The question asks to identify the individual who assumed the role of Comptroller and Auditor General (CAG) of India in 2017. This is a factual question related to appointments in significant government positions, which is a common topic in competitive exams.
Correct Option: A) Rajiv Mehrishi was indeed appointed as the Comptroller and Auditor General (CAG) of India in 2017. He took office on September 25, 2017, and served until August 7, 2020.
To find the angle between the hour hand and the minute hand, we need to calculate the angular position of each hand relative to the 12 o'clock mark at the given time. The difference between these positions will give us the angle. We must consider that the hour hand moves continuously, not just at the hour marks.
The minute hand completes a full circle (360°) in 60 minutes. So, its speed is \( \frac{360^\circ}{60 \text{ min}} = 6^\circ \) per minute.
At 37 minutes past the hour, the angle of the minute hand from the 12 o'clock mark is:
\[ \text{Angle}_{\text{minute}} = 37 \text{ min} \times 6^\circ/\text{min} = 222^\circ \]The hour hand completes a full circle (360°) in 12 hours. So, its speed is \( \frac{360^\circ}{12 \text{ hours}} = 30^\circ \) per hour.
It also moves \( \frac{30^\circ}{60 \text{ min}} = 0.5^\circ \) per minute.
At 4:37 p.m., the hour hand has moved past the 4 o'clock mark. Its position is determined by the hour (4) and the additional minutes (37).
Angle due to hours = \( 4 \text{ hours} \times 30^\circ/\text{hour} = 120^\circ \)
Angle due to minutes = \( 37 \text{ min} \times 0.5^\circ/\text{min} = 18.5^\circ \)
Total angle of the hour hand from the 12 o'clock mark is:
\[ \text{Angle}_{\text{hour}} = 120^\circ + 18.5^\circ = 138.5^\circ \]The difference between the positions of the two hands is:
\[ \text{Difference} = |\text{Angle}_{\text{minute}} - \text{Angle}_{\text{hour}}| = |222^\circ - 138.5^\circ| = 83.5^\circ \]The angle calculated is \( 83.5^\circ \). Since this is less than or equal to 180°, it is the acute angle.
B) 83.5° is the calculated acute angle between the hour and minute hands at 4:37 p.m.
This is an analogy question where we need to find the relationship between the first pair of words and then apply the same relationship to the second pair to find the missing word.
Correct Option: C) Victory is the desired outcome or result of matches, just as success is the desired outcome of an examination.
This problem involves ratios and ages. We can set up algebraic equations based on the given ratios of present ages and future ages, and then solve for the unknown variable to find the present ages.
Define variables for present ages:
Let the present age of Sai be \(5x\) years.
Let the present age of Satheesh be \(4x\) years.
Determine ages after three years:
After three years, Sai's age will be \(5x + 3\) years.
After three years, Satheesh's age will be \(4x + 3\) years.
Formulate the equation based on the future ratio:
According to the problem, three years hence, the ratio of their ages will be \(11 : 9\). So, we can write the equation:
Solve the equation for \(x\):
Cross-multiply to solve for \(x\):
Isolate \(x\):
Subtract \(44x\) from both sides:
Solve for \(x\):
Subtract \(27\) from both sides:
Calculate Satheesh's present age:
Satheesh's present age is \(4x\). Substitute the value of \(x\):
Correct Option: B) 24
Satheesh's present age is 24 years. Sai's present age would be \(5 \times 6 = 30\) years. After 3 years, Sai's age would be \(30+3 = 33\) and Satheesh's age would be \(24+3 = 27\). The ratio \(33:27\) simplifies to \(11:9\), which matches the condition given in the problem.
To find the kinetic energy of the ball, we need to use the formula for kinetic energy, which relates the mass of the object and its velocity. We will substitute the given values into the formula and calculate the result.
Kinetic Energy (\(KE\)) is given by the formula:
\[ KE = \frac{1}{2}mv^2 \]The kinetic energy of the ball is 4 Joules.
Correct Option: C) 4 J
Select the option that fits in the blank space in the given Problem Figure.
Problem Figure:
The problem involves identifying the pattern in the given figure and selecting the correct option that completes the sequence. The key is to observe the arrangement of arcs and how they interact within the grid.
Correct Option: C) The arcs in this option complete the circular pattern in the grid.
This question tests the understanding of Ohm's Law and the relationship between potential difference (V), current (I), and resistance (R). Ohm's Law states that the current flowing through a conductor between two points is directly proportional to the potential difference across the two points, and inversely proportional to the resistance between them, provided the temperature and other physical conditions remain constant.
where \(V\) is the potential difference, \(I\) is the current, and \(R\) is the resistance.
D) resistance decreases — As derived from Ohm's Law \(R = V/I\), if \(V\) is constant and \(I\) increases, then \(R\) must decrease.
This question asks about the atomic composition of an ozone molecule. To answer this, one needs to know the chemical formula for ozone.
Correct Option: C) 3
The question asks to identify the political party founded by Telugu film actor Chiranjeevi, which he later merged with the Indian National Congress. This requires knowledge of Indian political history, specifically related to prominent personalities and their political ventures.
Correct Option: D) Praja Rajyam Party was founded by Chiranjeevi in August 2008. He subsequently merged this party with the Indian National Congress in August 2011, and he was later made a Union Minister.
To solve this problem, we need to follow the order of operations, often remembered by the acronym BODMAS/PEMDAS. This means we perform operations in the following order: Brackets/Parentheses, Orders/Exponents, Division and Multiplication (from left to right), and Addition and Subtraction (from left to right).
Thus, the solution is \(– 12\).
Correct Option: C) -12
