To find the ratio of the height to the diameter of a cylindrical pillar, we will use the given curved surface area and volume. We will set up equations for these quantities in terms of radius (\(r\)) and height (\(h\)), solve for \(r\) and \(h\), and then calculate the required ratio.
Let the radius of the cylindrical pillar be \(r\) and its height be \(h\).
The formula for the curved surface area (CSA) of a cylinder is \(2\pi rh\).
Given CSA = 264 m².
\[ 2\pi rh = 264 \quad \text{(Equation 1)} \]The formula for the volume (V) of a cylinder is \(\pi r^2 h\).
Given Volume = 924 m³.
\[ \pi r^2 h = 924 \quad \text{(Equation 2)} \]Divide Equation 2 by Equation 1 to find the radius \(r\):
\[ \frac{\pi r^2 h}{2\pi rh} = \frac{924}{264} \]\[ \frac{r}{2} = \frac{924}{264} \]\[ r = 2 \times \frac{924}{264} \]\[ r = \frac{1848}{264} \]\[ r = 7 \text{ m} \]Substitute the value of \(r = 7\) m into Equation 1 to find the height \(h\):
\[ 2\pi (7) h = 264 \]\[ 14\pi h = 264 \]\[ 14 \times \frac{22}{7} \times h = 264 \]\[ 2 \times 22 \times h = 264 \]\[ 44h = 264 \]\[ h = \frac{264}{44} \]\[ h = 6 \text{ m} \]The diameter (\(d\)) of the cylinder is \(2r\).
\[ d = 2 \times 7 = 14 \text{ m} \]Now, find the ratio of its height to its diameter:
\[ \frac{\text{Height}}{\text{Diameter}} = \frac{h}{d} = \frac{6}{14} \]\[ \frac{6}{14} = \frac{3}{7} \]The ratio of height to diameter is 3 : 7.
D) 3 : 7
The question asks to identify the Indian archaeologist who first excavated the Indus Valley site of Mohenjo-daro. This requires knowledge of key figures in the archaeology of the Indus Valley Civilization.
B) RD Banerji — R.D. Banerji (Rakhal Das Banerji) was an officer of the Archaeological Survey of India who discovered the ancient city of Mohenjo-daro in 1922. His discovery, along with Daya Ram Sahni's excavation of Harappa, led to the official announcement of the Indus Valley Civilization by John Marshall in 1924.
This problem involves deductive reasoning, specifically using syllogistic logic. We need to determine if the conclusion logically follows from the given statements. We can use Venn diagrams or direct logical inference to solve this.
C) The conclusion is definitely true — The conclusion logically and necessarily follows from the given statements. If some individuals are weak in English, and all who are weak in English are artists, then those specific individuals must be artists. Therefore, some artists are individuals.
The question asks to identify which option is NOT an example of the heating effect of current. We need to understand what the heating effect of current is and then analyze each option.
B) The working of a fan primarily involves the conversion of electrical energy into mechanical energy (rotation) rather than heat. While some heat is inevitably produced in any electrical device due to resistance, it is not the intended or primary effect in a fan. Thus, it is NOT an example of the heating effect of current as its main operating principle.
If \(\sqrt{45}\) + \(\sqrt{125}\) = 17.88 then what will be the value of \(\sqrt{180}\) + \(\sqrt{80}\) ?
The problem requires us to find the value of an expression involving square roots, given the value of another similar expression. The key is to simplify the square roots by factoring out perfect squares and then combine like terms. This will allow us to relate the given expression to the one we need to find.
The given expression is \(\sqrt{45} + \sqrt{125} = 17.88\).
First, simplify each term:
Substitute these simplified forms back into the equation:
\[ 3\sqrt{5} + 5\sqrt{5} = 17.88 \]\[ 8\sqrt{5} = 17.88 \]From the simplified given expression, we can find the value of \(\sqrt{5}\):
\[ \sqrt{5} = \frac{17.88}{8} \]\[ \sqrt{5} = 2.235 \]We need to find the value of \(\sqrt{180} + \sqrt{80}\).
