Rank of a non zero matrix is always (A) 0 (B) 1 (C) `gt1` (D) `gt0`

If tan gamma=sec alpha sec beta+tan alpha tan beta, then cos2 gamma is necessarily (A) ge0 (B) le0 (C) lt0 (D) gt0

If the equation f(x)= ax^2+bx+c=0 has no real root, then (a+b+c)c is (A) =0 (B) gt0 (C) lt0 (D) not real

Let a,b, and c be three real numbers satistying [a,b,c][(1,9,7),(8,2,7),(7,3,7)]=[0,0,0] Let omega be a solution of x^3-1=0 with Im(omega)gt0. I fa=2 with b nd c satisfying (E) then the vlaue of 3/omega^a+1/omega^b+3/omega^c is equa to (A) -2 (B) 2 (C) 3 (D) -3

("lim")_(xvec0)(x^asin^b x)/(sin(x^c)) , where a , b , c in R ~{0},exists and has non-zero value. Then, a+c = (a) b (b) -1 0 (d) none of these

If [x] denotes the integral part of x and k=sin^-1 ((1+t^2)/(2t))gt0 then integral valueof alpha for which the equation (x-[k])(x+alpha)-1=0 has integral roots is (A) 1 (B) 2 (C) 4 (D) none of these

Let A=[(0,0,-1),(0,-1,0),(-1,0,0)] Then only correct statement about the matrix A is (A) A is a zero matrix (B) A^2=I (C) A^-1 does not exist (D) A=(-1) I where I is a unit matrix

For a matrix A of rank r (A) rank (A\')ltr (B) rank (A\')=r . (C) rank (A\')gtr (D) none of these

|z-i|lt|z+i| represents the region (A) Re(z)gt0 (B) Re(z)lt0 (C) Im(z)gt0 (D) Im(z)lt0

If A and B are independent events such that P(A) gt0, P(B) gt 0 , then

If A and B are independent events such that P(A) gt 0, P(B) gt 0 , then