Math - 2014 Past Year Paper


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35 Questions MCQ Test IIT JAM Past Year Papers and Model Test Paper (All Branches) | Math - 2014 Past Year Paper

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Math - 2014 Past Year Paper - Question 1

Let f(x) = |x– 25| for all x ∈ R. The total number of points of R at which f attains a local extremum (minimum or maximum) is

Math - 2014 Past Year Paper - Question 2

The coefficient of (x – 1)2 in the Taylor series expansion of f(x) = xex (x ∈ R) about the point x = 1 is

Math - 2014 Past Year Paper - Question 3

Math - 2014 Past Year Paper - Question 4

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

Math - 2014 Past Year Paper - 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

Math - 2014 Past Year Paper - Question 6

The value of the radius of convergence of f(n) = 2n, n<0 is ____________ 

Detailed Solution for Math - 2014 Past Year Paper - Question 6

The series is convergent if | z / 2 | < 1, that is | z | < 2 

Hence, ROC is | z | < 2.

Math - 2014 Past Year Paper - Question 7

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

Detailed Solution for Math - 2014 Past Year Paper - Question 7

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.

Math - 2014 Past Year Paper - Question 8

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

Math - 2014 Past Year Paper - 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

Math - 2014 Past Year Paper - Question 10

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

  is the interval

Math - 2014 Past Year Paper - 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

Math - 2014 Past Year Paper - 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

Math - 2014 Past Year Paper - 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

Math - 2014 Past Year Paper - 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

Math - 2014 Past Year Paper - 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

Math - 2014 Past Year Paper - Question 16

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

Math - 2014 Past Year Paper - Question 17

Math - 2014 Past Year Paper - 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 

Math - 2014 Past Year Paper - Question 19

where    Then

Math - 2014 Past Year Paper - Question 20

Math - 2014 Past Year Paper - Question 21

The set all limit points of the set 

Math - 2014 Past Year Paper - 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

Math - 2014 Past Year Paper - 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

Math - 2014 Past Year Paper - Question 24

For all (x, y) ∈ R2 , 

Then at the point (0, 0),

Math - 2014 Past Year Paper - Question 25

For all (x, y)  ∈ R2 

Math - 2014 Past Year Paper - 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

Math - 2014 Past Year Paper - Question 27

The value of   is 

Math - 2014 Past Year Paper - Question 28

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

  is

Math - 2014 Past Year Paper - 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  

Math - 2014 Past Year Paper - Question 30

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

Math - 2014 Past Year Paper - 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

Math - 2014 Past Year Paper - 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 

Math - 2014 Past Year Paper - 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

Math - 2014 Past Year Paper - Question 34

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

Math - 2014 Past Year Paper - Question 35

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

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