Math - 2017 Past Year Paper


60 Questions MCQ Test IIT JAM Past Year Papers and Model Test Paper (All Branches) | Math - 2017 Past Year Paper


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This mock test of Math - 2017 Past Year Paper for IIT JAM helps you for every IIT JAM entrance exam. This contains 60 Multiple Choice Questions for IIT JAM Math - 2017 Past Year Paper (mcq) to study with solutions a complete question bank. The solved questions answers in this Math - 2017 Past Year Paper quiz give you a good mix of easy questions and tough questions. IIT JAM students definitely take this Math - 2017 Past Year Paper exercise for a better result in the exam. You can find other Math - 2017 Past Year Paper extra questions, long questions & short questions for IIT JAM on EduRev as well by searching above.
QUESTION: 1

Consider the function f(x, y) = 5 – 4 sin x + y2 for 0 < x < 2p and y ∈ R. The set of critical points of f(x, y) consists of

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QUESTION: 2

Let φ : R → R be a differentiable function such that φ' is strictly increasing with φ(1) = 0. Let a and b denote the minimum and maximum values of φ(x) on the interval [2, 3], respectively.
Then which one of the following is TRUE ?

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QUESTION: 3

The number of generators of the additive group Z36 is equal to

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QUESTION: 4

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QUESTION: 5

Let f : R → R be a twice differentiable function. If g(u, v) = f(u2 – v2), then

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QUESTION: 6

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QUESTION: 7

Let f1(x), f2(x), g1(x), g2(x) be differentiable functions on R.   be the determinent of the matrix   . Then F'(x) is equal to 

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QUESTION: 8

Then which one of the following is TRUE ?

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QUESTION: 9

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QUESTION: 10

satisfies the assumptions of Rolle’s theorem in the interval [–1, 1], then the ordered pair (p, q) is

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QUESTION: 11

The flux of the vector field

along the outward normal, across the ellipse x2 + 16y2 = 4 is equal to

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QUESTION: 12

Let M be the set of all invertible 5 × 5 matrices with entries 0 and 1. For each 

and n0(M) denote the number of 1’s and 0’s in M, respectively. Then

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QUESTION: 13

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QUESTION: 14

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QUESTION: 15

The line integral of the vector field 

along the boundary of the triangle with vertices (1,0,0), (0,1,0) and (0,0,1), oriented anticlockwise, when viewed from the point (2,2,2) is

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QUESTION: 16

The area of the surface z = xy/3 intercepted by the cylinder x2 + y2  ≤ 16 lies in the interval

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QUESTION: 17

be the circle oriented anti- clockwise. Then

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QUESTION: 18

The flux of  along the outward normal, across the surface of the solid is equal to

 

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QUESTION: 19

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QUESTION: 20

Let f : R → [0, ∞) be a continuous function. Then which one of the following is NOT TRUE ?

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QUESTION: 21

The interval of convergence of the power series 

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QUESTION: 22

Let P3 denote the real vector space of all polynomials with real coefficients of degree at most 3. Consider the map T : P→ P3 given by 

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QUESTION: 23

Let f(x, y) =   for (x, y) ≠ (0, 0). Then

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QUESTION: 24

Let S be an infinite subset of R such that S\{a} is compact for some α ∈ S. Then which one of the following is TRUE ?

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QUESTION: 25

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QUESTION: 26

Then which one of the followings is NOT TRUE ?

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QUESTION: 27

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QUESTION: 28

Which one of the following is TRUE ?

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QUESTION: 29

A particular integral of the differential equation 

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QUESTION: 30

Let y(x) be the solution of the differential equation

satisfying y(0) = 1. Then y(–1) is equal to

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*Multiple options can be correct
QUESTION: 31

Then which of the following statements is/are TRUE ?

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*Multiple options can be correct
QUESTION: 32

The volume of the solid     is expressible as

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*Multiple options can be correct
QUESTION: 33

Let be a function. Then which of the following statements is/are TRUE ?

