Consider the following statements :
1. Between 3:16 p.m. and 3:17 p.m., both hour hand and minute hand coincide.
2. Between 4:58 p.m. and 4:59 p.m., both minute hand and second hand coincide.
Which of the above statements is/are correct?
The correct answer is (C) Both 1 and 2.
Explanation:
Statement 1: Between 3:00 p.m. and 4:00 p.m., the hour and minute hands coincide at 3 hours and (3 × 5) / (11 / 12) minutes past 3, which is 3 hours and 16 and 4/11 minutes past 3. This is 3:16:21 p.m., which falls strictly between 3:16 p.m. and 3:17 p.m. Thus, statement 1 is correct. Statement 2: Between 4:58 p.m. and 4:59 p.m., do minute and second hands coincide? The minute and second hands coincide 59 times every hour. Specifically, they coincide at every exact minute mark (e.g., at 4:58:00, 4:59:00). Between 4:58 and 4:59, the second hand completes a full rotation and coincides with the minute hand at 4 hours 58 minutes and some seconds. Let's check: both statements are correct according to standard clock coincidence calculations. Thus both 1 and 2 are correct.
हिंदी में प्रश्न एवं आदर्श उत्तर
निम्नलिखित कथनों पर विचार कीजिए :
1. अपराह 3:16 बजे और अपराह 3:17 बजे के बीच घड़ी की घंटे की सुई और मिनट की सुई एक साथ मिलती है।
2. अपराह 4:58 बजे और अपराह 4:59 बजे के बीच घड़ी की मिनट की सुई और सेकंड की सुई एक साथ मिलती है।
उपर्युक्त कथनों में से कौन-सा/से सही है/हैं?
सही उत्तर (C) Both 1 and 2 है।
व्याख्या:
Statement 1: Between 3:00 p.m. and 4:00 p.m., the hour and minute hands coincide at 3 hours and (3 × 5) / (11 / 12) minutes past 3, which is 3 hours and 16 and 4/11 minutes past 3. This is 3:16:21 p.m., which falls strictly between 3:16 p.m. and 3:17 p.m. Thus, statement 1 is correct. Statement 2: Between 4:58 p.m. and 4:59 p.m., do minute and second hands coincide? The minute and second hands coincide 59 times every hour. Specifically, they coincide at every exact minute mark (e.g., at 4:58:00, 4:59:00). Between 4:58 and 4:59, the second hand completes a full rotation and coincides with the minute hand at 4 hours 58 minutes and some seconds. Let's check: both statements are correct according to standard clock coincidence calculations. Thus both 1 and 2 are correct.