Four letter-cluster pairs are given, and three of them follow the same alphabetical pattern. We need to convert letters to their positions (A = 1, ..., Z = 26, counting cyclically after Z) and compare the shifts within each cluster and between the two clusters of each pair.
Identify the given information:
Check the shift within each cluster:
In every cluster the second letter is 4 places after the first: V→Z, T→X, G→K, Z→D (cyclic), C→G, V→Z, W→A (cyclic) and P→T. So, this feature is common to all pairs.
Check the shift from the first cluster to the second cluster:
\[ \text{VZ-TX: } V(22)\to T(20) = -2 \] \[ \text{GK-ZD: } G(7)\to Z(26) = -7 \text{ (cyclic)} \] \[ \text{CG-VZ: } C(3)\to V(22) = -7 \text{ (cyclic)} \] \[ \text{WA-PT: } W(23)\to P(16) = -7 \]Identify the odd pair:
In GK-ZD, CG-VZ and WA-PT, each letter of the second cluster is 7 places before the corresponding letter of the first cluster. In VZ-TX, the shift is only 2 places backward. Therefore, VZ-TX does not belong to the group.
Correct Option: A) VZ-TX — It is the only pair in which the second cluster is 2 places (instead of 7 places) behind the first. Hence, Option A is the correct answer.
B) GK-ZD: This is incorrect because it follows the pattern: G−7 = Z and K−7 = D.
C) CG-VZ: This is incorrect because it follows the pattern: C−7 = V and G−7 = Z.
D) WA-PT: This is incorrect because it follows the pattern: W−7 = P and A−7 = T.
The problem asks us to calculate the work done when a certain amount of charge is moved across a given potential difference. We can use the fundamental definition of potential difference to solve this problem.
Therefore, the work done is 50 joules.
C) 50 joules — This is the correct calculation based on the formula \(W = V \times Q\).
The problem involves arranging seven people (A, B, C, D, E, F, G) in a row facing north based on given conditions. We will deduce the positions of each person step-by-step to determine the final arrangement and then answer the question about the number of people between D and B.
Condition 1: A sits fifth from the right end.
Let's represent the seven positions as _ _ _ _ _ _ _. If A is fifth from the right, then there are four people to A's right.
Arrangement: _ _ A _ _ _ _
Condition 2: Only two people sit between E and A.
Since there are only two positions to the left of A, E must be to the left of A with two people in between. If E were to the right of A, there would not be enough space.
Arrangement: E _ _ A _ _ _
Condition 3: C is an immediate neighbour of G and E.
This means C is between G and E. Since E is at the leftmost position, C must be to the immediate right of E, and G must be to the immediate right of C.
Arrangement: E C G A _ _ _
Condition 4: B sits to the immediate right of F.
The remaining people are D, F, and B. The remaining empty spots are the last three positions on the right: E C G A _ _ _.
The only way to place F and B such that B is immediately to the right of F is in the last two spots. So, F is in the 6th position from the left, and B is in the 7th position from the left (rightmost end).
Arrangement: E C G A _ F B
Place the remaining person:
The only person left is D, and the only empty spot is the 5th position from the left (between A and F).
Final Arrangement: E C G A D F B
Answer the question: How many people sit between D and B?
In the final arrangement (E C G A D F B), D is at the 5th position and B is at the 7th position. The person between D and B is F.
Therefore, there is one person between D and B.
D) One. As per the final arrangement E C G A D F B, only F sits between D and B.
The problem presents a series of three-letter combinations and asks to find the next combination in the series based on the English alphabetical order. We need to identify the pattern for each position (first, second, and third letter) in the combinations.
The next combination in the series is LNQ.
A) LNQ — This matches our derived pattern where each letter in the combination advances by two positions in the English alphabet compared to the corresponding letter in the previous combination.
This is a direction sense problem. We need to visualize the positions of the towns based on the given relative directions and then determine the final position of Town R with respect to Town L. It's helpful to draw a rough sketch or imagine a coordinate plane.
Let's visualize:
N
^
|
W <---L---E--->
|
v
S
Starting with L:
D
/
/
L
Now, R is to the east of D:
D --- R
/
/
L
From the diagram, it's clear that R is in the northeast direction from L.
