The goal is to find the correct balanced chemical equation for the reaction between magnesium and oxygen to form magnesium oxide. A balanced chemical equation must satisfy the Law of Conservation of Mass, meaning the number of atoms of each element must be the same on both the reactant and product sides of the equation.
A) 2Mg(s) + O₂(g) → 2MgO(s) This equation correctly represents the reaction with the same number of magnesium and oxygen atoms on both sides, adhering to the Law of Conservation of Mass.
Which of the following states has the largest deposits of jet black granite?
The question asks to identify the Indian state with the largest deposits of jet black granite. This requires knowledge of the geographical distribution of mineral resources in India, specifically granite varieties.
D) Karnataka is the state with the largest deposits of jet black granite. It is a major producer and exporter of this specific variety of granite, which is highly valued for its uniform dark color and fine texture.
In which of the following states can we experience the local wind ‘Loo’ during the summer season?
The question asks to identify the state where the local wind 'Loo' is experienced during the summer season. This requires knowledge of the geographical distribution and characteristics of local winds in India.
Correct Option: B) Rajasthan
What is the difference between the molecular masses of two successive members of the homologous series?
The question asks for the difference in molecular masses between two successive members of a homologous series. A homologous series is a series of organic compounds with the same functional group but with each successive member differing by a \(\text{CH}_2\) group. We need to calculate the molecular mass of a \(\text{CH}_2\) group.
Understand Homologous Series: In organic chemistry, a homologous series is a series of compounds that have the same general formula, usually vary by a single parameter such as the length of a carbon chain, and have the same functional groups. Each successive member in such a series differs by a \(\text{CH}_2\) unit.
Identify the difference between successive members: For example, consider the alkane series:
The difference between ethane (\(\text{C}_2\text{H}_6\)) and methane (\(\text{CH}_4\)) is \(\text{C}_2\text{H}_6 - \text{CH}_4 = \text{CH}_2\).
The difference between propane (\(\text{C}_3\text{H}_8\)) and ethane (\(\text{C}_2\text{H}_6\)) is \(\text{C}_3\text{H}_8 - \text{C}_2\text{H}_6 = \text{CH}_2\).
Thus, two successive members of any homologous series differ by one \(\text{CH}_2\) group.
Calculate the molecular mass of a \(\text{CH}_2\) group:
Molecular mass of \(\text{CH}_2 = (\text{Atomic mass of C}) + 2 \times (\text{Atomic mass of H})\)
\[ = 12 \text{ u} + 2 \times 1 \text{ u} \]\[ = 12 \text{ u} + 2 \text{ u} \]\[ = 14 \text{ u} \]
Conclusion: The difference between the molecular masses of two successive members of the homologous series is \(14 \text{ u}\).
A) 14 u is correct because successive members of a homologous series differ by a \(\text{CH}_2\) group, and the molecular mass of a \(\text{CH}_2\) group is \(12 + (2 \times 1) = 14 \text{ u}\).
The question asks to identify the chemical solution used to detect the presence of starch in food. This is a common test in biology and chemistry to identify macromolecules.
D) Iodine solution — Iodine solution is used to test for the presence of starch. It turns blue-black in the presence of starch.
To find the population of the town in 2000, we need to calculate the population increase over two successive decades, with a 10% increase in each decade. This is a compound growth problem. We can calculate the population after the first decade and then use that as the base for the second decade's increase, or use the compound interest formula.
Initial population in 1980, \(P_0 = 2,25,000\).
Growth rate per decade, \(r = 10\% = 0.10\).
Number of decades, \(n = 2\) (from 1980 to 2000).
Population after 1st decade \(P_1 = P_0 \times (1 + r)\)
\[ P_1 = 2,25,000 \times (1 + 0.10) \] \[ P_1 = 2,25,000 \times 1.10 \] \[ P_1 = 2,47,500 \]Population after 2nd decade \(P_2 = P_1 \times (1 + r)\)
\[ P_2 = 2,47,500 \times (1 + 0.10) \] \[ P_2 = 2,47,500 \times 1.10 \] \[ P_2 = 2,72,250 \]Alternatively, using the compound interest formula directly:
\(P_n = P_0 \times (1 + r)^n\)
\[ P_2 = 2,25,000 \times (1 + 0.10)^2 \] \[ P_2 = 2,25,000 \times (1.10)^2 \] \[ P_2 = 2,25,000 \times 1.21 \] \[ P_2 = 2,72,250 \]The calculated population in 2000 is 2,72,250, which matches option A.
We need to determine the seating arrangement of six students (P, Q, R, S, T, U) in a straight row, all facing north, based on the given clues. We will build the arrangement step-by-step, starting with the most definitive clues.
A) Two
As determined from the final arrangement P Q S R U T, there are two persons (S and R) standing between Q and U.
The problem asks us to calculate the resistance of a bulb given its power rating and voltage rating. We can use the formula relating power, voltage, and resistance to find the resistance.
Identify the given values:
Recall the relevant formula:
The relationship between power \((P)\), voltage \((V)\), and resistance \((R)\) is given by:
Rearrange the formula to solve for resistance \((R)\):
\[ R = \frac{V^2}{P} \]Substitute the given values into the formula:
\[ R = \frac{(220 \text{ V})^2}{50 \text{ W}} \]Calculate the square of the voltage:
\[ (220)^2 = 48400 \]Perform the division to find the resistance:
\[ R = \frac{48400}{50} \]\[ R = 968 \text{ } \Omega \]Thus, the resistance of the bulb is \(968 \text{ } \Omega\).
D) 968 Ω is the correct resistance calculated using the given power and voltage ratings.
The question asks for the causative agent of warts. We need to identify which type of microorganism is responsible for causing warts from the given options.
A) Virus — Warts are indeed caused by the human papillomavirus (HPV), which is a type of virus. Therefore, this option is correct.
The roots of the quadratic equation x+\( \frac{10}{x} \) =7 are:
To find the roots of the given equation, we first need to convert it into a standard quadratic equation form \(ax^2 + bx + c = 0\). Once in this form, we can use either factorization, the quadratic formula, or completing the square method to find the roots. In this case, factorization will be a straightforward method.
The given equation is:
\[ x + \frac{10}{x} = 7 \]Multiply the entire equation by \(x\) to remove the denominator. Note that \(x \neq 0\).
\[ x(x) + x\left(\frac{10}{x}\right) = 7(x) \]\[ x^2 + 10 = 7x \]Move all terms to one side to get the standard form \(ax^2 + bx + c = 0\).
\[ x^2 - 7x + 10 = 0 \]We need to find two numbers that multiply to 10 and add up to -7. These numbers are -2 and -5.
\[ x^2 - 2x - 5x + 10 = 0 \]\[ x(x - 2) - 5(x - 2) = 0 \]\[ (x - 2)(x - 5) = 0 \]Set each factor equal to zero to find the values of \(x\).
\[ x - 2 = 0 \implies x = 2 \]\[ x - 5 = 0 \implies x = 5 \]For \(x=2\): \(2 + \frac{10}{2} = 2 + 5 = 7\). This is correct.
For \(x=5\): \(5 + \frac{10}{5} = 5 + 2 = 7\). This is also correct.
B) 5, 2 are the roots of the given quadratic equation.