The problem asks us to find the number of sides of a regular polygon given the measure of each of its exterior angles. We will use the property that the sum of the exterior angles of any convex polygon is 360 degrees, and for a regular polygon, all exterior angles are equal.
C) 9 is the correct answer because a regular polygon with 9 sides has each exterior angle equal to \(360^\circ / 9 = 40^\circ\).
Simplify: (25)(\( \frac{3}{2} \))
The problem asks us to simplify an expression involving a number raised to a fractional power. We need to understand the rules of exponents, particularly how to handle fractional exponents, which represent roots and powers.
Correct Option: C) 125
The question asks to identify Nepal's first woman President. This is a factual question related to current affairs and political history of Nepal. To answer correctly, one needs to recall the name of the individual who held this significant position.
B) Vidya Devi Bhandari is the correct answer. She was elected as the first female President of Nepal on 28 October 2015.
The length of a diagonal in cm of a rectangle of length 9 cm and width 5 cm is
\(\sqrt{106}\)
±\(\sqrt{106}\)
2\(\sqrt{14}\)
±2\(\sqrt{14}\)
To find the length of the diagonal of a rectangle, we can use the Pythagorean theorem. A diagonal divides a rectangle into two right-angled triangles, where the length and width of the rectangle are the two shorter sides (legs) of the triangle, and the diagonal is the hypotenuse.
A) \(\sqrt{106}\)
This matches our calculated positive value for the diagonal length.
The question asks to identify a function key on a Windows keyboard that can perform several functions and does not have a single assigned Windows default. This implies looking for a key whose primary function is often context-dependent or user-defined, rather than having a universal, fixed action in Windows.
F8 is the correct answer. The F8 key is primarily known for accessing the Windows Startup Settings (or Advanced Boot Options) during system startup, which allows users to boot into Safe Mode, enable boot logging, etc. However, once Windows has started, F8 does not have a universal default function assigned by Windows across all applications. Its functionality can vary greatly depending on the specific software being used (e.g., in some applications, it might be used for extending a selection, in others for specific developer tools, or it might have no function at all). This makes it a key that "can perform several functions, and does not have an assigned Windows default" in the general operating environment.
The problem asks us to find the standard deviation of a set of data, given its variance. We need to recall the fundamental relationship between variance and standard deviation.
Correct Option: B) 11
The question asks to identify the winner of the FIFA Ballon d'Or award for the best player in the World in 2015. This is a factual recall question related to sports awards.
Correct Option: C) Lionel Messi won the FIFA Ballon d'Or award for the best player in the World in 2015. He received 41.33% of the votes, followed by Cristiano Ronaldo (27.76%) and Neymar (7.86%).
The question asks to identify which of the given options is NOT a football stadium in India. This requires knowledge of prominent stadiums in India and their primary sports.
Correct Option: D) Sardar Patel Stadium, Ahmedabad
Sardar Patel Stadium (now officially Narendra Modi Stadium) in Ahmedabad is renowned as the world's largest cricket stadium. Its primary sport is cricket, not football. While it might be capable of hosting other events, it is not identified as a football stadium.
Anurag is twice as efficient as Manoj and together they can complete a work in 22 days. In how many days can Manoj alone complete the work?
This problem involves work and time, where the efficiency of individuals is given. We need to find the time taken by one person alone to complete the work. We can solve this by expressing their efficiencies as a ratio and then relating it to the total work done.
Define efficiencies:
Let Anurag's efficiency be \(E_A\) and Manoj's efficiency be \(E_M\).
The problem states that Anurag is twice as efficient as Manoj. So, we can write:
Express work done per day:
If Manoj completes a certain amount of work in a day, let's say \(x\) units, then Anurag completes \(2x\) units in a day.
Let Manoj's 1-day work be \(M\).
Then Anurag's 1-day work will be \(2M\).
Calculate combined 1-day work:
Together, their 1-day work is the sum of their individual 1-day works:
Relate combined work to total time:
They can complete the work together in 22 days. This means that their combined 1-day work, multiplied by the number of days, equals the total work.
Total Work = Combined 1-day work \(\times\) Number of days
Total Work = \(3M \times 22 = 66M\)
Calculate time for Manoj alone:
To find the number of days Manoj alone would take to complete the work, we divide the total work by Manoj's 1-day work:
Correct Option: B) 66
The question asks to identify the Viceroy or Governor-General who awarded the Kaiser-i-Hind medal to Mahatma Gandhi for his ambulance services in South Africa. This requires knowledge of the timeline of Mahatma Gandhi's activities in South Africa and the tenures of the British Viceroys/Governor-Generals in India.
Correct Option: C) Lord Hardinge