GATE MA format:mcq PYQs & Answers — Page 15

Questions 141–150 of 366. Imported answers require independent review unless marked reviewed.

The price of an item is 10% cheaper in an online store S compared to the price at another online store M. Store S charges ₹ 150 for delivery. There are no delivery charges for orders from the store M. A person bought the item from the store S and saved ₹ 100.

What is the price of the item at the online store S (in ₹) if there are no other charges than what is described above?

Your answerChoose one option.

250

220

175

150

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The letters P, Q, R, S, T and U are to be placed one per vertex on a regular convex hexagon, but not necessarily in the same order.

Consider the following statements:

• The line segment joining R and S is longer than the line segment joining P and Q. • The line segment joining R and S is perpendicular to the line segment joining P and Q. • The line segment joining R and U is parallel to the line segment joining T and Q.

Based on the above statements, which one of the following options is CORRECT?

Your answerChoose one option.

The line segment joining R and T is parallel to the line segment joining Q and S

The line segment joining T and Q is parallel to the line joining P and U

The line segment joining R and P is perpendicular to the line segment joining U and Q

The line segment joining Q and S is perpendicular to the line segment joining R and P

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An ant is at the bottom-left corner of a grid (point P) as shown above. It aims to move to the top-right corner of the grid. The ant moves only along the lines marked in the grid such that the current distance to the top-right corner strictly decreases.

Which one of the following is a part of a possible trajectory of the ant during the movement?

Your answerChoose one option.

Diagram for Mathematics question 10 (figure 2)

Diagram for Mathematics question 10 (figure 3)

Diagram for Mathematics question 10 (figure 4)

Diagram for Mathematics question 10 (figure 5)

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Suppose that the characteristic equation of

where

with

. Which of the following statements is TRUE?

Your answerChoose one option.

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Consider

P: Let

with

. If

, then the system of linear equations

has

as the only solution.

Q: Let

be a non-zero matrix such that

. Then

is a singular matrix.

Which of the following statements is TRUE?

Your answerChoose one option.

Both P and Q are TRUE

Both P and Q are FALSE

P is TRUE and Q is FALSE

P is FALSE and Q is TRUE

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Consider the real function of two real variables given by

Let

be the harmonic conjugate of

such that

. Let

and

, then the value of

Your answerChoose one option.

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The value of the integral

where

is the circle of radius 2 centred at the origin taken in the anti-clockwise direction is

Your answerChoose one option.

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Let

be a real normed linear space. Let

. If

contains two distinct points

and

and the line segment joining them, then, which of the following statements is TRUE?

Your answerChoose one option.

and

are linearly independent

and

are linearly dependent

and

are linearly independent

and

are linearly dependent

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Let

be an orthonormal basis for a Hilbert space

. Define

and

. Then

Your answerChoose one option.

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Consider

with the usual metric. Let

and

. Let

and

. Then, which of the following statements is TRUE?

Your answerChoose one option.

and

are connected

Neither

nor

is connected

is connected and

is not connected

is not connected and

is connected

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GATE MA format:mcq PYQs

Question 8

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Question 10

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Question 12

Question 13

Question 14

Question 15

Question 16

Question 17