To find the smallest ratio among the given options, we need to convert each ratio into a decimal or a common fraction form and then compare them. Converting to decimal form is often the easiest way to compare fractions.
A) \(20 : 51\) is approximately \(0.3921\), which is the smallest value among the given options.
This question asks about the products formed during a double displacement reaction between sodium sulfate and barium chloride. In a double displacement reaction, the ions of two compounds exchange places to form two new compounds. One of the products is often an insoluble precipitate, a gas, or water.
C) Sodium chloride and barium sulfate — As derived from the step-by-step ion exchange, sodium chloride (\(\text{NaCl}\)) and barium sulfate (\(\text{BaSO}_4\)) are the products.
To find the average speed, we need to calculate the total distance traveled and the total time taken. The average speed is then the total distance divided by the total time.
Given:
Time \(T_1 = \frac{D_1}{S_1}\)
\[ T_1 = \frac{138 \text{ km}}{46 \text{ km/h}} = 3 \text{ hours} \]Given:
Time \(T_2 = \frac{D_2}{S_2}\)
\[ T_2 = \frac{438 \text{ km}}{73 \text{ km/h}} = 6 \text{ hours} \]Total Distance \(D_{\text{total}} = D_1 + D_2\)
\[ D_{\text{total}} = 138 \text{ km} + 438 \text{ km} = 576 \text{ km} \]Total Time \(T_{\text{total}} = T_1 + T_2\)
\[ T_{\text{total}} = 3 \text{ hours} + 6 \text{ hours} = 9 \text{ hours} \]Average Speed \[S_{\text{avg}} = \frac{D_{\text{total}}}{T_{\text{total}}}\]
\[ S_{\text{avg}} = \frac{576 \text{ km}}{9 \text{ hours}} = 64 \text{ km/h} \]Correct Option: D) 64
The average speed of Shalini is 64 km/h.
The question asks to identify which statement is NOT a reason why Mendel chose garden peas for his genetic experiments. We need to evaluate each option based on the characteristics of garden peas that made them suitable for genetic studies.
Correct Option: D) They have a long generation time.
Which of the following statements is INCORRECT?
Sonia Gandhi became the Leader of Opposition in the 18th Lok Sabha.
Narendra Modi took oath as the Prime Minister of India in June 2024.
Om Birla is elected as the Speaker of the 18th Lok Sabha.
Amit Shah assumed charge as Union Home Minister and Minister of Cooperation in June 2024.
The question asks to identify the INCORRECT statement among the given options regarding recent political developments in India, specifically concerning the 18th Lok Sabha and the formation of the new government in June 2024. We need to verify the factual accuracy of each statement.
Correct Option: A) Sonia Gandhi became the Leader of Opposition in the 18th Lok Sabha.
The problem asks us to identify the letter-cluster pair that does not follow the same pattern as the others. We need to analyze the relationship between the letters in each pair, specifically their alphabetical positions.
Options A, B, and D follow the same pattern where the first letter of the second cluster is two positions before the first letter of the first cluster, and the second letter of the second cluster is one position after the second letter of the first cluster. Option C follows a different pattern where the first letter of the second cluster is one position before the first letter of the first cluster.
C) OF - NG is the letter-cluster pair that does NOT belong to the group because its pattern is \(-1, +1\), while the others follow the \(-2, +1\) pattern.
Write the expanded form of (6a + 8b + 3c)².
36a² + 64b² + 9c² + 96ab + 43bc + 36ac
36a² + 64b² + 9c² + 100ab + 48bc + 36ac
36a² + 64b² + 9c² + 96ab + 48bc + 46ac
36a² + 64b² + 9c² + 96ab + 48bc + 36ac
To expand the given expression \((6a + 8b + 3c)^2\), we will use the algebraic identity for the square of a trinomial: \((x + y + z)^2 = x^2 + y^2 + z^2 + 2xy + 2yz + 2zx\).
D) \(36a^2 + 64b^2 + 9c^2 + 96ab + 48bc + 36ac\) is the correct expanded form, matching our step-by-step calculation.
To calculate the simple interest, we need to determine the principal amount, the annual rate of interest, and the time period in years. The time period needs to be carefully calculated by counting the number of days between the given dates and then converting it into a fraction of a year. We will use the formula for simple interest: \[\text{SI} = \frac{\text{P} \times \text{R} \times \text{T}}{100}\].
First, determine if 2024 is a leap year. A year is a leap year if it is divisible by 4, unless it is a century year not divisible by 400. 2024 is divisible by 4, so it is a leap year, meaning February has 29 days.
Total number of days (\(\text{D}\)) = \(18 + 31 + 12 = 61\) days.
Since 2024 is a leap year, it has 366 days.
\[ \text{Time (T)} = \frac{\text{Number of days}}{\text{Number of days in a leap year}} = \frac{61}{366} \text{ years} \]Using the formula \[\text{SI} = \frac{\text{P} \times \text{R} \times \text{T}}{100}\]:
\[ \text{SI} = \frac{4000 \times 5.25 \times \frac{61}{366}}{100} \]\[ \text{SI} = \frac{4000 \times 5.25 \times 61}{100 \times 366} \]\[ \text{SI} = \frac{40 \times 5.25 \times 61}{366} \]\[ \text{SI} = \frac{210 \times 61}{366} \]\[ \text{SI} = \frac{12810}{366} \]\[ \text{SI} = 35 \]The calculated simple interest is exactly ₹35.
Correct Option: B) 35
The simple interest calculated for the given period is exactly ₹35.
The question asks to identify the Indian cricketer appointed as the brand ambassador for MotoGP in India in July 2024. This is a factual question related to current affairs and sports endorsements.
Correct Option: C) Shikhar Dhawan was appointed as the brand ambassador for MotoGP in India (MotoGP Bharat) in July 2024. This appointment aimed to leverage his popularity to promote the event in India.
To find the balanced equation for the decomposition of hydrogen peroxide, we need to ensure that the number of atoms of each element on the reactant side is equal to the number of atoms of the same element on the product side. Hydrogen peroxide (\(H_2O_2\)) decomposes into water (\(H_2O\)) and oxygen gas (\(O_2\)).
Reactants: \(2H_2O_2\)
Products: \(2H_2O + O_2\)
The number of atoms for each element is equal on both sides.
D) 2H₂O₂ → 2H₂O + O₂ is the correct balanced equation for the decomposition of hydrogen peroxide.