c. either a or b d. none of these

If (1,1, a) is the centroid of the triangle formed by the points (1,2,-3),(b,0,1)&(-1,1,-4) ,then b-a=

What is the reflection of the point (-3,1) in the line x =-2? (A) (-1,1) (B) (-3,-5) (c ) (1,1) (D) - 3,5)

L is a variable line such that the algebraic sum of the distances of the points (1,1) (2,0) and (0,2) from the line is equal to zero. The line L will always pass through a. (1,1) b. (2,1) c. (1,2) d. none of these

If a, b, c and d are four positive real numbers such that sum of a, b and c is even the sum of b,c and d is odd, then a^2-d^2 is necessarily

If n is any odd number greater than 1, then n backslash(n^(2)-1) is divisible by 24 always (b) divisible by 48 always (c) divisible by 96 always (d) None of these

If (1,1,a) is the centroid of the triangle formed by the points (1,2,-3),(b,0,1) and (-1,1,-4) then a-b=