Study the given pattern carefully and select the number from among the given options that can replace the question mark (?).
To solve this problem, we need to identify the pattern used in the given diagrams. Each circle is divided into four sections, each containing a number. The task is to find the number that completes the pattern in the third circle.
Correct Option: D) 81
The question asks to identify the city that is NOT located in the Indian state of Madhya Pradesh. This requires knowledge of the major cities and their respective states in India.
Bhopal is the capital of Madhya Pradesh. Jabalpur and Gwalior are also prominent cities within Madhya Pradesh. Raipur, however, is the capital of Chhattisgarh, a state that was carved out of Madhya Pradesh in 2000.
C) Raipur is the capital city of the state of Chhattisgarh, not Madhya Pradesh.
The question asks for the location of Asia's largest Indira Gandhi Memorial Tulip Garden. This requires knowledge of prominent geographical and tourist landmarks in India.
Correct Option: D) Srinagar is home to the Indira Gandhi Memorial Tulip Garden, which is renowned as Asia's largest tulip garden. It is located at the foothills of the Zabarwan Range, overlooking Dal Lake, and attracts a large number of tourists during its blooming season.
Mohan borrowed an amount of ₹18,000 and paid a simple interest of ₹2,700 at 10% per annum. Find the duration for which he kept the borrowed amount.
\( \frac{3}{2} \) years
\( \frac{2}{3} \) years
\( \frac{3}{20} \) years
3 years
This problem involves calculating the duration (time) for which an amount was borrowed, given the principal, simple interest, and annual interest rate. We will use the standard formula for simple interest to find the unknown duration.
The formula for simple interest is:
\[ \text{SI} = \frac{\text{P} \times \text{R} \times \text{T}}{100} \]Where:
To find the duration (T), we can rearrange the formula as:
\[ \text{T} = \frac{\text{SI} \times 100}{\text{P} \times \text{R}} \]Divide both the numerator and the denominator by their greatest common divisor, which is 9:
\[ \text{T} = \frac{27 \div 9}{18 \div 9} = \frac{3}{2} \]So, the duration for which the amount was borrowed is \(\frac{3}{2}\) years.
A) \( \frac{3}{2} \) years is the correct duration calculated using the simple interest formula.
Simplify: \(\sqrt{51+\sqrt{134+5\sqrt{42+\sqrt{16}+\sqrt{9}}}}\)
To simplify the given nested square root expression, we will work from the innermost square roots outwards. We will evaluate each square root step by step until the entire expression is simplified to a single numerical value.
Start with the innermost square roots: \(\sqrt{16}\) and \(\sqrt{9}\).
\[ \sqrt{16} = 4 \]\[ \sqrt{9} = 3 \]Substitute these values back into the expression:
\[ \sqrt{51+\sqrt{134+5\sqrt{42+4+3}}} \]Simplify the terms inside the next square root:
\[ 42+4+3 = 49 \]Now, evaluate \(\sqrt{49}\):
\[ \sqrt{49} = 7 \]Substitute this value back into the expression:
\[ \sqrt{51+\sqrt{134+5 \times 7}} \]Perform the multiplication inside the next square root:
\[ 5 \times 7 = 35 \]Add the terms inside the square root:
\[ 134+35 = 169 \]Evaluate \(\sqrt{169}\):
\[ \sqrt{169} = 13 \]Substitute this value back into the outermost square root:
\[ \sqrt{51+13} \]Add the terms:
\[ 51+13 = 64 \]Finally, evaluate the outermost square root:
\[ \sqrt{64} = 8 \]D) The simplified value of the expression is 8.
This question tests knowledge of chemical symbols for elements. Chemical symbols are standardized abbreviations used to represent elements in the periodic table. For Magnesium, we need to recall its specific symbol.
Correct Option: A) Mg is the correct chemical symbol for the element Magnesium.
To simplify the given expression, we need to add the decimal numbers. The most straightforward way to do this accurately is to align the decimal points of all numbers and then perform column-wise addition, starting from the rightmost digit.
1.100
1.001
10.010
+11.110
------A) \(23.221\) is the correct sum obtained by aligning the decimal points and adding the numbers.
The question asks to identify the disease carried by the Aedes mosquito. This requires knowledge of common vector-borne diseases and their respective carriers.
Correct Option: C) dengue. The Aedes mosquito, particularly Aedes aegypti and Aedes albopictus, is the primary vector for transmitting the dengue virus to humans. When an Aedes mosquito bites a person infected with the dengue virus, it becomes infected and can then transmit the virus to other healthy individuals through subsequent bites.
A hollow metallic sphere has internal and external radius of 3 cm and 5 cm respectively. It is melted and recast as a solid cylinder with radius 7 cm. What is the height of the cylinder?
8 cm
\( \frac{2}{3} \) cm
3 cm
\( \frac{8}{3} \) cm
When a metallic object is melted and recast into another shape, its volume remains constant. Therefore, the strategy is to calculate the volume of the hollow sphere and equate it to the volume of the solid cylinder to find the unknown height of the cylinder.
The volume of a hollow sphere is given by the formula for the volume of the outer sphere minus the volume of the inner sphere.
Given:
The formula for the volume of a sphere is \(V = \frac{4}{3}\pi r^3\).
Volume of hollow sphere, \[V_{\text{sphere}} = \frac{4}{3}\pi r_2^3 - \frac{4}{3}\pi r_1^3\]
\[ V_{\text{sphere}} = \frac{4}{3}\pi (r_2^3 - r_1^3) \]\[ V_{\text{sphere}} = \frac{4}{3}\pi (5^3 - 3^3) \]\[ V_{\text{sphere}} = \frac{4}{3}\pi (125 - 27) \]\[ V_{\text{sphere}} = \frac{4}{3}\pi (98) \text{ cm}^3 \]Given:
The formula for the volume of a cylinder is \(V = \pi R^2 H\).
\[ V_{\text{cylinder}} = \pi (7^2) H \]\[ V_{\text{cylinder}} = 49\pi H \text{ cm}^3 \]Since the sphere is melted and recast into a cylinder, their volumes are equal.
\[ V_{\text{sphere}} = V_{\text{cylinder}} \]\[ \frac{4}{3}\pi (98) = 49\pi H \]Divide both sides by \(\pi\):
\[ \frac{4}{3} (98) = 49 H \]\[ H = \frac{4 \times 98}{3 \times 49} \]Since \(98 = 2 \times 49\):
\[ H = \frac{4 \times (2 \times 49)}{3 \times 49} \]\[ H = \frac{4 \times 2}{3} \]\[ H = \frac{8}{3} \text{ cm} \]D) The height of the cylinder is \( \frac{8}{3} \) cm.
The problem involves decoding a word based on a given numerical value. We need to identify the pattern or rule used to convert the letters of 'LEGAL' into '37' and then apply the same rule to 'EAGLE'. Typically, such problems involve assigning numerical values to letters (e.g., A=1, B=2, ..., Z=26) and then performing arithmetic operations like summation, multiplication, or other transformations.
Therefore, 'EAGLE' will be written as '30'.
D) 30 is the correct answer. The pattern identified is to sum the alphabetical positions of the letters in the word.