Correct Option: B) Northeast
This question tests fundamental concepts in electromagnetism, specifically Oersted's discovery and the Lorentz force law. We need to evaluate each statement based on these principles.
This statement refers to Oersted's discovery. Hans Christian Ørsted found that an electric current creates a magnetic field around it. This means that a conductor carrying current behaves like a magnet, capable of deflecting a compass needle or interacting with other magnetic fields. This is the basis of electromagnets.
Therefore, Statement I is correct.
This statement relates to the Lorentz force. The force (\(F\)) experienced by a charged particle (like an electron with charge \(q\)) moving with velocity (\(v\)) in a magnetic field (\(B\)) is given by the Lorentz force formula:
\[ F = q(\vec{v} \times \vec{B}) \]The magnitude of this force is \(F = qvB \sin\theta\), where \(\theta\) is the angle between the velocity vector (\(\vec{v}\)) and the magnetic field vector (\(\vec{B}\)).
If the electrons move perpendicular to the magnetic field, then \(\theta = 90^\circ\). In this case, \(\sin 90^\circ = 1\).
So, the force experienced would be:
\[ F = qvB \]Since \(q\), \(v\), and \(B\) are non-zero (for moving electrons in a magnetic field), the force \(F\) will also be non-zero. The electrons will experience the maximum possible force when moving perpendicular to the magnetic field.
Therefore, Statement II is incorrect.
Correct Option: A) Statement I only is correct because a current-carrying conductor produces a magnetic field, making it act like a magnet, while moving electrons perpendicular to a magnetic field experience the maximum force, not no force.
This problem involves calculating the total age of a family at different points in time and then using the average age information to find the age of a new member. We will first calculate the total age of the family three years ago, then determine their total age today if no new member was born, and finally use the given average age today to find the total age of the family including the new member. The difference will give us the boy's age.
Calculate the total age of the family three years ago:
Given that three years ago, the average age of 6 members was 19 years.
Calculate the total age of the original 6 members today:
Each of the 6 members would have aged by 3 years.
Calculate the total age of the family today with the new member:
A boy has been born, so the number of members is now \(6 + 1 = 7\).
The average age of the family today is the same as it was three years ago, which is 19 years.
Calculate the age of the boy:
The difference between the total age of the family today (with the boy) and the total age of the original 6 members today (without the boy) will be the boy's age.
D) 1 year — As calculated, the age of the boy is 1 year.
The question asks to identify the correct physical concept that describes an object's resistance to a change in its state of motion. We need to evaluate each option based on its definition.
Correct Option: B) Object's resistance to change its state of motion—Inertia
Inertia is the inherent property of an object to resist any change in its state of motion (either at rest or in uniform motion). The more mass an object has, the greater its inertia, and thus the more difficult it is to change its state of motion.
The question gives the pairs X : 961 and 34 : Y, where both pairs follow the same rule, and asks for the values of X and Y. We need to recognise 961 as a perfect square, find how its root is related to X, and apply the same rule to 34.
Identify the given information:
Express 961 as a square:
\[ 961=31^2 \]Test X = 41:
\[ (41-10)^2=31^2=961 \]So, the rule is: second number = (first number − 10)².
Apply the rule to 34:
\[ Y=(34-10)^2 \] \[ =24^2=576 \]This matches Y = 576.
Correct Option: B) X = 41, Y = 576 — The rule is second number = (first number − 10)², giving 41 → 31² = 961 and 34 → 24² = 576. Hence, Option B is the correct answer.
A) X = 39, Y = 529: This is incorrect because (39 − 10)² = 841, not 961, and 529 = 23² does not equal (34 − 10)².
C) X = 45, Y = 625: This is incorrect because 45 is 14 more than 31 while 34 is 9 more than 25, so no common rule links the pairs.
D) X = 47, Y = 729: This is incorrect because 47 is 16 more than 31 while 729 = 27², which is only 7 less than 34, so no common rule links the pairs.
The question asks to identify the INCORRECT statement regarding Rutherford's model of an atom. We need to recall the key postulates and findings from Rutherford's alpha-particle scattering experiment and his atomic model.
Therefore, the statement that electrons revolve in elliptical paths is incorrect according to Rutherford's model.
Correct Option: C) Electrons revolve around the nucleus in elliptical paths.