For what value of n, double integral where region R is bounded by x + y = 1 in the first quadrant?
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If is harmonic in V then for any closed surface S consisting the volume V, the integral is equal to
The transformation T : R3 → R2 defined by,
T(x,y,z) = (x +y, y+z) is,
The radius of convergence of power series is,
A cauchy sequence in Q which does not have a limit in Q is
Suppose the matrix has a certain complex no. λ ≠ 0 as an eigenvalue. Which of the following no. must also be an eigenvalue of A?
If A and B are unbounded subsets of R, which of the following is necessarily unbounded?
Let f: R3 → R3 be the matrix transformation defined by
if we have,
then for the solution, i.e. for the existence of values of x,y and z.
Find the total no. of elements of order 12 in a cyclic group of order 60.
Which of the following pair of groups is isomorphic to each other?
If G is a group, then for every a ∈ G, what is (a−1)−1?
Let f' (sin x) < 0 and f' (cos x) > 0. and g (x) = f (sin x) + f (cos x) then which of the following is true?
Let be a constant vector and V is the volume enclosed by the closed surface S. The integral is equal to (where ñ is the outward going unit normal to the surface S)
If then find the length of the curve y = f(x) from the vertex (0, 0) to the point (a, a).
Given
and G(x) = (x - 1/2)2, x ∈ R
what is the area of the portion bounded between G(x) and f(x) inn the interval
are three vectors with magnitude |a| = 4, |b| = 4, |c| = 2 and such that is perpendicular to is perpendicular to is perpendicular to , then is equal to
If and = (1, a, a2)
are non-coplanar vectors, then abc is equal to
The differential equation determines a family of circles with,
The orthogonal trajectories of the hyperbolas xy = c is
Let P : R → R be a polynomial of the form P(x) with and
If |x| is the absolute value of x ∈ R, then
A: R6 → R6 be a linear transformation such that A2 = 0, then the rank of A is
Let V be the space of twice differentiable functions on R satisfying f'' - 2f' + f = 0. Define T : V → R2 by T(f) = (f'(0), f(0)), Then T is
Let f : denote the function defined by f(x) = Which of the following statement is correct?
Let {an} be a sequence of real no. such that Then
Consider the surface corresponding to the equation 4x2 + y2 + z = 0 A possible unit tangent to this surface at the point (1, 2, -8) is
If the surface integral of the field over the closed surface of an arbitrary unit sphere is to be zero, then the relationship between
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