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Math - 2015 Past Year Paper - IIT JAM MCQ


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30 Questions MCQ Test - Math - 2015 Past Year Paper

Math - 2015 Past Year Paper for IIT JAM 2024 is part of IIT JAM preparation. The Math - 2015 Past Year Paper questions and answers have been prepared according to the IIT JAM exam syllabus.The Math - 2015 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 - 2015 Past Year Paper below.
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Math - 2015 Past Year Paper - Question 1

Suppose N is a normal subgroup of a group G. Which one of the following is true?

Math - 2015 Past Year Paper - Question 2

Let y(x) = u(x) sin sin x + v(x) cos x be a solution of the differential equation y” + y = sec x.
Then u(x) is

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Math - 2015 Past Year Paper - Question 3

Let a, b, c, d be distinct non- zero real numbers with a + b = c + d. Then an eigenvalue of the
matrix    is

Math - 2015 Past Year Paper - Question 4

Let S be a nonempty subset of R. If S is a finite union of disjoint bounded intervals, then which one of the following is true?

Math - 2015 Past Year Paper - Question 5

Let {xn} be a convergent sequence of real numbers. 

for n ≥ 1, then which one of the following is the limit of this sequence?

Math - 2015 Past Year Paper - Question 6

The volume of the portion of the solid cylinder x2 + y2 ≤ 2 bounded above by the surface z = x2 + y2 and bounded below by the xy- plane is

Math - 2015 Past Year Paper - Question 7

Let f: R→R be a differentiable function with f(0) = 0. If for all x ∈ R, 1 < f'(x) < 2, then which one of the following statements is true on (0, ∝)?

Math - 2015 Past Year Paper - Question 8

If an integral curve of the differential equation  passes through (0, 0) and (α, 1),
then α is equal to

Math - 2015 Past Year Paper - Question 9

An integrating factor of the differential equation 

Math - 2015 Past Year Paper - Question 10

Let A be a nonempty subset of R Let I(A) denote the set of interior points of A. Then I(A) can be

Math - 2015 Past Year Paper - Question 11

Let S3 be the group of permutations of three distinct symbols. The direct sum    has an element of order

Math - 2015 Past Year Paper - Question 12

The orthogonal trajectories of the family of curves y = C1x3 are

Math - 2015 Past Year Paper - Question 13

Let G be a nonabelian group. Let α ∈ G have order 4 and let β ∈ G have order 3. Then the order of the element αβ in G

Math - 2015 Past Year Paper - Question 14

Let S be the bounded surface of the cylinder x2 + y2 = 1 cut by the planes z = 0 and z = 1 + x. Then the value of the surface integral    is equal to 

Math - 2015 Past Year Paper - Question 15

Suppose that the dependent variables z and w are functions of the independent variables x and y, defined by the equations f(x, y, z, w) = 0 and g(x, y, z, w) = 0, where fzgw – fwgz = 1.
Which one of the following is correct

Math - 2015 Past Year Paper - Question 16

Math - 2015 Past Year Paper - Question 17

Math - 2015 Past Year Paper - Question 18

Let P2(R) be the vector space of polynomials in x of degree at most 2 with real coefficients. Let M2(R) be the vector space of 2 × 2 real matrices. If a linear transformation    is defined as    then

Math - 2015 Past Year Paper - Question 19

Let B1 = {(1, 2), (2, –1)} and B2 = {(1, 0), (0, 1} be ordered bases of R2 . If T : R2 →  R2  is a linear transformation such that 

 

then T(5, 5) is equal to

Math - 2015 Past Year Paper - Question 20

  Which one of the following statements is FALSE?

Math - 2015 Past Year Paper - Question 21

Let f : R → R be a strictly increasing continuous function. If {an} is a sequence in [0, 1], then the sequence {f(an)} is

Math - 2015 Past Year Paper - Question 22

Which one of the following statements is true for the series 

Math - 2015 Past Year Paper - Question 23

Math - 2015 Past Year Paper - Question 24

If y(t) is a solution of the differential equation y” + 4y = 2et, then

  is equal to 

Math - 2015 Past Year Paper - Question 25

For what real values of x and y, does the integral  attain its maximum?

Math - 2015 Past Year Paper - Question 26

The area of the planar region bounded by the curves x = 6y2 – 2 and x = 2y2 is

Detailed Solution for Math - 2015 Past Year Paper - Question 26




Hence correct option is A.

Math - 2015 Past Year Paper - Question 27

For n ≥ 2, let fn: R → R be given by fn(x) = xn sin x. Then at x = 0, fn has a

Math - 2015 Past Year Paper - Question 28

Math - 2015 Past Year Paper - Question 29

Let G and H be nonempty subsets of R , where G is connected and G U H is not connected.
Which one of the following statements is true for all such G and H ?

Math - 2015 Past Year Paper - Question 30

Then the value of 

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