Model Test Paper, Math, Feb. - 2017 - IIT JAM MCQ

The area of the region that is inside the circle r = 2 cos q and outside the cardiod r = 2(1 – cos q).

Fg and Fe represents gravitational and electrostatic forces respectively, between the two electrons situated at a distance of 10 m. The ratio Fg/Fe is of the order of​

Consider the funnel formed by revolving the curve y = 1/x about the x- axis, between x = 1 and x = a, where a > 1 If Sa denote the surface area of the funnel then 

Let x ∈ R, n ∈ N then there exist a unique y ∈ R s.t. yⁿ = x if

If both f, g : R → R are discontinuous at 0, then the product function fg : R → R is

Let A be a n × n matrix and y be a n × 1 matrix (vector) such that the equation Ax = y for a n × 1 matrix (vector) y admits no solution then the rank of A is

Let b be an n × 1 (column) vector and A be an n × n positive definite matrix. Define P : Rⁿ → R by

Here t stands for transpose. If x₀ is a vector such that Ax₀ = B then which of the following is true? (where t is used for transpose)

U = {(x, y, z) | x = y = z}, V = {(x, y, z) | x = 0} what is U + V?

If A ⊂ R² is a countable set, then R² \ A is

Let A, B ⊂ Rⁿ and define, A + B = {a + b; a ∈ A, b ∈ B}. If A and B are open then which of the following statement is TRUE ?

The value of the integral   where R is the following solid region

Let S be the surface in R³ defined by the parametric equation

r = 2 + cos t + cos u

θ = t           0 ≤  t ≤ 2π

z = sin u     0 ≤ u ≤ 2π

then the using the divergence theorem what is the volume of the region inside S.

The following picture shows the parametric curve (x, y) = (t – t³, t²)

By using Green’s theorem what will be the area of the shaded region.

Let G be a finite group of order 2n for some integer n. Consider the map Ø : G → G given by Ø(a) = a². Then which of the following statement holds?

If F is a conservative vector field where    then what should be the value of λ

A rigid body is rotating with constant angular velocity ω about fixed axis. If V be the velocity at any point of the body then the value of curl V will be

An ideal gas has molecules with 5 degrees of freedom. The ratio of specific heats at constant pressure (Cp ) and at constant volume (Cv ) is :

For what values of λ and μ the system of equations

2x + 3y + 5z = 9

7x + 3y – 2z = 8

2x + 3y + λz = μ

has unique solution

Which of the following mapping is not linear ?

Closed unit interval [0, 1] is a

The value of y as t → ∞ for an initial value of y(1) = 0, for the differential equation

If y₁ = sinx and y₂ = sinx – cosx are linearly independent solutions of y” + y = 0. Then determine the constants c₁ and c₂ so that the solution sin x + 3cosx = c₁y₁ + c₂y₂.

General solution of the differential equation 

Let u₁, ... u_n be a linearly dependent set of functions on a ≤ x ≤ b, and let each function be(n – 1) times differentiable in (a, b). Then

   then the subsequence of <x_n> is

  then the sequence <x_n> is