In a certain code language, ‘BDSHF’ is written as ‘GHVJG’ and ‘FGLRU’ is written as ‘KKOTV’. How will ‘ELPHT’ be written in that language?
The problem is a coding-decoding question. We need to identify the pattern or rule used to transform the given words into their coded forms. Once the rule is established, we apply it to the target word to find its coded form.
C) JPSJU is the correct answer, as derived from applying the established coding pattern.
To determine which element is more reactive than copper, we need to refer to the reactivity series of metals. The reactivity series lists metals in order of their decreasing reactivity. A metal higher in the series is more reactive than a metal lower in the series and can displace it from its salt solution.
A) Zinc is more reactive than copper. It is placed higher than copper in the reactivity series.
The question gives the equation \(4a+3b=2c\) and asks us to find the value of \((4a)^3+(3b)^3+(-2c)^3\). We can use the algebraic identity \(x^3+y^3+z^3=3xyz\) when \(x+y+z=0\).
Identify the given equation:
\[ 4a+3b=2c \]Rearranging all terms to one side:
\[ 4a+3b-2c=0 \]Identify the required expression:
\[ (4a)^3+(3b)^3+(-2c)^3 \]Let:
From the given equation:
\[ x+y+z=0 \]Apply the algebraic identity:
The identity is:
\[ x^3+y^3+z^3-3xyz =(x+y+z)(x^2+y^2+z^2-xy-yz-zx) \]Since \(x+y+z=0\), the identity becomes:
\[ x^3+y^3+z^3=3xyz \]Substitute the values:
\[ (4a)^3+(3b)^3+(-2c)^3 =3(4a)(3b)(-2c) \]Multiplying the numerical coefficients:
\[ =3\times4\times3\times(-2)\times abc \] \[ =\boxed{-72abc} \]Therefore, the required value is \(-72abc\).
Correct Option: A) −72abc — Since \(4a+3b-2c=0\), we can apply the identity \(x^3+y^3+z^3=3xyz\) when \(x+y+z=0\). Substituting \(x=4a\), \(y=3b\), and \(z=-2c\), we get \(3(4a)(3b)(-2c)=-72abc\). Hence, Option A is the correct answer.
B) 0: This is incorrect because \(4a+3b-2c=0\) does not necessarily mean that the sum of their cubes is zero. The identity gives \(-72abc\), which is zero only when \(abc=0\).
C) 72abc: This is incorrect because the third term is \((-2c)^3\), which is negative. Therefore, the product \(3(4a)(3b)(-2c)\) gives \(-72abc\), not \(72abc\).
D) 1: This is incorrect because the algebraic identity gives \(-72abc\). The expression does not have a fixed numerical value of 1 for all values satisfying the given equation.
To answer this question, one needs to understand the basic circulation pathway of blood through the human heart, specifically focusing on the role of the pulmonary vein.
Therefore, the pulmonary vein is connected to the left auricle (atrium).
Correct Option: C) left auricle
The question asks to identify the primary difference between domestic and industrial solid waste. We need to analyze the characteristics of each type of waste to determine the most significant distinguishing factor among the given options.
D) The former is heterogeneous in composition. Domestic waste is characterized by its highly varied composition, including organic matter, plastics, paper, glass, metals, etc. Industrial waste, while potentially hazardous, is generally more uniform or specific to the particular industrial process.
Let 0.\(\overline{272}\) – 0.\(\overline{233}\) = x, where x is a proper fraction in the simplest form. Then the sum of the numerator and the denominator of x is:
To solve this problem, we need to convert the given recurring decimals into proper fractions. Then, we will subtract the second fraction from the first to find the value of \(x\). Finally, we will simplify \(x\) to its simplest form and calculate the sum of its numerator and denominator.
Let \(a = 0.\overline{272}\). This means \(a = 0.272272272...\)
Multiply by 1000 (since there are 3 repeating digits):
\[ 1000a = 272.272272... \]\[ 1000a = 272 + 0.272272... \]\[ 1000a = 272 + a \]\[ 999a = 272 \]\[ a = \frac{272}{999} \]Let \(b = 0.\overline{233}\). This means \(b = 0.233233233...\)
Multiply by 1000:
\[ 1000b = 233.233233... \]\[ 1000b = 233 + 0.233233... \]\[ 1000b = 233 + b \]\[ 999b = 233 \]\[ b = \frac{233}{999} \]Both 39 and 999 are divisible by 3.
\[ 39 \div 3 = 13 \]\[ 999 \div 3 = 333 \]\[ x = \frac{13}{333} \]Numerator = 13
Denominator = 333
Sum = \(13 + 333 = 346\)
A) 346 is the correct sum of the numerator and the denominator of \(x\).
The question asks to identify the foundational unit of the Panchayati Raj System, which is empowered by State Legislatures. Understanding the structure and hierarchy of the Panchayati Raj System in India is key to answering this question.
