The question asks about the purpose of denaturing ethanol. Denaturation is a process that alters the properties of a substance, often to prevent its misuse. We need to consider the common uses and misuses of ethanol to determine why it is denatured.
A) make it unsuitable for drinking — Denaturing ethanol involves adding substances that make it toxic or unpalatable, specifically to prevent its consumption as an alcoholic beverage and thus avoid excise duties on potable alcohol.
To identify which pair is NOT a pair of twin primes, we need to understand the definition of twin primes and prime numbers. A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. Twin primes are a pair of prime numbers that differ by 2.
Since 133 is not a prime number, the pair (131, 133) cannot be a pair of twin primes, even though their difference is \(133 - 131 = 2\).
A) 131, 133 — As shown above, 133 is divisible by 7 (133 = 7 × 19), making it a composite number, not a prime number. Therefore, this pair is not a pair of twin primes.
To find the length of the train, we need to understand that when a train crosses a platform, the total distance covered by the train is the sum of its own length and the length of the platform. We are given the speed of the train and the time taken to cross the platform. We will first convert the speed to meters per second and then use the formula: Distance = Speed \(\times\) Time.
Given speed of the train = 66 km/h.
To convert km/h to m/s, multiply by \(\frac{5}{18}\).
\[ \text{Speed} = 66 \times \frac{5}{18} \text{ m/s} \] \[ \text{Speed} = \frac{11 \times 5}{3} \text{ m/s} \] \[ \text{Speed} = \frac{55}{3} \text{ m/s} \]Time taken to cross the platform = 24 seconds.
Using the formula: Distance = Speed \(\times\) Time.
\[ \text{Total Distance} = \frac{55}{3} \text{ m/s} \times 24 \text{ s} \] \[ \text{Total Distance} = 55 \times 8 \text{ m} \] \[ \text{Total Distance} = 440 \text{ m} \]The total distance covered is the sum of the length of the train and the length of the platform.
Let the length of the train be \(L_T\).
Length of the platform = 200 m.
\[ \text{Total Distance} = L_T + \text{Length of Platform} \] \[ 440 \text{ m} = L_T + 200 \text{ m} \] \[ L_T = 440 - 200 \text{ m} \] \[ L_T = 240 \text{ m} \]Correct Option: B) 240 m
The problem asks us to identify implicit assumptions based on a given argument. An assumption is something taken for granted or supposed in advance. We need to evaluate if the government's action (issuing advisories about unhygienic roadside food) inherently implies the given assumptions.
C) Neither 1 nor 2 is implicit.
The question asks to identify a bisexual flower from the given options. A bisexual flower, also known as a perfect flower, contains both male (stamen) and female (pistil/carpel) reproductive organs within the same flower. Flowers that have only one type of reproductive organ (either male or female) are called unisexual or imperfect flowers.
Correct Option: A) Mustard
The problem involves calculating the height of an embankment formed by spreading earth from a well. The key principle is that the volume of earth dug out from the well is equal to the volume of the embankment formed. We will calculate the volume of the cylindrical well and then use this volume to find the height of the circular ring-shaped embankment.
The well is cylindrical. Its diameter is \(3 \text{ m}\), so its radius \(r_w\) is \(\frac{3}{2} \text{ m} = 1.5 \text{ m}\). The depth (height) of the well \(h_w\) is \(14 \text{ m}\).
The volume of a cylinder is given by the formula \(V = \pi r^2 h\).
\[ V_{\text{well}} = \pi r_w^2 h_w = \pi (1.5)^2 (14) = \pi (2.25)(14) = 31.5 \pi \text{ m}^3 \]The embankment is formed in the shape of a circular ring around the well. The width of the ring is \(4 \text{ m}\).
The inner radius of the embankment \(r_{\text{inner}}\) is the same as the radius of the well, which is \(1.5 \text{ m}\).
The outer radius of the embankment \(r_{\text{outer}}\) is the inner radius plus the width of the ring:
\[ r_{\text{outer}} = r_{\text{inner}} + \text{width} = 1.5 \text{ m} + 4 \text{ m} = 5.5 \text{ m} \]The embankment is a hollow cylinder (a circular ring). Its volume is the volume of the outer cylinder minus the volume of the inner cylinder, with height \(h_e\) (the height of the embankment, which we need to find).
\[ V_{\text{embankment}} = \pi r_{\text{outer}}^2 h_e - \pi r_{\text{inner}}^2 h_e \] \[ V_{\text{embankment}} = \pi h_e (r_{\text{outer}}^2 - r_{\text{inner}}^2) \] \[ V_{\text{embankment}} = \pi h_e ((5.5)^2 - (1.5)^2) \] \[ V_{\text{embankment}} = \pi h_e (30.25 - 2.25) \] \[ V_{\text{embankment}} = \pi h_e (28) \text{ m}^3 \]The volume of earth dug out from the well is equal to the volume of the embankment.
