This problem involves decoding a blood relation expression using a given set of symbols and then determining the relationship between two individuals. We will break down the expression step-by-step, assigning genders and relationships as we go, to build a family tree or a chain of relationships.
From the analysis:
We need to find how P is related to F.
Therefore, P is the sister of F's father (Q). This means P is F's paternal aunt, or father's sister.
D) Father's sister — As derived, P is the sister of Q, who is F's father. Thus, P is F's father's sister.
This is a syllogism problem. We need to evaluate the given conclusions based on the provided statements. We can use Venn diagrams or logical deduction to determine if the conclusions logically follow from the statements. Remember to take the statements as absolutely true, even if they contradict common knowledge.
Since neither conclusion (I) nor conclusion (II) logically follows from the given statements, the correct option is A.
Correct Option: A) Neither conclusion (I) nor (II) follows
If a light ray is travelling from medium of refractive index 'n1' to the medium of refractive index 'n2' such that angle of incidence is 'i' and angle of refraction 'r' (assuming 0 < i < 90 degree), then \(\frac{n_1}{n_2}\) is equal to ______.
\(\frac{\sin i}{\sin r}\)
sin r − sin i
\(\frac{\sin r}{\sin i}\)
sin i − sin r
This question tests the understanding of Snell's Law, which describes the relationship between the angles of incidence and refraction when light passes between two different media. We need to apply Snell's Law to find the ratio of refractive indices.
C) \(\frac{\sin r}{\sin i}\) is correct because it directly follows from Snell's Law, \(n_1 \sin i = n_2 \sin r\), when rearranged to solve for \(\frac{n_1}{n_2}\).
The equivalent resistance of the combination of resistors, when 1 ohm and 2 ohm are connected in parallel, is ______.
(\( \frac{2}{3} \)) ohm
2 ohm
3 ohm
\( \frac{3}{2} \) ohm
To find the equivalent resistance of resistors connected in parallel, we use the formula for parallel resistances. This formula states that the reciprocal of the equivalent resistance is equal to the sum of the reciprocals of individual resistances.
Identify the given resistances:
Recall the formula for equivalent resistance (\(R_{\text{eq}}\)) when two resistors are connected in parallel:
\[ \frac{1}{R_{\text{eq}}} = \frac{1}{R_1} + \frac{1}{R_2} \]Alternatively, for two resistors, this can be simplified to:
\[ R_{\text{eq}} = \frac{R_1 \times R_2}{R_1 + R_2} \]Substitute the given values into the formula:
\[ R_{\text{eq}} = \frac{1 \, \text{ohm} \times 2 \, \text{ohm}}{1 \, \text{ohm} + 2 \, \text{ohm}} \]Perform the multiplication and addition:
\[ R_{\text{eq}} = \frac{2 \, \text{ohm}^2}{3 \, \text{ohm}} \]Calculate the final equivalent resistance:
\[ R_{\text{eq}} = \frac{2}{3} \, \text{ohm} \]A) \( \frac{2}{3} \) ohm is the correct equivalent resistance when 1 ohm and 2 ohm resistors are connected in parallel.
The question asks to identify the compound used in soda-acid fire extinguishers. These extinguishers work on the principle of producing carbon dioxide gas, which helps in extinguishing fires by cutting off the oxygen supply.
Correct Option: C) Sodium bicarbonate is the compound used in soda-acid fire extinguishers. It reacts with an acid (like sulfuric acid) to produce carbon dioxide gas, which smothers the fire.
The question asks under what condition the average velocity of a body can be calculated as the arithmetic mean of its initial and final velocities. This is a fundamental concept in kinematics, specifically related to motion with constant acceleration.
Definition of Average Velocity: The average velocity (\(v_{\text{avg}}\)) is defined as the total displacement divided by the total time taken:
\[ v_{\text{avg}} = \frac{\text{Total Displacement}}{\text{Total Time}} \]Equations of Motion for Uniform Acceleration: For a body moving with uniform (constant) acceleration \(a\), the following equations of motion apply:
where \(u\) is the initial velocity, \(v\) is the final velocity, \(s\) is the displacement, and \(t\) is the time.
