To find the perimeter of a circle, also known as its circumference, we use a standard formula that relates the radius of the circle to its circumference. The formula for the circumference of a circle is \(C = 2\pi r\), where \(C\) is the circumference and \(r\) is the radius.
D) \(30\pi \text{ cm}\) is the correct answer because, by applying the formula for the circumference of a circle \(C = 2\pi r\) with a radius of \(15 \text{ cm}\), we get \(2 \times \pi \times 15 = 30\pi \text{ cm}\).
The question asks to identify the sport in which Abhishek Verma received the Arjuna Award in 2021. This requires knowledge of prominent Indian sports personalities and their achievements, specifically related to national sports awards.
C) Shooting β Abhishek Verma is an accomplished Indian shooter who was awarded the Arjuna Award in 2021 for his excellence in the sport.
To identify the type of reaction, we need to analyze the reactants and products and observe how atoms or ions are rearranged. We will compare the given reaction with the definitions of different types of chemical reactions.
Correct Option: A) double displacement reaction
The question asks about the role of transpiration in water transport in plants. We need to understand the mechanism by which water moves from the roots to the leaves against gravity.
Therefore, transpiration primarily creates a suction force that drives the upward movement of water.
Correct Option: A) It exerts a suction force.
The problem presents a proportion in the form \(a : b :: c : d\), which means \(a/b = c/d\). We need to find the value of \(y\) given the proportion \(361 : y :: y : 121\) and the condition \(y > 0\). This is a case of finding the geometric mean or mean proportional.
The given proportion is \(361 : y :: y : 121\).
This can be written as a fraction equality:
\[ \frac{361}{y} = \frac{y}{121} \]To solve for \(y\), cross-multiply the terms:
\[ 361 \times 121 = y \times y \]\[ 361 \times 121 = y^2 \]Now, take the square root of both sides to find \(y\):
\[ y = \sqrt{361 \times 121} \]We know that \(361 = 19^2\) and \(121 = 11^2\). Substitute these values:
\[ y = \sqrt{19^2 \times 11^2} \]Using the property \(\sqrt{a^2 \times b^2} = a \times b\):
\[ y = 19 \times 11 \]Calculate the product:
\[ y = 209 \]The problem states that \(y > 0\), and our calculated value \(209\) satisfies this condition.
D) 209 is the correct value for \(y\), as derived from the proportion.
Study the given diagram carefully and answer the question that follows.
The numbers in different sections indicate the number of schools/colleges/universities/gurukuls. 
How many Schools are Colleges and Universities but NOT Gurukuls?
To solve this problem, we need to identify the section of the diagram where Schools, Colleges, and Universities overlap, but which does not include Gurukuls.
Thus, the number of Schools that are also Colleges and Universities but not Gurukuls is 22.
Correct Option: B) 22
To evaluate the expression \(984^2 - 16^2\), we can use the algebraic identity for the difference of squares, which states that \(a^2 - b^2 = (a - b)(a + b)\). This method simplifies the calculation significantly compared to directly calculating the squares of large numbers.
Thus, \(984^2 - 16^2 = 968000\).
Correct Option: D) 968000
This is a scheduling puzzle. We need to determine the day each musical instrument class is held based on the given clues. We will create a table for the days of the week and fill in the classes step-by-step using the provided information.
| Day | Class |
|---|---|
| Monday | Drum |
| Tuesday | |
| Wednesday | |
| Thursday | |
| Friday | |
| Saturday |
| Day | Class |
|---|---|
| Monday | Drum |
| Tuesday | |
| Wednesday | |
| Thursday | |
| Friday | Flute |
| Saturday |
| Day | Class |
|---|---|
| Monday | Drum |
| Tuesday | |
| Wednesday | |
| Thursday | |
| Friday | Flute |
| Saturday | Sitar |
| Day | Class |
|---|---|
| Monday | Drum |
| Tuesday | Guitar |
| Wednesday | |
| Thursday | |
| Friday | Flute |
| Saturday | Sitar |
| Day | Class |
|---|---|
| Monday | Drum |
| Tuesday | Guitar |
| Wednesday | Harmonium |
| Thursday | Violin |
| Friday | Flute |
| Saturday | Sitar |
The question asks: On which day is Harmonium class scheduled?
From our table, Harmonium class is scheduled on Wednesday.
D) Wednesday
The question asks to identify the Indian footballer who surpassed Lionel Messi in international goal-scoring among active players in June 2021. This requires knowledge of significant achievements in Indian football.
Correct Option: A) Sunil Chhetri
The question asks to identify the specific scheme launched by the Rajasthan government in collaboration with 'IPE Global' that provides scholarship schemes to rural girls for secondary-level education. This requires knowledge of various government schemes related to girls' education and their specific objectives and partnerships.
Correct Option: B) Udaan
The 'Udaan' scheme in Rajasthan was indeed launched in collaboration with 'IPE Global'. Its primary objective is to provide scholarship schemes to rural girls, encouraging them to continue their education at the secondary level and reduce dropout rates. This scheme focuses on empowering girls through education, aligning perfectly with the description in the question.