\[ V_{\text{well}} = V_{\text{embankment}} \] \[ 31.5 \pi = 28 \pi h_e \]Divide both sides by \(\pi\):
\[ 31.5 = 28 h_e \] \[ h_e = \frac{31.5}{28} \]To simplify the fraction, multiply numerator and denominator by 10 to remove the decimal:
\[ h_e = \frac{315}{280} \]Both numbers are divisible by 5:
\[ h_e = \frac{63}{56} \]Both numbers are divisible by 7:
\[ h_e = \frac{9}{8} \text{ m} \]A) \( \frac{9}{8} \) m is the calculated height of the embankment.
To find the number of moles, we use the relationship between mass, molar mass, and the number of moles. The molar mass of an element is numerically equal to its atomic mass expressed in grams per mole.
The molar mass of Sulphur is numerically equal to its atomic mass, but expressed in grams per mole.
\[ \text{Molar mass of Sulphur} = 32 \, \text{g/mol} \]The number of moles (\(n\)) can be calculated using the formula:
\[ n = \frac{\text{Given mass}}{\text{Molar mass}} \]Substitute the given mass and the molar mass into the formula:
\[ n = \frac{16 \, \text{g}}{32 \, \text{g/mol}} \]\[ n = 0.5 \, \text{mol} \]Therefore, 16 grams of Sulphur contain 0.5 moles of Sulphur.
A) 0.5 moles of Sulphur is correct because the number of moles is calculated by dividing the given mass (16 g) by the molar mass (32 g/mol), which results in 0.5 moles.
The question asks to identify what the symbol 'R' represents in the context of electricity. This is a fundamental concept in basic electrical circuits and physics.
Correct Option: D) Resistance
This question tests the understanding of image formation by a concave mirror, specifically when the object is placed at the centre of curvature. We can determine the image position using ray tracing rules or the mirror formula.
For a concave mirror, the focal length \(f\) is negative, so \(f = -|f|\). The object is placed at the centre of curvature, so its distance from the mirror is \(u = -R\), where \(R\) is the radius of curvature. We know that \(R = 2|f|\), so \(u = -2|f|\). Substituting these values into the mirror formula:
\[ \frac{1}{v} + \frac{1}{-2|f|} = \frac{1}{-|f|} \]Rearranging the terms to solve for \(v\):
\[ \frac{1}{v} = \frac{1}{-|f|} - \frac{1}{-2|f|} \]\[ \frac{1}{v} = \frac{1}{2|f|} - \frac{1}{|f|} \]\[ \frac{1}{v} = \frac{1 - 2}{2|f|} \]\[ \frac{1}{v} = \frac{-1}{2|f|} \]Therefore, \(v = -2|f|\). Since \(R = 2|f|\), this means \(v = -R\). The negative sign indicates that the image is formed on the same side as the object, which is in front of the mirror. Thus, the image is formed at the centre of curvature (C).
Correct Option: C) the centre of curvature. When an object is placed at the centre of curvature of a concave mirror, the image formed is real, inverted, and of the same size as the object, and it is located at the centre of curvature itself.
This problem involves motion under constant acceleration. We will use the equations of motion, specifically the one relating distance, initial velocity, acceleration, and time, to find the distances covered in the specified time intervals. Since the particle starts from rest, its initial velocity is zero.
The equation of motion for distance \(s\) with constant acceleration \(a\), initial velocity \(u\), and time \(t\) is given by:
\[ s = ut + \frac{1}{2}at^2 \]Given that the particle starts from rest, the initial velocity \(u = 0\). So the equation simplifies to:
\[ s = \frac{1}{2}at^2 \]Calculate distance \(X_1\) (first 10 s):
For the first 10 seconds, \(t = 10 \text{ s}\). The distance covered is \(X_1\).
Calculate total distance covered in 20 s:
The total time is 20 s. Let the total distance be \(X_{\text{total}}\).
Calculate distance \(X_2\) (remaining 10 s):
The distance \(X_2\) is the distance covered in the time interval from \(t = 10 \text{ s}\) to \(t = 20 \text{ s}\). This can be found by subtracting \(X_1\) from \(X_{\text{total}}\).
Substitute the values from Equation 1 and Equation 2:
\[ X_2 = 200a - 50a \] \[ X_2 = 150a \quad \text{(Equation 3)} \]Compare \(X_1\) and \(X_2\):
Now, we need to find the relationship between \(X_1\) and \(X_2\). Divide Equation 3 by Equation 1:
Assuming \(a \neq 0\):
\[ \frac{X_2}{X_1} = 3 \] \[ X_2 = 3X_1 \]Correct Option: B) X 2 = 3 X 1