The question asks about the primary determinant of total consumption in a macroeconomic context, as described by a consumption function. We need to identify the key economic aggregate that directly influences consumption expenditure.
C) gross national income. The consumption function in macroeconomic analysis describes the relationship between total consumption and the total income available in an economy, which is best represented by gross national income (or disposable income derived from it).
To find the area of a rectangle, we need its length and breadth. We are given the diagonal and the perimeter. We can use the Pythagorean theorem and the perimeter formula to set up a system of equations to solve for the length and breadth, and then calculate the area.
Let the length of the rectangle be \(l\) and the breadth be \(b\).
The diagonal of a rectangle forms a right-angled triangle with its length and breadth. According to the Pythagorean theorem:
\[ l^2 + b^2 = (\text{diagonal})^2 \]Given the diagonal is 26 cm, we have:
\[ l^2 + b^2 = 26^2 \]\[ l^2 + b^2 = 676 \quad \text{(Equation 1)} \]The perimeter of a rectangle is given by:
\[ \text{Perimeter} = 2(l + b) \]Given the perimeter is 68 cm, we have:
\[ 68 = 2(l + b) \]\[ l + b = \frac{68}{2} \]\[ l + b = 34 \quad \text{(Equation 2)} \]Now we have two equations:
1) \(l^2 + b^2 = 676\)
2) \(l + b = 34\)
We know the algebraic identity: \((l + b)^2 = l^2 + b^2 + 2lb\)
Substitute the values from Equation 1 and Equation 2 into this identity:
\[ (34)^2 = 676 + 2lb \]\[ 1156 = 676 + 2lb \]Solve for \(2lb\):
\[ 2lb = 1156 - 676 \]\[ 2lb = 480 \]The area of the rectangle is given by \( \text{Area} = l \times b \). From the previous step, we can find \(lb\):
\[ lb = \frac{480}{2} \]\[ lb = 240 \]Therefore, the area of the rectangle is 240 cm².
Correct Option: A) 240 cm²
To solve this approximation problem, we need to round each number to its nearest whole number and then perform the operations following the order of operations (BODMAS/PEMDAS).
B) 188 is the correct approximate value.
To solve this problem, we first need to calculate the increased cost of 1 kg sugar in 2021 by applying the given percentage increase to the 2020 price. Once we have the cost per kg for 2021, we can then multiply it by 5 to find the total cost of 5 kg sugar.
Cost of 1 kg sugar in 2020:
The cost of 1 kg sugar in 2020 was Rs 46.
Calculate the increase in cost:
The cost increased by 2.5%. We need to find 2.5% of Rs 46.
\[ \text{Increase} = 2.5\% \times 46 \]\[ \text{Increase} = \frac{2.5}{100} \times 46 \]\[ \text{Increase} = 0.025 \times 46 \]\[ \text{Increase} = 1.15 \]Calculate the cost of 1 kg sugar in 2021:
Add the increase to the original cost.
\[ \text{Cost in 2021 (per kg)} = \text{Cost in 2020} + \text{Increase} \]\[ \text{Cost in 2021 (per kg)} = 46 + 1.15 \]\[ \text{Cost in 2021 (per kg)} = \text{Rs } 47.15 \]Calculate the cost of 5 kg sugar in 2021:
Multiply the cost per kg in 2021 by 5.
\[ \text{Total cost for 5 kg} = 5 \times \text{Cost in 2021 (per kg)} \]\[ \text{Total cost for 5 kg} = 5 \times 47.15 \]\[ \text{Total cost for 5 kg} = \text{Rs } 235.75 \]D) Rs 235.75 is the correct answer, as calculated above.
The problem asks us to divide a number (128) into two parts such that one part is three times the other. We need to find the value of the larger part. This can be solved by setting up algebraic equations based on the given conditions.
Let the two parts be \(x\) and \(y\).
The total sum of the two parts is 128:
\[ x + y = 128 \quad \text{(Equation 1)} \]One part is three times the other. Let's assume \(y\) is three times \(x\):
\[ y = 3x \quad \text{(Equation 2)} \]Substitute Equation 2 into Equation 1:
\[ x + (3x) = 128 \]\[ 4x = 128 \]Divide both sides by 4:
\[ x = \frac{128}{4} \]\[ x = 32 \]Now that we have \(x\), substitute its value back into Equation 2:
\[ y = 3x \]\[ y = 3 \times 32 \]\[ y = 96 \]The two parts are 32 and 96. The larger part is 96.
