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# Math - 2018 Past Year Paper

## 60 Questions MCQ Test Past Year Papers of IIT JAM Mathematics | Math - 2018 Past Year Paper

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This mock test of Math - 2018 Past Year Paper for IIT JAM helps you for every IIT JAM entrance exam. This contains 60 Multiple Choice Questions for IIT JAM Math - 2018 Past Year Paper (mcq) to study with solutions a complete question bank. The solved questions answers in this Math - 2018 Past Year Paper quiz give you a good mix of easy questions and tough questions. IIT JAM students definitely take this Math - 2018 Past Year Paper exercise for a better result in the exam. You can find other Math - 2018 Past Year Paper extra questions, long questions & short questions for IIT JAM on EduRev as well by searching above.
QUESTION: 1

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QUESTION: 2

Solution:
QUESTION: 3

### If {v1, v2, v3} is a linearly independent set of vectors in a vector space over then which one of the following sets is also linearly independent?

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QUESTION: 4

Let a be a positive real number. If f is a continuous and even function defined on the interval [–a, a], then is equal to :

Solution:
QUESTION: 5

The tangent plane to the surface at (1, 1, 2) is given by

Solution:
QUESTION: 6

In , the cosine of the acute angle between the surfaces x2 + y2 + z2 - 9 = 0 and z - x2 - y2 + 3 = 0 at the point (2, 1, 2) is :

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QUESTION: 7

Let f : be a scalar field, be a vector filed and let be a constant vector. If represents the position vector then which one of the following is FALSE?

Solution:
QUESTION: 8

In , the family of trajectories orthogonal to the family of asteroids x2/3 + y2/3 = a2/3 is given by

Solution:
QUESTION: 9

Consider the vector space V over of polynomial functions of degree less then or equal to 3 defined on . Let T : V → V be defined by (Tf)(x) = f(x) – xf’(x). Then the rank of T is

Solution:
QUESTION: 10

Let Then which one of the following is True for the sequence Solution:
QUESTION: 11

Let Then which one of the following is TRUE?

Solution:
QUESTION: 12

Let a, b, c . Which of the following values of a, b, c do NOT result in the convergence of the series Solution:
QUESTION: 13

Let Then the sum of the series is:

Solution:
QUESTION: 14

Let and let where Then which one of the following is true?

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QUESTION: 15

Suppose that f, g are differentiable functions such that f is strictly increasing and g is strictly decreasing. Define p(x) = f(g(x)) and q(x) = g(f(x)), Then, for t > 0, the sign of is :

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QUESTION: 16

For Then which one of the following is false?

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QUESTION: 17

Let Then which one of the following is true for f at the point (0, 0)?

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QUESTION: 18

Let a, b be a thrice differentiable function. If z = eu f(v), where u = ax + by and v = ax – by, then which one of the following is true?

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QUESTION: 19

Consider the region D in the yz plane bounded by the line y = 1/2 and the curve y2 + z2 = 1, where y≥0. If the region D is revolved about the z- axis in , then the volume of the resulting solid is :

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QUESTION: 20

If where C is the boundary of the triangular region bounded by the lines x = 0, y = 0 and x + y = 1 oriented in the anti- clockwise direction, is :

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QUESTION: 21

Let U, V and W be finite dimensional real vector spaces, T : U → V, S : V → W and P : W → U be linear transformations. If range (ST) = nullspace (P), nullspace (ST) = range (P) and rank (T) = rank (S), then which one of the following is true?

Solution:
QUESTION: 22

Let y(x) be the solution of the differential equation dy/dx + = , for x ≥ 0, y(0) = 0, where Then y(x) =

Solution:
QUESTION: 23

An integrating factor of the differential equation is:

Solution:
QUESTION: 24

A particular integral of the differential equation is:

Solution:
QUESTION: 25

Let G be a group satisfying the property that f : is a homomorphism implies f(g) = 0, Then a possible group G is :

Solution:
QUESTION: 26

Let H be the quotient group Consider the following statements.
I. Every cyclic subgroup of H is finite.
II. Every finite cyclic group is isomorphic to a subgroup of H.
Which one of the following holds?

Solution:
QUESTION: 27

Let I denote the 4 × 4 identity matrix. If the roots of the characteristic polynomial of a 4 × 4 matrix M are , then M8 =

Solution:
QUESTION: 28

Consider the group under component- wise addition. Then which of the following is a subgroup of ?

Solution:
QUESTION: 29

Let f : be a function and let J be a bounded open interval in Define Which one of the following is false?

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QUESTION: 30

For Then which one of the following is true?

Solution:
*Multiple options can be correct
QUESTION: 31

Let f : be defined by f ( x) = On which of the following interval(s) is f one- one?

