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# Math - 2016 Past Year Paper

## 60 Questions MCQ Test IIT JAM Past Year Papers and Model Test Paper (All Branches) | Math - 2016 Past Year Paper

Description
This mock test of Math - 2016 Past Year Paper for IIT JAM helps you for every IIT JAM entrance exam. This contains 60 Multiple Choice Questions for IIT JAM Math - 2016 Past Year Paper (mcq) to study with solutions a complete question bank. The solved questions answers in this Math - 2016 Past Year Paper quiz give you a good mix of easy questions and tough questions. IIT JAM students definitely take this Math - 2016 Past Year Paper exercise for a better result in the exam. You can find other Math - 2016 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

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QUESTION: 3

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

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QUESTION: 4

Let σ  be an element of the permutation group S Then the maximum possible order of σ is

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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?

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QUESTION: 6 Solution:
QUESTION: 7 Solution:
QUESTION: 8

The nonzero value of n for which the differential equation becomes exact is

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QUESTION: 9

One of the points which lies on the solution curve of the differential equation with the given condition y(0) = 1, is

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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

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QUESTION: 11

Let S  be the series and T be the series of real numbers. Then which one of the following is TRUE?

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QUESTION: 12

Let {an} be a sequence of positive real numbers satisfying Then all the terms of the sequence lie in

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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

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QUESTION: 17 Solution:
QUESTION: 18

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

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QUESTION: 19 Solution:
QUESTION: 20

Let y(x) be the solution of the differential equation Then y(2) is

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QUESTION: 21 Solution:
QUESTION: 22

The general solution of the differential equation with constant coefficients approaches zero as x → ∞ if

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QUESTION: 23 of S. Then which one of the following is FALSE?

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QUESTION: 24

The sum of the series is

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QUESTION: 25 Then which one of the following is TRUE?

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QUESTION: 26

The matrix is a unitary matrix when α is

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QUESTION: 27 a non-zero vector such that Mx = b for some  x ∈ R3

The value of xTb is

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QUESTION: 28

The number of group homomorphisms from the cyclic group Z4 to the cycle group Z7 is

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QUESTION: 29

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

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QUESTION: 30 At x = 0 , the function f is

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*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?

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

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*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?

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*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  ____

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*Answer can only contain numeric values
QUESTION: 42

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

then is

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*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

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*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 _____

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*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(y,y,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 ____________

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*Answer can only contain numeric values
QUESTION: 51

The value of is equal to

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*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 =  ____________

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*Answer can only contain numeric values
QUESTION: 57

The value of the double integral is

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*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   __

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*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: