The question asks to identify which of the given options is NOT a grassland. We need to understand the definition of a grassland and then evaluate each option.
B) Fen is a type of wetland (a mire) characterized by peat-forming vegetation and mineral-rich groundwater, not a grassland.
The question asks for the location of the Buland Darwaza. This is a direct factual recall question related to Indian history and architecture. One needs to know the historical context and location of this famous monument.
Correct Option: B) Buland Darwaza is located in Fatehpur Sikri, a city in Uttar Pradesh, India. It was built by Mughal emperor Akbar in 1601 A.D. to commemorate his victory over Gujarat. It serves as the main entrance to the Jama Masjid at Fatehpur Sikri.
To find when the traffic lights will change simultaneously again, we need to find the least common multiple (LCM) of the time intervals at which each light changes. The LCM will give us the minimum time after which all lights will change together again. We will then add this duration to the initial simultaneous change time.
Identify the given intervals: The traffic lights change after 48 seconds, 72 seconds, and 108 seconds.
Find the LCM of these intervals: First, find the prime factorization of each number:
\[ 48 = 2^4 \times 3^1 \\ 72 = 2^3 \times 3^2 \\ 108 = 2^2 \times 3^3 \]To find the LCM, take the highest power of each prime factor present in the numbers:
\[ \text{LCM}(48, 72, 108) = 2^4 \times 3^3 \\ = 16 \times 27 \\ = 432 \]So, the lights will change simultaneously again after 432 seconds.
Convert the LCM from seconds to minutes and seconds:
\[ 432 \text{ seconds} = \frac{432}{60} \text{ minutes} \\ = 7 \text{ minutes and } 12 \text{ seconds} \]This is because \(432 = 7 \times 60 + 12\).
Add this duration to the initial simultaneous change time: Initial time = 8:20 hours (which means 8 hours and 20 minutes)
Add 7 minutes and 12 seconds to 8:20:00 hours:
8 hours 20 minutes 00 seconds
+ 0 hours 07 minutes 12 seconds
= 8 hours 27 minutes 12 seconds
Therefore, the lights will change simultaneously again at 8:27:12 hours.
C) 8:27:12 hours
The question asks to identify the person credited with designing the Indian National Flag. This is a direct factual question related to Indian history and national symbols.
Correct Option: B) Pingali Venkayya is credited with designing the Indian National Flag. He presented his design to Mahatma Gandhi in 1921, which featured red and green bands and a spinning wheel. This design, with modifications, eventually evolved into the current Tricolour.
This problem involves calculating profit percentages based on different bases (selling price vs. cost price) and finding a common selling price given a difference in profits. We will use the definitions of profit percentage for both Lovely and Bunty, set up equations based on their common selling price and profit percentages, and then use the given difference in their profits to solve for the selling price.
Let the selling price be \(S\).
For Lovely:
Lovely calculates profit percentage on the selling price. His profit is 25% of the selling price.
\[ \text{Lovely's Profit} (P_L) = 25\% \text{ of } S = 0.25S \]For Bunty:
Bunty calculates profit percentage on the cost price. His profit is 25% of the cost price.
Let Bunty's cost price be \(C_B\).
\[ \text{Bunty's Profit} (P_B) = 25\% \text{ of } C_B = 0.25 C_B \]We know that \(\text{Selling Price} = \text{Cost Price} + \text{Profit}\).
For Bunty:
\[ S = C_B + P_B \]\[ S = C_B + 0.25 C_B \]\[ S = 1.25 C_B \]From the above equation, we can express Bunty's cost price in terms of the selling price:
\[ C_B = \frac{S}{1.25} = \frac{S}{5/4} = \frac{4S}{5} \]Now, we can find Bunty's profit in terms of the selling price:
\[ P_B = 0.25 C_B = 0.25 \left(\frac{4S}{5}\right) = \frac{1}{4} \times \frac{4S}{5} = \frac{S}{5} = 0.2S \]The problem states that the difference in their profits is ₹100.
Since profit calculated on selling price is generally lower for the same selling price and profit percentage (as the base is larger), Lovely's profit will be less than Bunty's profit.
\[ P_B - P_L = 100 \]\[ 0.2S - 0.25S = 100 \]Wait, this gives a negative difference, which means Lovely's profit is actually higher than Bunty's profit for the same profit percentage value, because Lovely calculates it on the selling price which is always greater than the cost price. So, Lovely's profit (25% of S) will be greater than Bunty's profit (25% of C.P., where C.P. < S).
Let's re-evaluate the difference:
\[ P_L - P_B = 100 \]\[ 0.25S - 0.2S = 100 \]\[ 0.05S = 100 \]Solve for \(S\):
\[ S = \frac{100}{0.05} = \frac{100}{\frac{5}{100}} = 100 \times \frac{100}{5} = 20 \times 100 = 2000 \]So, the selling price is ₹2,000.
Let's verify:
Selling Price \(S = 2000\)
Lovely's Profit \(P_L = 0.25 \times 2000 = 500\)
Bunty's Cost Price \(C_B = \frac{4}{5} \times 2000 = 1600\)
Bunty's Profit \(P_B = 0.25 \times 1600 = 400\)
Difference in profits \(P_L - P_B = 500 - 400 = 100\). This matches the given information.
Thus, the selling price is ₹2,000.
