The question asks to identify the new head coach of the junior men's hockey team appointed in August 2024. This requires knowledge of recent sports appointments in India.
In August 2024, Hockey India announced the appointment of PR Sreejesh, the veteran goalkeeper, as the head coach of the junior men's hockey team.
D) PR Sreejesh — PR Sreejesh, a highly decorated and experienced Indian hockey goalkeeper, was appointed as the head coach of the junior men's hockey team in August 2024. This marks a significant transition for him from player to a coaching role, leveraging his vast experience to mentor young talent.
The curved surface area of a cone is 22176 cm², and the diameter is 84 cm. What is its total surface area (in cm²)? (Use π = \( \frac{22}{7} \))
To find the total surface area of a cone, we need the curved surface area and the area of the base. We are given the curved surface area and the diameter, from which we can calculate the radius. The area of the base is a circle, which can be calculated using the radius. Then, sum the curved surface area and the base area to get the total surface area.
The radius is half of the diameter.
\[ r = \frac{\text{Diameter}}{2} = \frac{84 \text{ cm}}{2} = 42 \text{ cm} \]The base of a cone is a circle, and its area is given by the formula \( \pi r^2 \).
\[ \text{Area of base} = \pi r^2 = \frac{22}{7} \times (42 \text{ cm})^2 \]\[ \text{Area of base} = \frac{22}{7} \times 42 \times 42 \]\[ \text{Area of base} = 22 \times 6 \times 42 \]\[ \text{Area of base} = 132 \times 42 \]\[ \text{Area of base} = 5544 \text{ cm}^2 \]The total surface area of a cone is the sum of its curved surface area and the area of its base.
\[ \text{TSA} = \text{Curved Surface Area} + \text{Area of base} \]\[ \text{TSA} = 22176 \text{ cm}^2 + 5544 \text{ cm}^2 \]\[ \text{TSA} = 27720 \text{ cm}^2 \]B) 27,720
The question asks to identify the pricing approach where a product's price is set equal to its marginal cost. We need to understand the definitions of each pricing method provided in the options.
C) Marginal cost pricing is a pricing strategy where the price of a product or service is set equal to the marginal cost of producing one additional unit. This is precisely what the question describes.
To expand the given expression \((5a + 4b + 9c)^2\), we will use the algebraic identity for the square of a trinomial, which is \((x + y + z)^2 = x^2 + y^2 + z^2 + 2xy + 2yz + 2zx\).
In our expression \((5a + 4b + 9c)^2\), we have:
Substitute these values into the identity \((x + y + z)^2 = x^2 + y^2 + z^2 + 2xy + 2yz + 2zx\).
\[ (5a + 4b + 9c)^2 = (5a)^2 + (4b)^2 + (9c)^2 + 2(5a)(4b) + 2(4b)(9c) + 2(9c)(5a) \]Add all the calculated terms together:
\[ (5a + 4b + 9c)^2 = 25a^2 + 16b^2 + 81c^2 + 40ab + 72bc + 90ac \]Correct Option: B) The expanded form is \(25a^2 + 16b^2 + 81c^2 + 40ab + 72bc + 90ac\), which matches our derived expression.
The question asks about the period when the atmospheric ozone concentration began to decline significantly. This is a factual question related to environmental science and historical observations of ozone depletion.
Correct Option: B) 1980
The amount of ozone in the atmosphere began to drop sharply in the 1980s. This period is marked by the discovery of the Antarctic ozone hole and widespread scientific consensus on the issue, leading to global action.
The question describes the thermal decomposition of lead nitrate and asks to identify the brown gas produced during the reaction. We need to recall the products of this decomposition and their characteristic properties, especially their color.
Correct Option: A) nitrogen dioxide (NOâ‚‚)
A trader lost 10% by selling a shirt for ₹850. He will gain x% by selling it for ₹1,360. The value of x is:
The problem involves calculating profit percentage. First, we need to determine the cost price (CP) of the shirt using the given selling price (SP) and loss percentage. Once the CP is known, we can calculate the new profit percentage when the shirt is sold at a different SP.
So, the value of x is 44.
A) 44 is the correct profit percentage when the shirt is sold for ₹1,360.
The problem requires us to modify a given number based on specific rules for odd and even digits and then find the difference between the first and last digits of the newly formed number.
C) The difference between the last and the first digits of the new number is \(6\).
The question asks to identify which of the given options can be broken down by biological processes. This refers to the concept of biodegradability. Biodegradable materials are those that can be decomposed by microorganisms (like bacteria and fungi) into simpler substances, returning to the natural cycle.
Correct Option: C) Vegetable peels can be broken down by biological processes because they are organic matter readily decomposed by microorganisms.
The question asks to identify the article of the Indian Constitution that empowers the President to make regulations for the peace, progress, and good government of Union Territories. We need to recall the specific provisions related to the administration of Union Territories.
Correct Option: C) Article 240 empowers the President to make regulations for the peace, progress, and good government of certain Union Territories, specifically Andaman and Nicobar Islands, Lakshadweep, Dadra and Nagar Haveli, Daman and Diu, and Puducherry. These regulations can have the same force and effect as an Act of Parliament.