Solution:
*Multiple options can be correct
QUESTION: 32

The solution(s) of the differential equation satisfying y(0) = 0 is (are)

Solution:
*Multiple options can be correct
QUESTION: 33

Suppose f, g, h are permutations of the set where
f interchanges ∝ and β but fixes γ and δ
g interchanges β and γ but fixes ∝ and δ,
h interchanges γ and δ but fixes ∝ and β.
Which of the following permutations interchange(s) ∝ and δ but fix(es) β and γ?

Solution:
*Multiple options can be correct
QUESTION: 34

Let P and Q be two non- empty disjoint subsets of Which of the following is (are) false?

Solution:
*Multiple options can be correct
QUESTION: 35

Let denote the group of non- zero complex numbers under multiplication. Suppose Which of the following is (are) subgroup(s) of ?

Solution:
*Multiple options can be correct
QUESTION: 36

Suppose Consider the following system of linear equations. x + y + z = α, x + βy + z = γ, x + y + αz = β. If this system has at least one solution, then which of the following statements is (are) true?

Solution:
*Multiple options can be correct
QUESTION: 37

Let m, Then which of the following is (are) Not possible?

Solution:
*Multiple options can be correct
QUESTION: 38

If then which among the following is (are) true?

Solution:
*Multiple options can be correct
QUESTION: 39

Which of the following subsets of is (are) connected?

Solution:
*Multiple options can be correct
QUESTION: 40

Let S be a subset of ¡ such that 2018 is an interior point of S. Which of the following is (are) true?

Solution:
*Answer can only contain numeric values
QUESTION: 41

The order of the element (1 2 3)(2 4 5)(4 5 6) in the group S6 is _______ .

Solution:
*Answer can only contain numeric values
QUESTION: 42

Let Then the absolute value of the directional derivative of φ in the direction of the line at the point (1, – 2, 1) is _______ .

Solution:
*Answer can only contain numeric values
QUESTION: 43

Let Then the value of is _______ .

Solution:
*Answer can only contain numeric values
QUESTION: 44

Let be given by Then at the point (0, 0) is _______ .

Solution:
*Answer can only contain numeric values
QUESTION: 45

Let for (x, y) Then fx(1, 1) + fy(1, 1) = _______ .

Solution:
*Answer can only contain numeric values
QUESTION: 46

Let be continuous on and differentiable on then f(6) = _______ .

Solution:
*Answer can only contain numeric values
QUESTION: 47

Let Then the radius of convergence of the power series about x = 0 is _______ .

Solution:
*Answer can only contain numeric values
QUESTION: 48

Let A6 be the group of even permutations of 6 distinct symbols. Then the number of elements of order 6 in A6 is _______ .

Solution:
*Answer can only contain numeric values
QUESTION: 49

Let W1 be the real vector space of all 5 × 2 matrices such that the some of the entries in each row is zero. Let W2 be the real vector space of all 5 × 2 matrices such that the sum of the entries in each column is zero. Then the dimension of the space is _______ .

Solution:
*Answer can only contain numeric values
QUESTION: 50

The coefficient of x4 in the power series expansion of esin x about x = 0 is _______ (correct up to three decimal places).

Solution:
*Answer can only contain numeric values
QUESTION: 51

Let where k, Then is _______ . (correct up to one decimal places).

Solution:
*Answer can only contain numeric values
QUESTION: 52

Let be such that f" is continuous on and f(0) = 1, f'(0) = 0 and f"(0) = – 1. Then is _______ (correct up to three decimal places).

Solution:
*Answer can only contain numeric values
QUESTION: 53

Suppose x, y, z are positive real number such that x + 2y + 3z = 1. If M is the maximum value of xyz2, then the value of 1/M is _______ .

Solution:
*Answer can only contain numeric values
QUESTION: 54

If the volume of the solid in bounded by the surfaces x = – 1, x = 1, y = – 1, y = 1, z = 2, y2 + z2 = 2 is α– π, then a = _______ .

Solution:
*Answer can only contain numeric values
QUESTION: 55

If then the value of is _______ .

Solution:
*Answer can only contain numeric values
QUESTION: 56

The value of the integral is _______ . (correct up to three decimal places).

Solution:
*Answer can only contain numeric values
QUESTION: 57

Suppose is a matrix of rank 2. Let T : be the linear transformation defined by T(P) = QP. Then the rank of T is _______ .

Solution:
*Answer can only contain numeric values
QUESTION: 58

The area of the parametrized surface is _______ (correct up to two decimal places).

Solution:
*Answer can only contain numeric values
QUESTION: 59

If x(t) is the solution to the differential equation satisfying x(0) = 1, then the value of x (√2 ) is _______ (correct up to two decimal places).

Solution:
*Answer can only contain numeric values
QUESTION: 60

If y(x) = v(x) sec x is the solution of y" – (2 tan x)y' + 5y = 0, satisfying y(0) = 0 and y '(0) =  √6, then v is _______ . (correct up to two decimal places).

Solution: