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# Math - 2014 Past Year Paper

## 35 Questions MCQ Test Past Year Papers of IIT JAM Mathematics | Math - 2014 Past Year Paper

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This mock test of Math - 2014 Past Year Paper for IIT JAM helps you for every IIT JAM entrance exam. This contains 35 Multiple Choice Questions for IIT JAM Math - 2014 Past Year Paper (mcq) to study with solutions a complete question bank. The solved questions answers in this Math - 2014 Past Year Paper quiz give you a good mix of easy questions and tough questions. IIT JAM students definitely take this Math - 2014 Past Year Paper exercise for a better result in the exam. You can find other Math - 2014 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

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QUESTION: 4

For a, b, c ∈ R, if the differential equation (ax2 + bxy + y2)dx + (2x2 + cxy + y2)dy = 0 is exact, then

Solution:
QUESTION: 5

If f(x, y, z) = x2y + y2z + z2x for all (x, y, z) ∈ R3 and then the value of  at (1, 1, 1) is

Solution:
QUESTION: 6

The radius of convergence of the power series Solution:
QUESTION: 7

Let G be a group of order 17. The total number of non- isomorphic subgroups of G is

Solution:

As 17 is a prime, and the order of a subgroup must divide the order of the group, G has only two subgroups, the unity subgroup and G itself. So the answer is 2.

QUESTION: 8

Which one of the following is a subspace of the vector space R3 ?

Solution:
QUESTION: 9

Let T : R3 →  R3 be the linear transformation defined by T(x, y, z) = (x + y, z + z, z + x) for all (x, y, z) ∈ R3. Then

Solution:
QUESTION: 10

Let f:  R → R be a continuous function satisfying for all x ∈ R . Then the set is the interval

Solution:
QUESTION: 11

Directions: Q.11 – Q.35 carry two marks each.

The system of linear equations

x – y + 2z = b1

x + 2y – z = b2

2y – 2z = b3
is inconsistent when (b1, b2, b3) equals

Solution:
QUESTION: 12 be a matrix with real entries. If the sum and the product of all the eigenvalues
of A are 10 30 respectively, then a2 + b2 equals

Solution:
QUESTION: 13

Consider the subspace W = {(x1, x2, ..., x10) ∈ R10 : x n = xn–1 + xn–2 for 3 ≤  n ≤ 10} of the vector space R10. The dimension of W is

Solution:
QUESTION: 14

Let y1(x) and y2(x) be two linearly independent solutions of the differential equation

x2 y”(x) – 2xy’(x) – 4y(x) = 0 for x ∈ [1, 10].

Consider the Wronskian W(x) = y1(x)y2’(x) – y2(x)y1’(x). If W(1) = 1, then W(3) – W(2) equals

Solution:
QUESTION: 15

The equation of the curve passing through the point ,(π/2, 1) and having slope at each
point (x, y) with x ≠ 0 is

Solution:
QUESTION: 16

The value of α ∈ R for which the curves x2 + αy2 = 1 and y = x2 intersect orthogonally is

Solution:
QUESTION: 17 Solution:
QUESTION: 18

Let {xn} be a sequence of real numbers such that where c is a positive real number. Then then sequence {xn /n} is

Solution:
QUESTION: 19 where Then

Solution:
QUESTION: 20 Solution:
QUESTION: 21

The set all limit points of the set Solution:
QUESTION: 22

Let S = [0, 1] ∪  [2, 3) and let f : S → R be defined by If T = {f(x) : x ∈ S}, then the inverse function f–1 : T → S

Solution:
QUESTION: 23

Let f(x) = x3 + x and g(x) = x3 – x for all x ∈ R. If f–1 denotes the inverse function of f, then the derivative of the composite function g o f–1 at the point 2 is

Solution:
QUESTION: 24

For all (x, y) ∈ R2 , Then at the point (0, 0),

Solution:
QUESTION: 25

For all (x, y)  ∈ R2  Solution:
QUESTION: 26

Let f : R →  R be a function with continuous derivative such that f ( √2 ) = 2 and f(x) = for all x ∈ R. Then f(3) equals

Solution:
QUESTION: 27

The value of is

Solution:
QUESTION: 28

If C is a smooth curve in R3 from (–1, 0, 1) to (1, 1, –1), then the value of is

Solution:
QUESTION: 29

Let C be the boundary of the region R = {(x, y) ∈ R2 : –1 ≤ y ≤ 1, 0 ≤ x ≤ 1 – y2} oriented in the counterclockwise direction. Then the value of Solution:
QUESTION: 30

Let G be a cyclic group of order 24. The total number of group isomorphism’s of G onto itself is

Solution:
QUESTION: 31

Let Sn be the group of all permutations on the set {1, 2, ..., n} under the composition of mappings.
For n > 2, if H is the smallest subgroup of Sn containing the transposition (1, 2) and the cycle (1, 2, ..., n), then

Solution:
QUESTION: 32

Let S be the oriented surface x2 + y2 + z2 = 1 with the unit normal n pointing outward. For the vector field F(x, y, z) = xi + yj + zk, the value of Solution:
QUESTION: 33

Let f : (0, ∞ ) → R be a differentiable function such that f'(x2) = 1 - x3 for all x > 0 and f(1) = 0.
Then f(4) equals

Solution:
QUESTION: 34

Which one of the following conditions on a group G implies that G is abelian?

Solution:
QUESTION: 35

Let S = {x ∈ R : x6 – x5 ≤ 100} and T = {x2 – 2x : x ∈ (0, ∞)}. Then set S ∩ T is

Solution: