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Math - 2016 Past Year Paper


60 Questions MCQ Test Past Year Papers of IIT JAM Mathematics | Math - 2016 Past Year Paper


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Attempt Math - 2016 Past Year Paper | 60 questions in 180 minutes | Mock test for IIT JAM preparation | Free important questions MCQ to study Past Year Papers of IIT JAM Mathematics for IIT JAM Exam | Download free PDF with solutions
QUESTION: 1

The sequence {Sn} of real numbers given by 

Solution:
QUESTION: 2

Let  be the vector space (over R)  of all polynomials of degree ≤ 3 with real coefficients. Consider the linear transformation T: P → P defined by 

Then the matrix representation M of T  with respect to the ordered basis {1, x, x2, x2 }satisfies 

Solution:
QUESTION: 3

Let f : [-1,1] → R be a continuous function. Then the integral 

 is equal to

Solution:
QUESTION: 4

Let σ  be an element of the permutation group S5  Then the maximum possible order of σ is 
Solution:
QUESTION: 5

Let f be a strictly monotonic continuous real valued function defined on [a,b]  such that f(a) < a  and f(b) >b Then which one of the following is TRUE? 
Solution:
QUESTION: 6

Solution:
QUESTION: 7

Solution:
QUESTION: 8

The nonzero value of n for which the differential equation 

becomes exact is 
Solution:
QUESTION: 9

One of the points which lies on the solution curve of the differential equation  

with the given condition y(0) = 1, is
Solution:
QUESTION: 10

Let S be a closed set of R, T a compact set of R such that S ∩ T ≠ Ø. Then S ∩ T is 
Solution:
QUESTION: 11

Let S  be the series  

and T be the series 

of real numbers. Then which one of the following is TRUE?  
Solution:
QUESTION: 12

Let {an} be a sequence of positive real numbers satisfying  

Then all the terms of the sequence lie in  
Solution:
QUESTION: 13

The largest eigenvalue of the matrix 

Solution:
QUESTION: 14

The value of the integral 
Solution:
QUESTION: 15

If the triple integral over the region bounded by the planes 2x + y + z = 4, x = 0 , y = 0, z = 0
is given by   then the function 

Solution:
QUESTION: 16

The surface area of the portion of the plane y + 2z = 2 within the cylinder  x2 + y2 = 3 is
Solution:
QUESTION: 17

Solution:
QUESTION: 18

The function f(x,y) = 3x2y + 4y3 -3x2 - 12y2 + 1 has a saddle point at
Solution:
QUESTION: 19

Solution:
QUESTION: 20

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

Then y(2) is 
Solution:
QUESTION: 21

Solution:
QUESTION: 22

The general solution of the differential equation with constant coefficients  

approaches zero as x → ∞ if 
Solution:
QUESTION: 23

of S. Then which one of the following is FALSE?
Solution:
QUESTION: 24

The sum of the series  

  is 
Solution:
QUESTION: 25

Then which one of the following is TRUE? 
Solution:
QUESTION: 26

The matrix     is a unitary matrix when α is  
Solution:
QUESTION: 27

  a non-zero vector such that Mx = b for some  x ∈ R3

The value of xTb is
Solution:
QUESTION: 28

The number of group homomorphisms from the cyclic group Z4 to the cycle group Z7 is 
Solution:
QUESTION: 29

In the permutation group Sn (n ≥ 5) , if H  is the smallest subgroup containing all the 3-cycles, then which one of the following is TRUE?  
Solution:
QUESTION: 30

At x = 0 , the function f is 
Solution:
*Multiple options can be correct
QUESTION: 31

 be a sequence of positive real numbers satisfying  

If α and β are the roots of the equation 

then which of the following statement(s) is(are) TRUE ?
Solution:
*Multiple options can be correct
QUESTION: 32

The value(s) of the integral  

.    is 
Solution:
*Multiple options can be correct
QUESTION: 33

Then at the point (0, 0) which of the following statement(s) is(are) TRUE ? 
Solution:
*Multiple options can be correct
QUESTION: 34

Solution:
*Multiple options can be correct
QUESTION: 35

Consider the differential equation

Then which of the following statement(s)  is(are) TRUE? 
Solution:
*Multiple options can be correct
QUESTION: 36

Which of the following statement(s)  is(are) TRUE?  
Solution:
*Multiple options can be correct
QUESTION: 37

  Then which of the following statement(s) is(are) 
TRUE? 
Solution:
*Multiple options can be correct
QUESTION: 38

Let G  be a finite group and o(G)  denotes its order. Then which of the following statement(s) is(are) TRUE? 
Solution:
*Multiple options can be correct
QUESTION: 39

Consider the set  For which of the following choice(s) the set V  becomes a two dimensional subspace of  R3 over  R ? 
Solution:
*Multiple options can be correct
QUESTION: 40

 Then which of the following statement(s) is(are) TRUE? 
Solution:
*Answer can only contain numeric values
QUESTION: 41

Let {Sn} be a sequence of real numbers given by 

Then the least upper bound of the sequence {Sn}  is  ____

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

Let {Sk} be a sequence of real numbers, where

then    is 

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

Let    be a non-zero vector and    Then the dimension of the vector space    over R is 

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

Let f be a real valued function defined by  

Then the value of     at any point (x,y) where x > 0, y > 0,  is _____

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

 Then the value of integral  from (0, 0) to (1, 1) along the path  

 


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

  is expressed as 

where ξ  lies between 2 and x , then the value of c is ____

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

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

If the Wronskian W(y1 ,y2 ,y3) is of the form kebx for some constant k, then the value of b is____________ 

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

The radius of convergence of the power series 

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

Let f : (0,∝ ) → R be a continuous function such that 

Then the value of  

 

 

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

Let G be a cyclic group of order 12. Then the number of  non-isomorphic subgroups of G  is ____________

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

The value of   is equal to 

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

Let R be the region enclosed by    and     . Then the value of 

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

Let

Then Mx = 0 has infinitely many solutions if  trace(M) is 

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

Let C  be the boundary of the region enclosed by y = x2 ,y = x + 2, and x = 0.  Then the value of the line integral  

where C is traversed in the counter clockwise direction, is _____

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

Let S be the closed surface forming the boundary of the region V bounded by x2 + y2 = 3,

z = 0, z = 6,    Then the value of 

where n^ is the unit outward drawn normal to the surface S, is ______

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

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

Then y(x) attains its maximum value at x =  ____________ 

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

The value of the double integral  

  is 

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

Let H denote the group of all 2x 2 invertible matrices over Z5  under usual matrix multiplication. Then the order of the matrix    in H is ----

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

N(A) the null space of A and R(B) the range space of B. Then the dimension of N(A )∩ R(B)over R is   __

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

The maximum value of f(x,y) = x2 + 2y2 subject to the constraint  y - x2 + 1 = 0 is  ___________

Solution:
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