B) Gram Sabha — The Gram Sabha is the assembly of all registered voters residing in the area of a Gram Panchayat. It is the most fundamental unit of the Panchayati Raj System, serving as the direct democratic forum at the village level. It is entrusted with powers and functions by the State Legislatures, making it the foundation upon which the entire system rests.
The given table shows the use of chemicals (in litres) in three science laboratories of a school from 2002 to 2006. Study the table and answer the question that follows.
| Year | Laboratory | ||
| Biology | Physics | Chemistry | |
| 2002 | 52 | 61 | 47 |
| 2003 | 81 | 56 | 51 |
| 2004 | 67 | 49 | 57 |
| 2005 | 91 | 67 | 69 |
| 2006 | 93 | 73 | 72 |
What is the ratio of the total use of chemicals (in litres) in the Biology laboratory to the total use of chemicals (in litres) in the Chemistry laboratory from 2002 to 2006?
To find the ratio of the total use of chemicals in the Biology laboratory to the total use in the Chemistry laboratory, we need to sum the chemical usage for each laboratory over the given years (2002 to 2006) and then express these sums as a ratio in their simplest form.
Sum the values for Biology from 2002 to 2006:
\[ \text{Total Biology} = 52 + 81 + 67 + 91 + 93 \] \[ \text{Total Biology} = 384 \text{ litres} \]Sum the values for Chemistry from 2002 to 2006:
\[ \text{Total Chemistry} = 47 + 51 + 57 + 69 + 72 \] \[ \text{Total Chemistry} = 296 \text{ litres} \]The ratio of total Biology to total Chemistry is:
\[ \text{Ratio} = \frac{\text{Total Biology}}{\text{Total Chemistry}} = \frac{384}{296} \]To simplify the ratio, find the greatest common divisor (GCD) of 384 and 296.
Both numbers are divisible by 8:
\[ 384 \div 8 = 48 \] \[ 296 \div 8 = 37 \]So, the simplified ratio is \(48 : 37\).
A) 48 : 37 — This matches our calculated and simplified ratio.
The problem provides two ratio relationships between three numbers: \(a\), \(b\), and \(192\), and a constant \(24\). We need to use these ratio relationships to form equations, solve for \(a\) and \(b\), and then find their sum \((a+b)\).
Formulate equations from the given ratios:
The first relationship is \(a : 24 :: 24 : b\). This means the ratio of \(a\) to \(24\) is equal to the ratio of \(24\) to \(b\). We can write this as:
\[ \frac{a}{24} = \frac{24}{b} \]Cross-multiplying gives us:
\[ ab = 24 \times 24 \] \[ ab = 576 \quad \text{(Equation 1)} \]The second relationship is \(a : b :: b : 192\). This means the ratio of \(a\) to \(b\) is equal to the ratio of \(b\) to \(192\). We can write this as:
\[ \frac{a}{b} = \frac{b}{192} \]Cross-multiplying gives us:
\[ b^2 = 192a \quad \text{(Equation 2)} \]Solve the system of equations:
From Equation 1, we can express \(a\) in terms of \(b\):
\[ a = \frac{576}{b} \]Substitute this expression for \(a\) into Equation 2:
\[ b^2 = 192 \left( \frac{576}{b} \right) \]Multiply both sides by \(b\):
\[ b^3 = 192 \times 576 \]To simplify the calculation, we can express \(192\) and \(576\) in terms of their prime factors or common factors. We know that \(576 = 24^2\). Also, \(192 = 8 \times 24\).
\[ b^3 = (8 \times 24) \times 24^2 \] \[ b^3 = 8 \times 24^3 \]Now, take the cube root of both sides:
\[ b = \sqrt[3]{8 \times 24^3} \] \[ b = \sqrt[3]{8} \times \sqrt[3]{24^3} \] \[ b = 2 \times 24 \] \[ b = 48 \]Find the value of \(a\):
Substitute the value of \(b = 48\) back into Equation 1 (\(ab = 576\)):
\[ a \times 48 = 576 \] \[ a = \frac{576}{48} \]We know that \(576 = 24 \times 24\), and \(48 = 2 \times 24\). So,
\[ a = \frac{24 \times 24}{2 \times 24} \] \[ a = \frac{24}{2} \] \[ a = 12 \]Calculate \((a+b)\):
\[ a + b = 12 + 48 \] \[ a + b = 60 \]Correct Option: D) 60
The problem asks us to find the missing number in an analogy. We need to identify the relationship between the first two pairs of numbers and then apply the same relationship to the third pair to find the missing number.
Analyze the first pair: 139 : 150
Find the difference between the second number and the first number:
\(150 - 139 = 11\)
So, the relationship is that the second number is 11 more than the first number.
Analyze the second pair: 73 : 84
Find the difference between the second number and the first number:
\(84 - 73 = 11\)
This confirms the pattern: the second number is 11 more than the first number.
Apply the pattern to the third pair: 17 : ?
Based on the established pattern, the missing number should be 11 more than 17.
\(17 + 11 = 28\)
Therefore, the missing number is 28.
C) 28 is the correct answer because adding 11 to 17 gives 28, which follows the pattern established by the first two pairs.