The question asks to identify which economic curve among the given options is 'inverse U-shaped'. This requires knowledge of the typical shapes of various cost and production curves in economics.
C) Marginal product curve. The marginal product curve is inverse U-shaped because of the law of diminishing marginal returns. Initially, marginal product rises due to increasing returns, then reaches a maximum, and subsequently falls as diminishing returns set in.
The question asks for the unit of magnification. Magnification is a ratio of two similar quantities. Understanding the definition of magnification will help determine if it has a unit.
or
\[ \text{Magnification} = \frac{\text{Image Distance}}{\text{Object Distance}} \]D) It has no unit
As explained, magnification is a ratio of two lengths (heights or distances), so the units cancel out, making it a dimensionless quantity.
The problem asks us to evaluate two conclusions based on a given statement. We must assume the statement is true and determine which conclusions logically follow beyond a reasonable doubt. This is a common type of logical reasoning question where we need to distinguish between direct consequences and assumptions or external factors not explicitly stated.
D) Only conclusion II follows. Conclusion II is a direct and logical consequence of the destruction of agricultural crops, which reduces supply and thus increases prices. Conclusion I is an assumption about debt repayment, which is not supported by the given statement.
The expression (3.7)3−3×(3.7)2×(0.7)+3(3.7)×(0.7)2−(0.7)3 is equal to:
The given expression resembles the algebraic identity for the cube of a difference, \((a-b)^3\). We will identify the values of 'a' and 'b' from the given expression and then apply the identity to simplify it.
The given expression is:
\[ (3.7)^3 - 3 \times (3.7)^2 \times (0.7) + 3 \times (3.7) \times (0.7)^2 - (0.7)^3 \]Recall the algebraic identity for the cube of a difference:
\[ (a-b)^3 = a^3 - 3a^2b + 3ab^2 - b^3 \]By comparing the given expression with the identity, we can identify:
Substitute these values into the identity:
\[ (3.7 - 0.7)^3 \]Perform the subtraction inside the parenthesis:
\[ (3.0)^3 \]Calculate the cube:
\[ 3^3 = 3 \times 3 \times 3 = 27 \]Correct Option: B) 27
Select the option that represents the letters that, when placed from left to right in the blanks below, will complete the letter series.
K P _ L Z _ P _ M Z K _ B _ Z _ P B _ Z
B K B P N P O
B K B P N K O
B K B P N K P
B K P P O K P
The problem presents a letter series with blanks. The goal is to identify the repeating pattern in the series and then fill in the blanks with the correct letters from the given options to complete the pattern.
B) B K B P N K O — When these letters are placed in the blanks, the series becomes K P B L Z K P B M Z K P B N Z K P B O Z. This forms a clear sequential pattern of KPB_Z, where the blank is filled by L, M, N, O respectively in each block.
If x ≠ y, z > 0 and (x + z)2 : (y + z)2 :: x : y, then find a, where a > 0, such that x : a :: a : y.
The problem provides a proportion involving \(x\), \(y\), and \(z\), and asks to find a value \(a\) such that \(x:a::a:y\). The first step is to simplify the given proportion to find a relationship between \(x\), \(y\), and \(z\). Then, we will use the definition of geometric mean to find \(a\).
Analyze the given proportion:
The given proportion is \((x + z)^2 : (y + z)^2 :: x : y\). This can be written as:
\[ \frac{(x + z)^2}{(y + z)^2} = \frac{x}{y} \]Simplify the proportion:
Take the square root of both sides. Since \(z > 0\), \(x+z\) and \(y+z\) will have the same sign as \(x\) and \(y\) respectively, or be positive if \(x\) and \(y\) are positive. Assuming the positive square root (as ratios usually imply positive values unless specified otherwise, and we are looking for a positive \(a\)), we get:
\[ \frac{x + z}{y + z} = \sqrt{\frac{x}{y}} \]Rearrange the equation:
Cross-multiply to eliminate the denominators:
\[ y(x + z)^2 = x(y + z)^2 \]\[ y(x^2 + 2xz + z^2) = x(y^2 + 2yz + z^2) \]\[ x^2y + 2xyz + yz^2 = xy^2 + 2xyz + xz^2 \]Further simplify the equation:
Subtract \(2xyz\) from both sides:
\[ x^2y + yz^2 = xy^2 + xz^2 \]\[ x^2y - xy^2 = xz^2 - yz^2 \]\[ xy(x - y) = z^2(x - y) \]Solve for \(z^2\):
Since \(x \ne y\), we know that \(x - y \ne 0\). Therefore, we can divide both sides by \((x - y)\):
\[ xy = z^2 \]Analyze the second proportion:
We are asked to find \(a\) such that \(x : a :: a : y\). This means \(a\) is the geometric mean of \(x\) and \(y\). The proportion can be written as:
\[ \frac{x}{a} = \frac{a}{y} \]Solve for \(a\):
Cross-multiply:
\[ a^2 = xy \]Substitute the value from step 5:
From step 5, we found that \(xy = z^2\). Substitute this into the equation for \(a^2\):
\[ a^2 = z^2 \]Find \(a\):
Take the square root of both sides. Since the problem states \(a > 0\) and \(z > 0\), we take the positive square root:
\[ a = z \]B) z — As derived in the step-by-step solution, \(a = z\).
To solve this problem, we need to compare the original position of each letter in the given word with its position after arranging all the letters in alphabetical order. We will count how many letters retain their original position.
| Original Position | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
|---|---|---|---|---|---|---|---|
| Original Word | G | E | R | M | A | N | Y |
| Alphabetical Order | A | E | G | M | N | R | Y |
| Match? | No | Yes | No | Yes | No | No | Yes |
A) 3 — As determined in the step-by-step analysis, three letters (E, M, Y) remain in their original positions when the word GERMANY is arranged alphabetically.
The problem requires us to evaluate a given mathematical expression after interchanging specific arithmetic operators. We need to replace '+' with '−', '−' with '+', '×' with '÷', and '÷' with '×'. Then, we will apply the order of operations (BODMAS/PEMDAS) to solve the modified expression.
A) 192 is the correct answer, as derived from the step-by-step calculation.
The question asks to identify the social reformer who founded the Satyashodhak Samaj. This requires knowledge of prominent social reformers in India and the organizations they established.
Correct Option: C) Jyotirao Phule founded the Satyashodhak Samaj (Truth-Seekers' Society) in 1873 in Maharashtra. Its primary aim was to secure human rights and social justice for the Shudras and Ati-Shudras (lower castes and untouchables) and to liberate them from exploitation by Brahmins and other upper castes.
The problem presents a series of numbers and asks us to find the next number in the sequence. To solve this, we need to identify the pattern or rule governing the series by examining the differences between consecutive terms.
D) 51 is the correct option because by following the identified pattern of decreasing differences (10, 9, 8, 7, 6, 5, ...), the next number in the series is obtained by subtracting 4 from 55, which results in 51.