Derivation for Average Velocity with Uniform Acceleration: Let's use the second equation of motion to find the displacement:
\[ s = ut + \frac{1}{2}at^2 \]Now, substitute this into the average velocity formula:
\[ v_{\text{avg}} = \frac{ut + \frac{1}{2}at^2}{t} \]Simplify the expression:
\[ v_{\text{avg}} = u + \frac{1}{2}at \]From the first equation of motion, we know that \(at = v - u\). Substitute this into the expression for \(v_{\text{avg}}\):
\[ v_{\text{avg}} = u + \frac{1}{2}(v - u) \]\[ v_{\text{avg}} = u + \frac{1}{2}v - \frac{1}{2}u \]\[ v_{\text{avg}} = \frac{1}{2}u + \frac{1}{2}v \]\[ v_{\text{avg}} = \frac{u + v}{2} \]This derivation shows that the average velocity is indeed the arithmetic mean of the initial and final velocities \((u+v)/2\) only when the acceleration is uniform (constant). If the acceleration is not uniform, this formula does not hold true.
A) moving with uniform acceleration: As derived above, the formula \(v_{\text{avg}} = (u+v)/2\) is a direct consequence of the equations of motion which are valid only for uniform acceleration. Therefore, this is the correct condition.
The problem requires us to determine the number of people between F and E based on a series of relative seating arrangements. We will use a step-by-step approach to place each person in the row of seven, facing north, which means left is west and right is east.
Total people and direction: There are 7 people (A, B, C, D, E, F, G) sitting in a row, facing North. This means the left end is position 1 and the right end is position 7.
Positions: 1 2 3 4 5 6 7
E sits third from the left end: This means E is at position 3.
_ _ E _ _ _ _
Positions: 1 2 3 4 5 6 7
Only one person sits to the right of D: Since there are 7 positions, if only one person sits to the right of D, D must be at position 6.
_ _ E _ _ D _
Positions: 1 2 3 4 5 6 7
G sits second to the left of D: D is at position 6. Second to the left of D means position \(6 - 2 = 4\). So, G is at position 4.
_ _ E G _ D _
Positions: 1 2 3 4 5 6 7
B sits to the immediate right of C: This means C and B are adjacent, in the order CB. The available consecutive spots are (1,2) or (5,7) is not possible. So, C and B must be at positions 1 and 2 respectively.
C B E G _ D _
Positions: 1 2 3 4 5 6 7
F does not sit to the right of A: This implies F sits to the left of A. The remaining empty spots are position 5 and position 7. The remaining people are A and F.
C B E G F D A
Positions: 1 2 3 4 5 6 7
Final arrangement: C B E G F D A
Count people between F and E: F is at position 5 and E is at position 3. The people between E and F are G. There is only one person (G) between F and E.
B) One. As determined in the step-by-step explanation, there is only one person (G) sitting between F and E.
The question asks to identify the option that contains only biodegradable substances. Biodegradable substances are those that can be broken down naturally by microorganisms (like bacteria and fungi) into simpler, harmless components over time. Non-biodegradable substances, on the other hand, cannot be broken down naturally or take a very long time to do so.
A) Eggshells, Tea leaves, Potato peelings — All these items are organic and can be decomposed by microorganisms, making them biodegradable.
The problem provides a ratio between two variables, \(x\) and \(y\), and asks for the ratio of two expressions involving \(x\) and \(y\). We can express \(x\) and \(y\) in terms of a common constant from the given ratio and then substitute these expressions into the required ratio.
We are given that \(x : y = 7 : 3\). This can be written as a fraction:
\[ \frac{x}{y} = \frac{7}{3} \]From the ratio, we can assume that \(x\) and \(y\) are multiples of 7 and 3, respectively, by some common constant \(k\). So, let:
\[ x = 7k \]\[ y = 3k \]First, calculate \((x - y)\):
\[ x - y = 7k - 3k = 4k \]Next, calculate \((x + y)\):
\[ x + y = 7k + 3k = 10k \]Now, substitute these results back into the required ratio \((x - y) : (x + y)\):
\[ (x - y) : (x + y) = 4k : 10k \]Divide both parts of the ratio by the common term \(k\) (assuming \(k \neq 0\)):
\[ 4k : 10k = 4 : 10 \]Further simplify the ratio by dividing by the greatest common divisor of 4 and 10, which is 2:
\[ 4 : 10 = \frac{4}{2} : \frac{10}{2} = 2 : 5 \]Thus, \((x - y) : (x + y) = 2 : 5\).
C) 2 : 5