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*Multiple options can be correct
QUESTION: 34

If X and Y are n × n matrices with real entries, then which of the following is/are TRUE ?

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*Multiple options can be correct
QUESTION: 35

Let G be a group of order 20 in which the conjugacy classes have sizes 1, 4, 5, 5, 5. Then which of the followings is/are TRUE ?

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*Multiple options can be correct
QUESTION: 36

Let {xn} be a real sequence such that  Then which of the following statements is/are TRUE ?

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*Multiple options can be correct
QUESTION: 37

Let S be the set of all rational numbers in (0, 1). Then which of the following statements is/are TRUE ?

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*Multiple options can be correct
QUESTION: 38

Let M be an n × n matrix with real entries such that M3 = I. Suppose that Mv ≠ v for any nonzero vector v. Then which of the following statements is/are TRUE ?

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*Multiple options can be correct
QUESTION: 39

Let y(x) be the solution of the differential equation

satisfying the condition y(0) = 2. Then which of the following is/are TRUE ?

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*Multiple options can be correct
QUESTION: 40

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*Answer can only contain numeric values
QUESTION: 41

 Evaluation of 83 × 82 × 8-5 is.......


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*Answer can only contain numeric values
QUESTION: 42

Let G be a subgroup of    Then the order of G is -----


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*Answer can only contain numeric values
QUESTION: 43

Consider the permutations  

   in S8 . The number of η ∈  S8  such that  


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*Answer can only contain numeric values
QUESTION: 44

Let P be the point on the surface closet to the point (4,2,0). Then the square of the distance between the origin and P is ______.


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*Answer can only contain numeric values
QUESTION: 45


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*Answer can only contain numeric values
QUESTION: 46

  Let M be the matrix whose columns are v1, v2, 2v1 – v2, v1 + 2v2 in that order. Then the number of linearly independent solutions of the homogeneous system of linear equations Mx = 0 is __________.


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*Answer can only contain numeric values
QUESTION: 47


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*Answer can only contain numeric values
QUESTION: 48

Let P be a 7 × 7 matrix of rank 4 with real entries. Let a ∈ R7 be a column vector. Then the rank of P + aaT is at least ________.


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*Answer can only contain numeric values
QUESTION: 49

For x > 0, let |x| denote the greatest integer less than or equal to x. Then


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ANSWER :- 55

Solution :-  lim x -->0  1/x  => 1/0

= ∞ i.e Apply L-hospital rule

lim x-->0 x[1/x + 2/x + 3/x + 4/x +.......................10/x]

lim x→0  x[10*11]/2 * 1/x

= [10*11]/2    => 55

*Answer can only contain numeric values
QUESTION: 50

The number of subgroups of Z7 x Zof order 7 is _______.


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*Answer can only contain numeric values
QUESTION: 51

Let y(x), x > 0 be the solution of the differential equation

satisfying the conditions y(1) = 1 and y’(1) = 0. Then the value of e2y(e) is ______


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*Answer can only contain numeric values
QUESTION: 52

Let T be the smallest positive real number such that the tangent to the helix

at t = T is orthogonal to the tangent at t = 0. Then the line integral of     along the section of the helix from t = 0 to t = T is _____


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*Answer can only contain numeric values
QUESTION: 53


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*Answer can only contain numeric values
QUESTION: 54

The maximum order of a permutation s in the symmetric group S10 is ____


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*Answer can only contain numeric values
QUESTION: 55


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*Answer can only contain numeric values
QUESTION: 56

For a real number x, define [x] to be the smallest integer greater than or equal to x. Then


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*Answer can only contain numeric values
QUESTION: 57

For x > 1, let

The number of tangents to the curve y = f(x) parallel to the line x + y = 0 is ____


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*Answer can only contain numeric values
QUESTION: 58


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*Answer can only contain numeric values
QUESTION: 59

The radius of convergence of the power series  


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*Answer can only contain numeric values
QUESTION: 60


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