Question : In $\triangle PQR, PQ=QR$ and $O$ is an interior point of $\triangle PQR$ such that $\angle OPR=\angle ORP$.
Consider the following statements:
(i) $\triangle POR$ is an isosceles triangle.
(ii) $O$ is the centroid of $\triangle PQR$.
(iii) $\triangle PQO$ is congruent to $\triangle RQO$.
Which of the above statements is/are correct?

Option 1: Only (i) and (ii)

Option 2: Only (i) and (iii)

Option 3: Only (ii) and (iii)

Option 4: Only (ii)

Question : Directions: Three statements are given followed by three conclusions numbered I, II, and III. Assuming the statements to be true, even if they seem to be at variance with commonly known facts, decide which of the conclusions logically follow(s) from the statements.
Statements:
All rice is grains.
All pulses are grains.
All grains are edibles.
Conclusions:
I. All rice is edible.
II. All pulses are edible.
III. Some edibles are grains.

Option 1: All conclusions follow

Option 2: Only conclusions II and III follow

Option 3: Only conclusions I and II follow

Option 4: Only conclusions I and III follow

Question : Which of the following statement(s) is/are TRUE?
I. The total number of positive factors of 72 is 12.
II. The sum of the first 20 odd numbers is 400.
III. The largest two-digit prime number is 97.

Option 1: Only I and II

Option 2: Only II and III

Option 3: Only I and III

Option 4: All are true.

Question : Directions: Three Statements are given followed by three conclusions numbered I, II, and III. Assuming the statements to be true, even if they seem to be at variance with commonly known facts, decide which of the conclusions logically follow(s) from the statements.
Statements:
All rice is wheat.
Some wheats are pulses.
No pulses are a vegetable.
Conclusions:
I. Some vegetables are rice.
II. Some pulses are rice.
III. Some vegetables are wheat.

Option 1: None of the conclusions follows

Option 2: Both conclusions I and II follow

Option 3: Both conclusions II and III follow

Option 4: All conclusions follow

Question : Directions: Three statements are given followed by three conclusions numbered I, II, and III. Assuming the statements to be true, even if they seem to be at variance with commonly known facts, decide which of the conclusions logically follow(s) from the statements.
Statements:
I. All cancers are diseases.
II. All tuberculosis is a disease.
III. All diseases are curable.
Conclusions:
I. All tuberculosis is curable.
II. Some cancers are tuberculosis.
III. All cancers are curable.

Option 1: Only conclusions II and III follow

Option 2: Only conclusions I and III follow

Option 3: All conclusions follow

Option 4: Only conclusions I and II follow