kilowatt hour is equal to 
Joule.
gives 
, 
is the inverse of 
A real quadratic form xᵀAx is called positive definite exactly when
-
xᵀAx > 0 for every nonzero real vector x.
A fundamental theorem says that if A is real and symmetric, then this happens if and only if all of A’s eigenvalues are strictly positive.
-
If every eigenvalue λ > 0, then in an orthonormal eigenbasis the form becomes a sum of positive multiples of squares, and is always > 0.
-
If any eigenvalue were zero or negative, you could pick an eigenvector for that eigenvalue to make xᵀAx zero or negative, violating positive definiteness.
The choice “all eigenvalues ≥ 0” only ensures positive semidefiniteness (xᵀAx ≥ 0), not strict positivity. The other options are clearly wrong.
Hence none of the listed answers captures “all eigenvalues strictly positive,” so the correct response is (d) None of these.
is
is
(bounded below)
(bounded above)
is bounded sequence
and 
Then which of the following is correct?
and 
for 
is
has jump at 
has discontinuity of first kind.
let,
forms a decreasing sequence of measurable sets.
and we have
so that
, i.e.
The 
th term of the sequence