First, simplify each term:
Substitute these simplified forms:
\[ 6\sqrt{5} + 4\sqrt{5} = 10\sqrt{5} \]Now, substitute the value of \(\sqrt{5} = 2.235\) into the simplified expression:
\[ 10\sqrt{5} = 10 \times 2.235 \]\[ 10\sqrt{5} = 22.35 \]B) The calculated value is 22.35, which matches option B.
The question asks to identify the Indian organization related to nuclear energy development that is located in Kolkata. This requires knowledge of the major nuclear research institutions in India and their respective locations.
Correct Option: D) Variable Energy Cyclotron Centre (VECC)
The Variable Energy Cyclotron Centre (VECC) is a premier research and development unit of the Department of Atomic Energy, Government of India. It is located in Kolkata, West Bengal. VECC is involved in accelerator science and technology, nuclear physics, material science, and other interdisciplinary areas.
The question asks for the intersection point of the North-South and East-West corridors of the Indian Highway network. This is a factual question related to India's major highway development projects.
B) Jhansi — Jhansi is the correct answer as it is the city where the North-South and East-West corridors of the Indian Highway network intersect.
The problem presents a series of letter clusters. We need to identify the pattern in the given clusters (CF, IL, OR) and apply it to find the next cluster in the series. The pattern usually involves the positional values of the letters in the English alphabet.
D) UX is the correct option because both letters follow a consistent pattern of adding 6 to their positional values from the previous cluster.
The question asks to identify a Swiss professional tennis player known for specific record achievements: eight Wimbledon titles and five consecutive US Open titles. This requires knowledge of prominent tennis players and their career Grand Slam records.
Correct Option: C) Roger Federer is a Swiss professional tennis player who holds the record for eight Wimbledon titles and five consecutive US Open titles (2004-2008).
If tanA = \( \frac{8}{15} \) then find sinA + cosA.
\( \frac{15}{11} \)
\( \frac{7}{17} \)
\( \frac{23}{17} \)
\( \frac{8}{11} \)
To find the value of \(\text{sinA} + \text{cosA}\) given \(\text{tanA}\), we can use the trigonometric ratios in a right-angled triangle. We'll determine the sides of the triangle using the given \(\text{tanA}\) value and then calculate \(\text{sinA}\) and \(\text{cosA}\) using the Pythagorean theorem.
Understand the given information:
We are given \(\text{tanA} = \frac{8}{15}\).
Relate \(\text{tanA}\) to sides of a right-angled triangle:
In a right-angled triangle, \[\text{tanA} = \frac{\text{Opposite side}}{\text{Adjacent side}}\].
So, let the opposite side be \(8k\) and the adjacent side be \(15k\) for some constant \(k\).
Calculate the hypotenuse using the Pythagorean theorem:
Let the hypotenuse be \(h\).
\[ h^2 = (\text{Opposite side})^2 + (\text{Adjacent side})^2 \]
\[ h^2 = (8k)^2 + (15k)^2 \]
\[ h^2 = 64k^2 + 225k^2 \]
\[ h^2 = 289k^2 \]
\[ h = \sqrt{289k^2} \]
\[ h = 17k \]
Calculate \(\text{sinA}\) and \(\text{cosA}\):
\[\text{sinA} = \frac{\text{Opposite side}}{\text{Hypotenuse}} = \frac{8k}{17k} = \frac{8}{17}\]
\[\text{cosA} = \frac{\text{Adjacent side}}{\text{Hypotenuse}} = \frac{15k}{17k} = \frac{15}{17}\]
Find the sum \(\text{sinA} + \text{cosA}\):
\[ \text{sinA} + \text{cosA} = \frac{8}{17} + \frac{15}{17} \]
\[ \text{sinA} + \text{cosA} = \frac{8 + 15}{17} \]
\[ \text{sinA} + \text{cosA} = \frac{23}{17} \]
C) \(\frac{23}{17}\) is the correct answer, as calculated above.