GATE MA format:mcq PYQs & Answers — Page 5

Questions 41–50 of 366. Imported answers require independent review unless marked reviewed.

A square paper, shown in figure (I), is folded along the dotted lines as shown in the figures (II) and (III). Then a few cuts are made as shown in figure (IV). Which one of the following patterns will be obtained when the paper is unfolded?

Note: The figures shown are representative.

Figures (I)–(IV):

Your answerChoose one option.

Diagram for Mathematics question 9 (figure 2)

Diagram for Mathematics question 9 (figure 3)

Diagram for Mathematics question 9 (figure 4)

Diagram for Mathematics question 9 (figure 5)

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A shop has 4 distinct flavors of ice-cream. One can purchase any number of scoops of any flavor. The order in which the scoops are purchased is inconsequential. If one wants to purchase 3 scoops of ice-cream, in how many ways can one make that purchase?

Your answerChoose one option.

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Let

be diagonalizable and

, where

. Then, which one of the following is TRUE?

Your answerChoose one option.

is compact and connected

is neither compact nor connected

is compact but not connected

is connected but not compact

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Given that the Laplace transforms of

and

exist, where

is the Bessel function. Let

be the Laplace transform of the Bessel function

. Then, which one of the following is TRUE?

Your answerChoose one option.

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To find a real root of the equation

in the interval

by using the fixed-point iteration scheme, consider the following two statements:

S1: The iteration scheme

, converges for any initial guess

S2: The iteration scheme

, diverges for some initial guess

Then, which one of the following is correct?

Your answerChoose one option.

S1 is TRUE and S2 is FALSE

S2 is TRUE and S1 is FALSE

both S1 and S2 are TRUE

neither S1 nor S2 is TRUE

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For the linear programming problem:

Maximize

Subject to

consider the following two statements:

S1: If

and

, then

forms an optimal basis.

S2: If

and

, then

forms an optimal basis.

Then, which one of the following is correct?

Your answerChoose one option.

S1 is TRUE and S2 is FALSE

S2 is TRUE and S1 is FALSE

both S1 and S2 are TRUE

neither S1 nor S2 is TRUE

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Consider the following subsets of the Euclidean space

, and

Then, which one of the following is TRUE?

Your answerChoose one option.

is connected, but

and

are not connected

and

are connected, but

is not connected

and

are connected, but

is not connected

and

are connected, but

is not connected

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Consider the system of ordinary differential equations

where

is a

skew-symmetric matrix with entries in

. Then, for this system, the origin is a stable critical point for

Your answerChoose one option.

any such matrix

only such matrices

whose rank is 2

only such matrices

whose rank is 4

only such matrices

whose rank is 6

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Let

with the norm

, where

is the space of all real-valued continuous functions on

. Let

with the norm

. Let

and

be the closed unit balls in

and

centred at the origin, respectively. Consider

and

given by

Consider the following statements:

S1:

is attained at a point of

S2:

is attained at a point of

Then, which one of the following is correct?

Your answerChoose one option.

S1 is TRUE and S2 is FALSE

S2 is TRUE and S1 is FALSE

both S1 and S2 are TRUE

neither S1 nor S2 is TRUE

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Let

be defined in

, where

is a continuously differentiable non-zero homogeneous function of degree 4. Then,

holds for

Your answerChoose one option.

all points

on the line given by

all points

in the region of

except on the line given by

all points

on the line given by

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GATE MA format:mcq PYQs

Question 9

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Question 18