The question asks for a common classification that applies to both liquids and gases. We need to recall the fundamental properties of different states of matter and their classifications in physics.
Correct Option: A) fluids — Both liquids and gases exhibit the characteristic property of flowing and taking the shape of their container. This is the defining characteristic of a fluid.
The question asks to identify the type of chemical reaction where a single reactant breaks down into simpler products. We need to recall the definitions of different types of chemical reactions to determine the correct answer.
Correct Option: A) Decomposition
The question asks to identify a single-celled organism from the given options. This requires knowledge of basic biological classification and the characteristics of unicellular versus multicellular organisms.
Correct Option: A) Amoeba
The problem uses a direct letter-to-digit coding scheme. We need to identify the unique code assigned to each letter by comparing the given coded words. Once the code for 'K' is found, we can select the correct option.
The question asks to identify which statement is NOT a characteristic of particles of matter. We need to recall the fundamental properties of matter's constituent particles.
Correct Option: A) Particles of matter are static.
This statement is incorrect because particles of matter are in a continuous state of motion, possessing kinetic energy. Even in solids, particles vibrate about their mean positions.
To determine the ratio by mass of hydrogen to oxygen atoms in a water molecule, we need to consider the chemical formula of water and the atomic masses of hydrogen and oxygen. The chemical formula for water is \(\text{H}_2\text{O}\), which indicates that one molecule of water consists of two hydrogen atoms and one oxygen atom.
Thus, the ratio by mass of hydrogen to oxygen atoms in a water molecule is 1:8.
C) 1 : 8 is the correct ratio by mass of hydrogen to oxygen in a water molecule, as calculated from their atomic masses and the molecular formula.
The question asks to identify the High Court that struck down the amended Information Technology Rules 2023 related to the Fact Check Unit (FCU). This is a current affairs question requiring knowledge of recent legal developments in India.
C) Bombay High Court: In September 2024, the Bombay High Court struck down the amended Information Technology Rules 2023, which empowered the Centre to set up a fact-check unit (FCU) to identify fake, false, and misleading information about the government and its establishments on social media. The court held that the rules were unconstitutional and violated freedom of speech and expression.
To find the number divisible by both 7 and 11, we need to check each option for divisibility by 7 and 11. A number is divisible by 7 if, when we subtract twice the last digit from the number formed by the remaining digits, the result is a multiple of 7. A number is divisible by 11 if the alternating sum of its digits is a multiple of 11 (including 0).
Using the divisibility rule for 7: \(301 - 2 \times 4 = 301 - 8 = 293\).
Repeat: \(29 - 2 \times 3 = 29 - 6 = 23\). 23 is not divisible by 7. So, 3014 is not divisible by 7.
Using the divisibility rule for 7: \(268 - 2 \times 4 = 268 - 8 = 260\).
Repeat: \(26 - 2 \times 0 = 26\). 26 is not divisible by 7. So, 2684 is not divisible by 7.
Using the divisibility rule for 7: \(177 - 2 \times 1 = 177 - 2 = 175\).
Repeat: \(17 - 2 \times 5 = 17 - 10 = 7\). 7 is divisible by 7. So, 1771 is divisible by 7.
Correct Option: D) 1771
This problem involves determining relative directions and positions of towns. We will use a standard compass direction system (North, South, East, West) to plot the positions of the towns based on the given statements. By visualizing or sketching the positions, we can determine the final relative position.
Let's place B at the origin \((0,0)\).
We need to find the position of Town D with respect to Town M.
M is at \((x_C, y_M)\) (North-East quadrant relative to B).
D is at \((x_D, y_D)\) (West of B, so \(x_D < 0\)). Since A is north-east of D, D must be south-west of A. As A is north of B, D must be somewhere in the south-west direction relative to A. If D is west of B, its y-coordinate could be positive, zero, or negative. However, the statement "A is to the north-east of D" means D is to the south-west of A. Since A is north of B, D must be to the west of B. Therefore, D is in the west or south-west quadrant relative to B.
Comparing D \((x_D, y_D)\) with M \((x_C, y_M)\):
Let's draw a simple diagram:
A
|
B -- C
/| |
D M
This diagram is not perfectly to scale but shows the relative directions. A is north of B. C is east of B. D is west of B (derived from A being north-east of D). M is north of C. If you stand at M, D is to your left (west) and below (south). Therefore, D is to the South-West of M.
A) South-west: Based on the step-by-step analysis and visualization, Town D is positioned to the south-west of Town M.
To find the single equivalent discount for two successive discounts, we can assume an initial price (e.g., Rs. 100) and apply each discount sequentially. Alternatively, we can use the formula for equivalent discount.
Let the initial marked price be \(P\).
First Discount: A 10% discount is applied. The price after the first discount will be:
\[ P_1 = P - (0.10 \times P) = P(1 - 0.10) = 0.90P \]Second Discount: A 5% discount is applied to the discounted price \(P_1\). The price after the second discount will be:
\[ P_2 = P_1 - (0.05 \times P_1) = P_1(1 - 0.05) = 0.95P_1 \]Substitute \(P_1\): Now, substitute the value of \(P_1\) into the equation for \(P_2\):
\[ P_2 = 0.95 \times (0.90P) = 0.855P \]Calculate Total Discount: The final price is \(0.855P\). The total discount is the difference between the original price and the final price:
\[ \text{Total Discount} = P - P_2 = P - 0.855P = 0.145P \]Express as Percentage: To express this as a percentage, multiply by 100:
\[ \text{Equivalent Discount Percentage} = 0.145 \times 100\% = 14.5\% \]Alternatively, using the formula for equivalent discount for two successive discounts \(d_1\) and \(d_2\):
\[ \text{Equivalent Discount} = \left(d_1 + d_2 - \frac{d_1 d_2}{100}\right)\% \]Given \(d_1 = 10\%\) and \(d_2 = 5\%\):
\[ \text{Equivalent Discount} = \left(10 + 5 - \frac{10 \times 5}{100}\right)\% \] \[ \text{Equivalent Discount} = \left(15 - \frac{50}{100}\right)\% \] \[ \text{Equivalent Discount} = (15 - 0.5)\% \] \[ \text{Equivalent Discount} = 14.5\% \]C) The single equivalent discount is 14.5%.