Math - 2015 Past Year Paper - IIT JAM MCQ

Let S be a nonempty subset of R. If S is a finite union of disjoint bounded intervals, then which one of the following is true?

Let {x_n} be a convergent sequence of real numbers. 

for n ≥ 1, then which one of the following is the limit of this sequence?

The volume of the portion of the solid cylinder x² + y² ≤ 2 bounded above by the surface z = x² + y² and bounded below by the xy- plane is

Let f: R→R be a differentiable function with f(0) = 0. If for all x ∈ R, 1 < f^'(x) < 2, then which one of the following statements is true on (0, ∝)?

If an integral curve of the differential equation  passes through (0, 0) and (α, 1),
then α is equal to

An integrating factor of the differential equation 

Let A be a nonempty subset of R Let I(A) denote the set of interior points of A. Then I(A) can be

Let S₃ be the group of permutations of three distinct symbols. The direct sum    has an element of order

The orthogonal trajectories of the family of curves y = C₁x³ are

Let G be a nonabelian group. Let α ∈ G have order 4 and let β ∈ G have order 3. Then the order of the element αβ in G

Let S be the bounded surface of the cylinder x² + y² = 1 cut by the planes z = 0 and z = 1 + x. Then the value of the surface integral    is equal to 

Suppose that the dependent variables z and w are functions of the independent variables x and y, defined by the equations f(x, y, z, w) = 0 and g(x, y, z, w) = 0, where f_zg_w – f_wg_z = 1.
Which one of the following is correct

Let P₂(R) be the vector space of polynomials in x of degree at most 2 with real coefficients. Let M₂(R) be the vector space of 2 × 2 real matrices. If a linear transformation    is defined as    then

Let B₁ = {(1, 2), (2, –1)} and B₂ = {(1, 0), (0, 1} be ordered bases of R² . If T : R² →  R²  is a linear transformation such that 

then T(5, 5) is equal to

  Which one of the following statements is FALSE?

Let f : R → R be a strictly increasing continuous function. If {a_n} is a sequence in [0, 1], then the sequence {f(a_n)} is

Which one of the following statements is true for the series 

If y(t) is a solution of the differential equation y” + 4y = 2e^t, then

  is equal to 

For what real values of x and y, does the integral  attain its maximum?

The area of the planar region bounded by the curves x = 6y² – 2 and x = 2y² is

For n ≥ 2, let f_n: R → R be given by f_n(x) = xⁿ sin x. Then at x = 0, f_n has a

Let G and H be nonempty subsets of R , where G is connected and G U H is not connected.
Which one of the following statements is true for all such G and H ?

Then the value of