If `A=[[3,-3, 4], [2,-3, 4], [0,-1, 1]]` , then a. `a d j(a d j A)=A` b. `|a d j(a d j A)|=1` c. `a d j A=I` d. none of these

If a >0, then least value of (a^3+a^2+a+1)^2 is (a) 64 a^2 (b) 16 a^4 (c) 16 a^3 (d)d. none of these

If A is a square matrix of order n such that |a d j(a d jA)|=|A|^9, then the value of n can be 4 b. 2 c. either 4or2 d. none of these

The unit vector orthogonal to vector -hat i+ hat j+2 hat k and making equal angles with the x and y-axis a. +-1/3(2 hat i+2 hat j- hat k) b. +-1/3( hat i+ hat j- hat k) c. +-1/3(2 hat i-2 hat j- hat k) d. none of these

Let x^2+3y^2=3 be the equation of an ellipse in the x-y plane. Aa n dB are two points whose position vectors are -sqrt(3) hat ia n d-sqrt(3) hat i+2 hat kdot Then the position vector of a point P on the ellipse such that /_A P B=pi//4 is a. +- hat j b. +-( hat i+ hat j) c. +- hat i d. none of these

Let {D_1, D_2, D_3 ,D_n} be the set of third order determinant that can be made with the distinct non-zero real numbers a_1, a_2, a_qdot Then a. sum_(i=1)^n D_i=1 b. sum_(i=1)^n D_i=0 c. D_i-D_j ,AAi ,j d. none of these

Let vecalpha=a hat i+b hat j+c hat k , vecbeta=b hat i+c hat j+a hat ka n d vecgamma=c hat i+a hat j+b hat k are three coplanar vectors with a!=b ,a n d vec v= hat i+ hat j+ hat kdot Then v is perpendicular to vecalpha b. vecbeta c. vecgamma d. none of these

Value of lambda such that the line (x-1)/2=(y-1)/3=(z-1)/lambda is _|_ to normal to the plane vec r.(2 vec i+3 vec j+4 vec k)=0 is a. -(13)/4 b. -(17)/4 c. 4 d. none of these

Each question has four choices a, b, c and d, out of which only one is correct. Each question contains STATEMENT 1 and STATEMENT 2. Both the statements are TRUE and STATEMENT 2 is the correct explanation of STATEMENT1. Both the statements are TRUE but STATEMENT 2 is NOT the correct explanation of STATEMENT 1. STATEMENT 1 is TRUE and STATEMENT 2 is FALSE. STATEMENT 1 is FALSE and STATEMENT 2 is TRUE. Statement 1: |a d j(a d j(a d j A))|=|A|^(n-1)^3 , where n is order of matrix Adot Statement 2: |a d jA|=|A|^ndot

The centre of the circle given by vec r.( hat i+2 hat j+2 hat k)=15a n d| vec r.( hat j+2 hat k)|=4 is a. (0,1,2) b. (1,3,4) c. (-1,3,4) d. none of these

The points with position vectors 60 i+3j ,40 i-8j ,a i-52 j are collinear if a. a=-40 b. a=40 c. a=20 d. none of these