Math - 2017 Past Year Paper - IIT JAM MCQ

Let f : R → R be a twice differentiable function. If g(u, v) = f(u² – v²), then

Let f₁(x), f₂(x), g₁(x), g₂(x) be differentiable functions on R.   be the determinent of the matrix   . Then F'(x) is equal to 

Then which one of the following is TRUE ?

satisfies the assumptions of Rolle’s theorem in the interval [–1, 1], then the ordered pair (p, q) is

The flux of the vector field

along the outward normal, across the ellipse x² + 16y² = 4 is equal to

Let M be the set of all invertible 5 × 5 matrices with entries 0 and 1. For each 

and n₀(M) denote the number of 1’s and 0’s in M, respectively. Then

The line integral of the vector field 

along the boundary of the triangle with vertices (1,0,0), (0,1,0) and (0,0,1), oriented anticlockwise, when viewed from the point (2,2,2) is

The area of the surface z = xy/3 intercepted by the cylinder x² + y²  ≤ 16 lies in the interval

be the circle oriented anti- clockwise. Then

The flux of  along the outward normal, across the surface of the solid is equal to

Let f : R → [0, ∞) be a continuous function. Then which one of the following is NOT TRUE ?

The interval of convergence of the power series 

Let P₃ denote the real vector space of all polynomials with real coefficients of degree at most 3. Consider the map T : P₃ → P₃ given by 

Let f(x, y) =   for (x, y) ≠ (0, 0). Then

Let S be an infinite subset of R such that S\{a} is compact for some α ∈ S. Then which one of the following is TRUE ?

Then which one of the followings is NOT TRUE ?

Which one of the following is TRUE ?

A particular integral of the differential equation 

Let y(x) be the solution of the differential equation

satisfying y(0) = 1. Then y(–1) is equal to