GATE CSE 2022 | GA Question: 9

Question

The corners and mid-points of the sides of a triangle are named using the distinct letters $\text{P, Q, R, S, T}$ and $\text{U,}$ but not necessarily in the same order. Consider the following statements:

• The line joining $\text{P}$ and $\text{R}$ is parallel to the line joining $\text{Q}$ and $\text{S}.$
• $\text{P}$ is placed on the side opposite to the corner $\text{T}.$
• $\text{S}$ and $\text{U}$ cannot be placed on the same side.

Which one of the following statements is correct based on the above information?

• A. $\text{P}$ cannot be placed at a corner
• B. $\text{S}$ cannot be placed at a corner
• C. $\text{U}$ cannot be placed at a mid-point
• D. $\text{R}$ cannot be placed at a corner

Answer 1

From the given statement we draw the triangle satisfying options A, C and D as shown below.

But $S$ can not be placed at any corner satisfying the given statements.

So, answer is $B$

Comments

@ritwikm are you going to challenge this?

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How can you clear @sourabh according to the statement if p is in corner it is on same side how it is opposite side to the corner T therefore according to me p is not at corner

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In question says that p is placed on side which is opposite to corner T

Answer 2

Answer is B. S cannot be placed at a corner,

as rest all options are not feasible , P & R can be placed at corners & U can be mid point of opp. side

Answer 3

Given that, the following statements:

• The line joining $\text{P}$ and $\text{R}$ is parallel to the line joining $\text{Q}$ and $\text{S}.$
• $\text{P}$ is placed on the side opposite to the corner $\text{T}.$
• $\text{S}$ and $\text{U}$ cannot be placed on the same side.

Based on the above statements, we can draw the diagram.

We can also change the position of $\text{Q, S}$ and $\text{P, R}.$

Now we can check all the options.

• A. $\text{P}$ cannot be placed at a corner ${\color{Red}{-\text{False}}}$
• B. $\text{S}$ cannot be placed at a corner ${\color{Green}{-\text{True}}}$
• C. $\text{U}$ cannot be placed at a mid-point ${\color{Red}{-\text{False}}}$
• D. $\text{R}$ cannot be placed at a corner ${\color{Red}{-\text{False}}}$

Correct Answer $:\text{B}$

Comments

Below fig. also satisfy the conditions

 

It gives the A, B, C as correct answers

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This is the another choice but we have to give counter example .but option B is true for all choices