D) ₹2,000
The question asks for the location of the headquarters of the National Institute of Oceanography (NIO). This is a factual question requiring knowledge of the geographical locations of prominent research institutions in India.
A) Goa is the correct answer. The headquarters of the National Institute of Oceanography (NIO) is located in Dona Paula, Goa. NIO is a constituent laboratory of the Council of Scientific & Industrial Research (CSIR).
A cord is in the form of a square enclosing an area of 22 cm². If the same cord is formed into a circle, then find the area enclosed by that circle. [Take π = \( \frac{22}{7} \)]
The problem involves a cord that is first shaped into a square and then into a circle. The key concept here is that the length of the cord remains constant, which means the perimeter of the square will be equal to the circumference of the circle. We will first find the side of the square using its area, then calculate the perimeter. This perimeter will give us the circumference of the circle, from which we can find its radius and finally its area.
Given that the area of the square is \(22 \text{ cm}^2\).
\[ \text{Area of square} = \text{side}^2 = a^2 \]So,
\[ a^2 = 22 \text{ cm}^2 \] \[ a = \sqrt{22} \text{ cm} \]The perimeter of a square is \(4 \times \text{side}\).
\[ \text{Perimeter of square} = 4a = 4\sqrt{22} \text{ cm} \]Since the same cord is used, the length of the cord is constant.
\[ \text{Circumference of circle} = \text{Perimeter of square} \] \[ 2\pi r = 4\sqrt{22} \]Substitute \(\pi = \frac{22}{7}\) into the equation:
\[ 2 \times \frac{22}{7} \times r = 4\sqrt{22} \] \[ \frac{44}{7} r = 4\sqrt{22} \] \[ r = \frac{4\sqrt{22} \times 7}{44} \] \[ r = \frac{\sqrt{22} \times 7}{11} \text{ cm} \]The area of a circle is given by \(\pi r^2\).
\[ \text{Area of circle} = \pi r^2 \] \[ \text{Area of circle} = \frac{22}{7} \times \left( \frac{7\sqrt{22}}{11} \right)^2 \] \[ \text{Area of circle} = \frac{22}{7} \times \frac{49 \times 22}{121} \] \[ \text{Area of circle} = \frac{22}{7} \times \frac{49 \times 22}{11 \times 11} \]Cancel out common terms:
\[ \text{Area of circle} = \frac{2 \times 11}{7} \times \frac{7 \times 7 \times 22}{11 \times 11} \] \[ \text{Area of circle} = 2 \times \frac{7 \times 22}{11} \] \[ \text{Area of circle} = 2 \times 7 \times 2 \] \[ \text{Area of circle} = 28 \text{ cm}^2 \]Correct Option: C) 28 cm²
Select the option that will fill in the blank and complete the series.
PE11, QD2, RC9, SB4, ___
The problem presents a series of terms, each consisting of two letters and a number. We need to identify the pattern in the letters and the numbers separately to find the missing term.
Analyze the first letter of each term:
The pattern for the first letter is an increment of 1 in alphabetical order. So, the next letter should be T (20th letter).
Analyze the second letter of each term:
The pattern for the second letter is a decrement of 1 in alphabetical order. So, the next letter should be A (1st letter).
Analyze the number in each term:
Let's look at the differences or a possible alternating pattern:
The pattern for the numbers is an alternating subtraction and addition, where the magnitude of the change decreases by 2 each time: \(-9, +7, -5\). Following this pattern, the next operation should be \(+3\).
So, the next number will be \(4 + 3 = 7\).
Combine the findings:
The next first letter is T.
The next second letter is A.
The next number is 7.
Therefore, the complete next term in the series is TA 7.
Correct Option: B) TA 7
The problem presents a series of Roman numerals. To identify the missing term, we first need to convert the Roman numerals into their corresponding Arabic (decimal) values. Then, we can analyze the pattern or relationship between these numbers.
The series in Arabic numbers is: 12, 5, 10, __, 8, 125.
Let's look for a pattern. Notice the numbers 5, 10, and 125. These are powers of 5:
Let's re-examine the series and look for alternating patterns or operations.
Consider two interleaved series:
Series 1 (1st, 3rd, 5th terms): 12, 10, 8
In this series, each term is decreasing by 2:
This pattern holds true for the odd-positioned terms.
Series 2 (2nd, 4th, 6th terms): 5, __, 125
In this series, the terms are powers of 5:
Therefore, the missing term in the second series is \(5^2 = 25\).
The missing number is 25. In Roman numerals, 25 is XXV.
C) XXV — The series consists of two interleaved patterns. The odd-positioned terms (1st, 3rd, 5th) follow a decreasing arithmetic progression (12, 10, 8, where each term is 2 less than the previous). The even-positioned terms (2nd, 4th, 6th) follow a geometric progression of powers of 5 (5, 25, 125, which are \(5^1, 5^2, 5^3\)). The missing term is the 4th term, which should be \(5^2 = 25\). In Roman numerals, 25 is XXV.
The question asks to identify the winner of the Purple Cap for the most wickets in the IPL 2020 season. This requires knowledge of the IPL 2020 statistics, specifically the leading wicket-taker.
Correct Option: B) Kagiso Rabada
Kagiso Rabada won the Purple Cap in IPL 2020 by taking 30 wickets for the Delhi Capitals.