Math - 2017 Past Year Paper


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

Math - 2017 Past Year Paper for IIT JAM 2022 is part of IIT JAM Past Year Papers and Model Test Paper (All Branches) preparation. The Math - 2017 Past Year Paper questions and answers have been prepared according to the IIT JAM exam syllabus.The Math - 2017 Past Year Paper MCQs are made for IIT JAM 2022 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Math - 2017 Past Year Paper below.
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Math - 2017 Past Year Paper - 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

Math - 2017 Past Year Paper - 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 ?

Math - 2017 Past Year Paper - Question 3

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

Math - 2017 Past Year Paper - Question 4

Math - 2017 Past Year Paper - Question 5

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

Math - 2017 Past Year Paper - Question 6

Math - 2017 Past Year Paper - 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 

Math - 2017 Past Year Paper - Question 8

Then which one of the following is TRUE ?

Math - 2017 Past Year Paper - Question 9

Math - 2017 Past Year Paper - Question 10

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

Math - 2017 Past Year Paper - Question 11

The flux of the vector field

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

Math - 2017 Past Year Paper - 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

Math - 2017 Past Year Paper - Question 13

Math - 2017 Past Year Paper - Question 14

Math - 2017 Past Year Paper - 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

Math - 2017 Past Year Paper - Question 16

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

Math - 2017 Past Year Paper - Question 17

be the circle oriented anti- clockwise. Then

Math - 2017 Past Year Paper - Question 18

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

 

Math - 2017 Past Year Paper - Question 19

Math - 2017 Past Year Paper - Question 20

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

Math - 2017 Past Year Paper - Question 21

The interval of convergence of the power series 

Math - 2017 Past Year Paper - 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 

Math - 2017 Past Year Paper - Question 23

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

Math - 2017 Past Year Paper - 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 ?

Math - 2017 Past Year Paper - Question 25

Math - 2017 Past Year Paper - Question 26

Then which one of the followings is NOT TRUE ?

Math - 2017 Past Year Paper - Question 27

Math - 2017 Past Year Paper - Question 28

Which one of the following is TRUE ?

Math - 2017 Past Year Paper - Question 29

A particular integral of the differential equation 

Math - 2017 Past Year Paper - Question 30

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

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

*Multiple options can be correct
Math - 2017 Past Year Paper - Question 31

Then which of the following statements is/are TRUE ?

*Multiple options can be correct
Math - 2017 Past Year Paper - Question 32

The volume of the solid     is expressible as

*Multiple options can be correct
Math - 2017 Past Year Paper - Question 33

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

*Multiple options can be correct
Math - 2017 Past Year Paper - Question 34

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

*Multiple options can be correct
Math - 2017 Past Year Paper - 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 ?

*Multiple options can be correct
Math - 2017 Past Year Paper - Question 36

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

*Multiple options can be correct
Math - 2017 Past Year Paper - Question 37

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

*Multiple options can be correct
Math - 2017 Past Year Paper - 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 ?

*Multiple options can be correct
Math - 2017 Past Year Paper - 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 ?

*Multiple options can be correct
Math - 2017 Past Year Paper - Question 40

*Answer can only contain numeric values
Math - 2017 Past Year Paper - Question 41

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


*Answer can only contain numeric values
Math - 2017 Past Year Paper - Question 42

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


*Answer can only contain numeric values
Math - 2017 Past Year Paper - Question 43

Consider the permutations  

   in S8 . The number of η ∈  S8  such that  


*Answer can only contain numeric values
Math - 2017 Past Year Paper - 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 ______.


*Answer can only contain numeric values
Math - 2017 Past Year Paper - Question 45


*Answer can only contain numeric values
Math - 2017 Past Year Paper - 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 __________.


*Answer can only contain numeric values
Math - 2017 Past Year Paper - Question 47


*Answer can only contain numeric values
Math - 2017 Past Year Paper - 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 ________.


*Answer can only contain numeric values
Math - 2017 Past Year Paper - Question 49

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


Detailed Solution for Math - 2017 Past Year Paper - Question 49

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
Math - 2017 Past Year Paper - Question 50

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


*Answer can only contain numeric values
Math - 2017 Past Year Paper - 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 ______


*Answer can only contain numeric values
Math - 2017 Past Year Paper - 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 _____


*Answer can only contain numeric values
Math - 2017 Past Year Paper - Question 53


*Answer can only contain numeric values
Math - 2017 Past Year Paper - Question 54

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


*Answer can only contain numeric values
Math - 2017 Past Year Paper - Question 55


*Answer can only contain numeric values
Math - 2017 Past Year Paper - Question 56

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


*Answer can only contain numeric values
Math - 2017 Past Year Paper - Question 57

For x > 1, let

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


*Answer can only contain numeric values
Math - 2017 Past Year Paper - Question 58


*Answer can only contain numeric values
Math - 2017 Past Year Paper - Question 59

The radius of convergence of the power series  


*Answer can only contain numeric values
Math - 2017 Past Year Paper - Question 60


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