BOE'19 (132-200 Q) & BOE'21 PADT (1-84 Q)

The eigen values of a real symmetric matrix are

• all zero

• all real

• purely imaginary

• both real and imaginary

Two matrices A and B are said to be similar if there exists a non-singular matrix P such that

• A P=B'AB

• B:P‘AP

• A=#P'BP

• P+B'AB

Inverse of an orthogonal matrix is

• a null matrix

• an identity matrix

• an orthogonal matrix

• a unitary matrix

Which one of the following ordinary differential equation is Legendre’s linear equation?

• Y+ -y=x

• gy - ¥ +3y=logx

• x*y -3xy+4y=Q1+x)f

• (2x+3)y —(2x+3)y'-12y =6

Solve (xz -y )dx +2xydy =0

• x*-y*=Cx

• x*-y'=C

• Mx2+y2:Cx

• O x*+y*=C

Find the particular integral (P.1.) of [(D +2)(D —1)21)' =2sinhx, where D = %x

• PI=Xe*:&

• PI=Xe*:+S

• PI=e4l

• MPJ:ic—e"-e

The maximum directional derivative of ¢ = ch:z!2 at (1, 0, 3) is along.

• X - axis

• Y - axis

• Z - axis

• i+j+k

Final ‘@’ so that the vector A = (ax2 -y x); - (ny + y); is irrotational.

• 4 only

• -2 only

• 2 only

• for all values of ‘@’

If S is the surface of a sphere of radius ‘@’ then H(x dydz+ydzdx+zdxdy) is

• 4za’

• %naa

• -;—flaz

• 27

Which one of the following function is of exponential order?

• t*

• sect

• tant

• o