Math - 2016 Past Year Paper - IIT JAM MCQ

# Math - 2016 Past Year Paper - IIT JAM MCQ

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## 60 Questions MCQ Test - Math - 2016 Past Year Paper

Math - 2016 Past Year Paper for IIT JAM 2024 is part of IIT JAM preparation. The Math - 2016 Past Year Paper questions and answers have been prepared according to the IIT JAM exam syllabus.The Math - 2016 Past Year Paper MCQs are made for IIT JAM 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Math - 2016 Past Year Paper below.
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Math - 2016 Past Year Paper - Question 1

### The sequence {Sn} of real numbers given by

Math - 2016 Past Year Paper - 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

Math - 2016 Past Year Paper - Question 3

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

Math - 2016 Past Year Paper - Question 4

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

Math - 2016 Past Year Paper - 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?

Math - 2016 Past Year Paper - Question 6

Math - 2016 Past Year Paper - Question 7

Math - 2016 Past Year Paper - Question 8

The nonzero value of n for which the differential equation

becomes exact is

Math - 2016 Past Year Paper - Question 9

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

with the given condition y(0) = 1, is

Math - 2016 Past Year Paper - 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

Math - 2016 Past Year Paper - Question 11

Let S  be the series

and T be the series

of real numbers. Then which one of the following is TRUE?

Math - 2016 Past Year Paper - Question 12

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

Then all the terms of the sequence lie in

Math - 2016 Past Year Paper - Question 13

The largest eigenvalue of the matrix

Math - 2016 Past Year Paper - Question 14

The value of the integral

Math - 2016 Past Year Paper - 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

Math - 2016 Past Year Paper - Question 16

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

Math - 2016 Past Year Paper - Question 17

Math - 2016 Past Year Paper - Question 18

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

Math - 2016 Past Year Paper - Question 19

Math - 2016 Past Year Paper - Question 20

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

Then y(2) is

Math - 2016 Past Year Paper - Question 21

Math - 2016 Past Year Paper - Question 22

The general solution of the differential equation with constant coefficients

approaches zero as x → ∞ if

Math - 2016 Past Year Paper - Question 23

of S. Then which one of the following is FALSE?

Math - 2016 Past Year Paper - Question 24

The sum of the series

is

Math - 2016 Past Year Paper - Question 25

Then which one of the following is TRUE?

Math - 2016 Past Year Paper - Question 26

The matrix     is a unitary matrix when α is

Math - 2016 Past Year Paper - Question 27

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

The value of xTb is

Math - 2016 Past Year Paper - Question 28

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

Math - 2016 Past Year Paper - 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?

Math - 2016 Past Year Paper - Question 30

At x = 0 , the function f is

Detailed Solution for Math - 2016 Past Year Paper - Question 30

*Multiple options can be correct
Math - 2016 Past Year Paper - 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 ?

*Multiple options can be correct
Math - 2016 Past Year Paper - Question 32

The value(s) of the integral

.    is

*Multiple options can be correct
Math - 2016 Past Year Paper - Question 33

Then at the point (0, 0) which of the following statement(s) is(are) TRUE ?

*Multiple options can be correct
Math - 2016 Past Year Paper - Question 34

*Multiple options can be correct
Math - 2016 Past Year Paper - Question 35

Consider the differential equation

Then which of the following statement(s)  is(are) TRUE?

*Multiple options can be correct
Math - 2016 Past Year Paper - Question 36

Which of the following statement(s)  is(are) TRUE?

*Multiple options can be correct
Math - 2016 Past Year Paper - Question 37

Then which of the following statement(s) is(are)
TRUE?

*Multiple options can be correct
Math - 2016 Past Year Paper - Question 38

Let G  be a finite group and o(G)  denotes its order. Then which of the following statement(s) is(are) TRUE?

*Multiple options can be correct
Math - 2016 Past Year Paper - Question 39

Consider the set  For which of the following choice(s) the set V  becomes a two dimensional subspace of  R3 over  R ?

*Multiple options can be correct
Math - 2016 Past Year Paper - Question 40

Then which of the following statement(s) is(are) TRUE?

*Answer can only contain numeric values
Math - 2016 Past Year Paper - Question 41

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

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

*Answer can only contain numeric values
Math - 2016 Past Year Paper - Question 42

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

then    is

*Answer can only contain numeric values
Math - 2016 Past Year Paper - Question 43

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

*Answer can only contain numeric values
Math - 2016 Past Year Paper - 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 _____

*Answer can only contain numeric values
Math - 2016 Past Year Paper - Question 45

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

*Answer can only contain numeric values
Math - 2016 Past Year Paper - Question 46

is expressed as

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

*Answer can only contain numeric values
Math - 2016 Past Year Paper - 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____________

*Answer can only contain numeric values
Math - 2016 Past Year Paper - Question 48

The radius of convergence of the power series

*Answer can only contain numeric values
Math - 2016 Past Year Paper - Question 49

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

Then the value of

*Answer can only contain numeric values
Math - 2016 Past Year Paper - Question 50

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

*Answer can only contain numeric values
Math - 2016 Past Year Paper - Question 51

The value of   is equal to

*Answer can only contain numeric values
Math - 2016 Past Year Paper - Question 52

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

*Answer can only contain numeric values
Math - 2016 Past Year Paper - Question 53

Let

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

*Answer can only contain numeric values
Math - 2016 Past Year Paper - 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 _____

*Answer can only contain numeric values
Math - 2016 Past Year Paper - 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 ______

*Answer can only contain numeric values
Math - 2016 Past Year Paper - Question 56

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

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

*Answer can only contain numeric values
Math - 2016 Past Year Paper - Question 57

The value of the double integral

is

*Answer can only contain numeric values
Math - 2016 Past Year Paper - 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 ----

*Answer can only contain numeric values
Math - 2016 Past Year Paper - 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   __

*Answer can only contain numeric values
Math - 2016 Past Year Paper - Question 60

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

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