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


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30 Questions MCQ Test IIT JAM Past Year Papers and Model Test Paper (All Branches) - Model Test Paper, Math, Feb. - 2017

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Model Test Paper, Math, Feb. - 2017 - Question 1

   is differentiable, then f is strictly increasing on the interval

Model Test Paper, Math, Feb. - 2017 - Question 2

Let f : [a, b] → R be a differentiable function s.t. f(x) ≠ 0 for  x ∈ [a, b] then    is equal to 

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Model Test Paper, Math, Feb. - 2017 - Question 3

  and    then the function
F : [0, 2] → R is

Model Test Paper, Math, Feb. - 2017 - Question 4

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

Model Test Paper, Math, Feb. - 2017 - Question 5

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​

Model Test Paper, Math, Feb. - 2017 - Question 6

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 

Model Test Paper, Math, Feb. - 2017 - Question 7

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

Model Test Paper, Math, Feb. - 2017 - Question 8

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

Model Test Paper, Math, Feb. - 2017 - Question 9

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

Model Test Paper, Math, Feb. - 2017 - Question 10

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)

Model Test Paper, Math, Feb. - 2017 - Question 11

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

Model Test Paper, Math, Feb. - 2017 - Question 12

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

Model Test Paper, Math, Feb. - 2017 - Question 13

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 ?

Model Test Paper, Math, Feb. - 2017 - Question 14

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

Model Test Paper, Math, Feb. - 2017 - Question 15

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.

Model Test Paper, Math, Feb. - 2017 - Question 16

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.

Model Test Paper, Math, Feb. - 2017 - Question 17

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?

Model Test Paper, Math, Feb. - 2017 - Question 18

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

Model Test Paper, Math, Feb. - 2017 - Question 19

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

Model Test Paper, Math, Feb. - 2017 - Question 20

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 :

Model Test Paper, Math, Feb. - 2017 - Question 21

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

Model Test Paper, Math, Feb. - 2017 - Question 22

Which of the following mapping is not linear ?

Model Test Paper, Math, Feb. - 2017 - Question 23

Model Test Paper, Math, Feb. - 2017 - Question 24

Closed unit interval [0, 1] is a

Model Test Paper, Math, Feb. - 2017 - Question 25

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

Model Test Paper, Math, Feb. - 2017 - Question 26

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.

Model Test Paper, Math, Feb. - 2017 - Question 27

General solution of the differential equation 

Model Test Paper, Math, Feb. - 2017 - Question 28

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

Model Test Paper, Math, Feb. - 2017 - Question 29

   then the subsequence of <xn> is

Model Test Paper, Math, Feb. - 2017 - Question 30

  then the sequence <xn> is

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