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.
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Correct Answer: All are true.
Solution : Let's verify each of the statements one by one. Statement 1: 1. Factors of 72 is 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72, i.e., total = 12. Statement 2: 2. Sum of 20 odd numbers $S = \frac{n}{2}[2a+(n–1)d]$ $S = \frac{20}{2}[2\times1+(20–1)2]$ $S = \frac{20}{2}[2+(19×2)]$ $S = \frac{20}{2}[40]$ $S = 400$ Statement 3: 3. The largest 2-digit prime number nearest to 100 is 97. (A number divisible by only 1 or itself is a prime number.) So, here all statements are true. Hence, the correct answer is 'All are true'.
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Question : If the digits of a two-digit number are reversed, then the number is decreased by 36. Which of the following is correct regarding the number? I. The difference between the digits is 4. II. The value of the number can be 84. III. Number is always a composite number.
Option 1: I, II, and III
Option 2: II and III
Option 3: I and III
Option 4: I and II
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 : Which of the following can be considered as an example of a flow variable?
(i) Production of rice (ii) Import of cloth (iii) Change in capital
Option 1: None of (i), (ii) and (iii)
Option 2: Only (iii)
Option 3: All of (i), (ii) and (iii)
Option 4: Only (i) and (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 from the statements. Statements: I. All blocks are toys. II. All toys are books. III. All books are stories. Conclusions: I. Some toys are blocks. II. Some blocks are books. III. Some stories are toys.
Option 1: Only conclusions I and III follow
Option 2: Only conclusions II and III follow
Option 3: Only conclusions I and II follow
Option 4: All the 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
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