Check if the sum of the parts is 128: \(32 + 96 = 128\). This confirms our calculations are correct.
Correct Option: B) 96
Study the given letter, number, symbol series and answer the question that follows.
(Left) A 9 % B @ 6 & L # K 9 @ 7 # 6 K M * 7 & B (Right)
How many such letters are there that are immediately preceded by a symbol and also immediately followed by a number?
The problem asks us to identify letters in a given series that satisfy two conditions: they must be immediately preceded by a symbol and immediately followed by a number. We will scan the series from left to right, looking for patterns of "Symbol - Letter - Number".
A 9 % B @ 6 & L # K 9 @ 7 # 6 K M * 7 & BA 9 %: Letter - Number - Symbol (Does not fit)9 % B: Number - Symbol - Letter (Does not fit)% B @: Symbol - Letter - Symbol (Does not fit)B @ 6: Letter - Symbol - Number (Does not fit)@ 6 &: Symbol - Number - Symbol (Does not fit)6 & L: Number - Symbol - Letter (Does not fit)& L #: Symbol - Letter - Symbol (Does not fit)L # K: Letter - Symbol - Letter (Does not fit)# K 9: Symbol - Letter - Number. Here, 'K' is the letter, '#' is the preceding symbol, and '9' is the following number. This is one such instance.K 9 @: Letter - Number - Symbol (Does not fit)9 @ 7: Number - Symbol - Number (Does not fit)@ 7 #: Symbol - Number - Symbol (Does not fit)7 # 6: Number - Symbol - Number (Does not fit)# 6 K: Symbol - Number - Letter (Does not fit)6 K M: Number - Letter - Letter (Does not fit)K M *: Letter - Letter - Symbol (Does not fit)M * 7: Letter - Symbol - Number. Here, 'M' is the letter, '*' is the preceding symbol, and '7' is the following number. This is another such instance.* 7 &: Symbol - Number - Symbol (Does not fit)7 & B: Number - Symbol - Letter (Does not fit)C) 2
To solve this problem, we need to apply the given rules to each letter in the word "PRISON". We will identify vowels and consonants, apply the respective changes (preceding letter for vowels, following letter for consonants), and then determine the fourth letter from the right in the newly formed word.
Q S H T N O
The letters are Q, S, H, T, N, O.
Counting from the right:
Correct Option: D) H
The problem presents a series of number pairs and asks us to find the missing number in the last pair. We need to identify the mathematical relationship between the numbers in the given pairs and apply the same logic to the third pair.
A) 21 is the correct answer because applying the pattern of adding \(5\) to the first number gives \(16 + 5 = 21\).
The problem requires us to transform each letter in the given words to the next letter in the English alphabetical order and then count how many of the resulting words contain no vowels. The vowels are A, E, I, O, U.
Wait, let's re-evaluate the condition. We are looking for words that will have NO vowel after transformation. This means that if any letter in the original word is a vowel, its transformed letter must NOT be a vowel. Similarly, if any letter in the original word is a consonant, its transformed letter must NOT be a vowel.
Let's list the letters that, when changed to the next letter, result in a vowel:
If any of these letters (D, H, N, T) are present in the original word, or if any vowel (A, E, I, O, U) is present in the original word, the transformed word will contain a vowel.
Let's re-check each word based on this understanding:
Only one word, BOXES, when transformed, results in a word with no vowels.
A) One. Only the word BOXES results in a word (CPYFT) with no vowels after transformation.
The question asks to identify which cell type is NOT a part of the vascular tissue in plants. Vascular tissue consists of xylem and phloem, which are responsible for transport. We need to recall the components of xylem and phloem and identify the cell type that does not belong to these tissues.
B) Collenchyma is a simple permanent tissue that provides mechanical support to plants, especially in young stems and petioles. It is not involved in transport and is not a component of the vascular tissue (xylem or phloem).