The question asks for the definition of mechanical energy. Mechanical energy is a fundamental concept in physics, representing the energy associated with the motion and position of an object. It is the sum of two primary forms of energy.
Correct Option: B) Kinetic energy + Potential energy
The question asks about the element added to iron to increase its hardness and strength. This refers to the process of making steel, which is an alloy of iron. We need to identify the primary alloying element responsible for these properties.
Correct Option: C) Carbon is the primary element added to iron to make it hard and strong, forming various types of steel.
To solve this problem, we need to follow the order of operations, often remembered by the acronym BODMAS/PEMDAS. This means we perform Division and Multiplication before Addition and Subtraction. The given expression is \(122 + 345 - 3 \div 1116 \times 372\).
A) 466 is the correct answer after following the order of operations.
This problem involves understanding the direction of shadows during the morning and using relative directions to determine the facing direction of a person. The key is to know that in the morning, the sun is in the East, and shadows fall towards the West.
X was facing East. This is because in the morning, the sun is in the East, so shadows fall to the West. If Y's shadow falls on X, it means X is standing to the West of Y. Since X and Y are walking towards each other, and X is to the West of Y, X must be walking towards the East.
This problem involves a faulty clock that loses time. To find when it will show the correct time again, we need to determine how much time it must lose to complete a full 12-hour cycle. A clock shows the correct time again when it has either gained or lost exactly 12 hours (or a multiple of 12 hours) relative to the actual time.
Calculate the time lost per hour:
The watch loses 5 minutes every hour.
Determine the total time to be lost for the watch to show the correct time:
A clock shows the correct time again when it has lost (or gained) exactly 12 hours. This is because the clock face repeats every 12 hours. So, the watch needs to lose 12 hours.
Convert 12 hours into minutes:
\[ 12 \text{ hours} = 12 \times 60 \text{ minutes} = 720 \text{ minutes} \]Calculate the number of hours it takes for the watch to lose 720 minutes:
Since the watch loses 5 minutes per hour, the number of actual hours required to lose 720 minutes is:
\[ \text{Total hours} = \frac{\text{Total minutes to lose}}{\text{Minutes lost per hour}} = \frac{720 \text{ minutes}}{5 \text{ minutes/hour}} = 144 \text{ hours} \]Convert the total hours into days:
\[ \text{Total days} = \frac{144 \text{ hours}}{24 \text{ hours/day}} = 6 \text{ days} \]Determine the date and time when the watch will show the correct time again:
The watch was set right at 6 a.m. on a Monday. After 6 days, it will be 6 a.m. on the next Sunday.
A) 6 a.m. on next Sunday is the correct answer because the watch will show the correct time again exactly 6 days after it was set, which falls on Sunday at the same time.
B) 3 a.m. on next Monday — This option is incorrect because it implies a total time difference of 7 days minus 3 hours, which does not align with the calculated 6 days.
C) 3 a.m. on next Sunday — This option is incorrect because it implies a total time difference of 6 days minus 3 hours, which is not the 6 full days required.
D) 6 a.m. on next Monday — This option is incorrect because it implies a total time difference of 7 days, whereas the watch needs exactly 6 days to lose 12 hours and show the correct time again.
The question asks to identify the UPA's candidate for the Vice President's post in the 2017 elections. This requires knowledge of Indian political history, specifically the candidates put forth by major political alliances during that period.
Correct Option: B) Gopalkrishna Gandhi was the candidate nominated by the United Progressive Alliance (UPA) and 18 other opposition parties for the Vice President's post in the 2017 elections.
Select the Answer Figure that correctly fits in the blank space in the given Problem Figure.
Problem Figure:
Answer Figures:
The problem involves identifying patterns in the given grid of circles with shaded halves and arrows. The goal is to determine which option completes the sequence logically.
Correct Option: A) The pattern of shading and arrow direction fits the sequence.
Select the picture which does NOT belong to the group.
The task is to identify the image that does not belong to the group based on a common pattern or characteristic shared by the other images.
Correct Option: D) The hexagon shape in Option D does not match the simpler geometric shapes in the other options.
This problem involves applying Newton's Second Law of Motion, \(F = ma\). We need to first calculate the individual masses of the blocks using the given force and accelerations. Then, we combine these masses to find the total mass when they are tied together and calculate the new acceleration under the same force.
Given force \(F = 5 \text{ N}\) and acceleration \(a_1 = 10 \text{ ms}^{-2}\).
Using Newton's Second Law, \(F = m_1 a_1\):
\[ m_1 = \frac{F}{a_1} = \frac{5 \text{ N}}{10 \text{ ms}^{-2}} = 0.5 \text{ kg} \]Given force \(F = 5 \text{ N}\) and acceleration \(a_2 = 20 \text{ ms}^{-2}\).
Using Newton's Second Law, \(F = m_2 a_2\):
\[ m_2 = \frac{F}{a_2} = \frac{5 \text{ N}}{20 \text{ ms}^{-2}} = 0.25 \text{ kg} \]When the blocks are tied together, their masses add up:
\[ M_{\text{total}} = m_1 + m_2 = 0.5 \text{ kg} + 0.25 \text{ kg} = 0.75 \text{ kg} \]The same force \(F = 5 \text{ N}\) acts on the combined mass \(M_{\text{total}}\).
Using Newton's Second Law, \(F = M_{\text{total}} a_{\text{combined}}\):
\[ a_{\text{combined}} = \frac{F}{M_{\text{total}}} = \frac{5 \text{ N}}{0.75 \text{ kg}} \] \[ a_{\text{combined}} = \frac{5}{3/4} \text{ ms}^{-2} = \frac{5 \times 4}{3} \text{ ms}^{-2} = \frac{20}{3} \text{ ms}^{-2} \] \[ a_{\text{combined}} \approx 6.666... \text{ ms}^{-2} \approx 6.67 \text{ ms}^{-2} \]Correct Option: A) 6.67 ms⁻²
The question asks to identify the incorrect statement regarding periodic trends and properties of elements. We need to evaluate each option based on established principles of the periodic table.
Correct Option: C) Isotopes of the same element are placed in different groups.
This statement is incorrect because isotopes of the same element have the same atomic number and thus belong to the same element and occupy the same position in the periodic table. Their chemical properties are identical, and their placement is determined by atomic number, not mass number.