If `0 < alpha < pi/6 and sin alpha + cos alpha =sqrt(7 )/2,` then `tan alpha/2` is equal to

If x ,\ y ,\ z are non-zero real numbers, then the inverse of the matrix A=[[x,0, 0],[ 0,y,0],[ 0, 0,z]] , is (a) [[x^(-1),0 ,0 ],[0,y^(-1),0],[ 0, 0,z^(-1)]] (b) x y z[[x^(-1),0 ,0],[ 0,y^(-1),0],[ 0, 0,z^(-1)]] (c) 1/(x y z)[[x,0, 0],[ 0,y,0],[ 0, 0,z]] (d) 1/(x y z)[[1, 0, 0],[ 0 ,1, 0],[ 0, 0, 1]]

If x, y, z are non-zero real numbers, then the inverse of matrix A=[(x,0, 0) ,(0,y,0),( 0, 0,z)] is (A) [[x^(-1),0,0],[0,y^(-1),0],[0,0,z^(-1)]] (B) xyz[[x^(-1),0,0],[0,y^(-1),0],[0,0,z^(-1)]] (C) (1)/(xyz)[[x,0,0],[0,y,0],[0,0,z]] (D) (1)/(xyz)[[1,0,0],[0,1,0],[0,0,1]]

If a plane through the points (2,0,0) , (0,3,0) AND (0,0,4) the equation of plane is "_______."

If A is a square matrix such that A*(AdjA)=[{:(4,0,0),(0,4,0),(0,0,4):}] , then

The value of 0. 23 +\ 0. 22 is (a) 0. 45 \ (b) 0. 43 \ (c) 0. 47 \ (d) 0. 41

If A is a square matrix of order 3 such that A("adj A")=[(-3,0,0),(0,-3,0),(0,0,-3)] , then |A| is equal to

If A is a square matrix of order 3 such that A (adj A) =[(-2,0,0),(0,-2,0),(0,0,-2)] , then |adj A| is equal to

If A dn B be 3xx3 matrices the AB=0 implies (A) A=0 or B=0 (B) A=0 and B=0 (C) |A|=0 or |B|=0 (D) |A|=0 and |B|=0

If A= [(0,1),(1,0)] and B= [(0,-x),(x,0)] , then

If A=[(0,0,0,0),(0,0,0,0),(1,0,0,0),(0,1,0,0)] then (A) A^2=I (B) A^2=0 (C) A^3=0 (D) none of these