The correct relation between refractive index (μ), speed of light in air (c), and speed of light in the medium (v) is:
c = \(\frac{\mu}{v}\)
v = \(\frac{\mu}{c}\)
\(\frac{1}{\mu}\) = \(\frac{c}{v}\)
μ = \(\frac{c}{v}\)
This question asks for the correct relationship between the refractive index of a medium, the speed of light in air (or vacuum), and the speed of light in that medium. This is a fundamental definition in optics.
Correct Option: D) \(\mu = \frac{c}{v}\)
This option correctly represents the definition of the refractive index, which is the ratio of the speed of light in air (or vacuum) to the speed of light in the given medium.
The question asks about the forces acting on the arms of an electric motor's armature that are perpendicular to the magnetic field. This involves understanding the principle of the electric motor and Fleming's Left-Hand Rule.
C) equal in magnitude and opposite in direction. As explained above, the forces on the two active arms of the armature are equal in magnitude because they carry the same current, have the same length, and are in the same magnetic field. They are opposite in direction due to the opposite direction of current flow in the arms, which is essential for producing a rotational torque.
The Fundamental Duties in the Indian Constitution were added by which amendment to the Constitution?
The question asks about the specific constitutional amendment that added Fundamental Duties to the Indian Constitution. To answer this, one needs to recall the major amendments and their provisions, particularly those related to fundamental rights and duties.
Correct Option: A) The 42nd Amendment Act of 1976 added the Fundamental Duties (Part IV-A, Article 51-A) to the Indian Constitution. This amendment is often referred to as the 'Mini Constitution' due to its extensive changes.
To solve this problem, we need to track Suresh's movements step-by-step, noting his displacement in the East-West and North-South directions. We can represent East as positive X, West as negative X, North as positive Y, and South as negative Y. Finally, we calculate the net displacement from Point A to Point B and then determine the path from Point B back to Point A.
Therefore, to reach Point A from Point B, he should drive 7 km towards the South.
Correct Option: A) 7 km towards the south
The question asks to identify the incorrect statement about the Rann of Kutch. We need to evaluate each option based on geographical and ecological facts about the Rann of Kutch.
Correct Option: C) It is located in the Eastern Ghat in Odisha state.
Which of the following Acts of Constitution seeks to provide a common framework for the structure and mandate of urban local bodies to enable them to function as effective democratic units of Local Self Government?
10th Amendment Act, 1966
74th Amendment Act, 1992
4th Amendment Act, 1956
70th Amendment Act, 1990
The question asks to identify the Constitutional Amendment Act that provides a common framework for urban local bodies, enabling them to function as effective democratic units of Local Self Government. This points directly to the amendments related to urban municipalities.
B) 74th Amendment Act, 1992: This Act gave constitutional status to urban local bodies (municipalities). It added Part IXA (The Municipalities) and the Twelfth Schedule to the Constitution, providing a common framework for the structure, composition, powers, and functions of urban local bodies, thereby enabling them to function as effective democratic units of local self-government.
The problem asks us to find a set of three numbers that follows the same logical relationship as the given sets: (32, 166, 19) and (49, 230, 17). We need to identify the pattern connecting the three numbers in each given set and then apply that pattern to the options.
Let the numbers be \(A\), \(B\), and \(C\). So, \(A = 32\), \(B = 166\), \(C = 19\).
Let's try to find a relationship between \(A\), \(C\), and \(B\). A common pattern in such problems involves multiplication and addition/subtraction.
Consider the operation \((A - C) \times X + Y = B\).
Let's try \((A - C)\): \(32 - 19 = 13\).
Now, how can we get 166 from 13? We can try multiplying 13 by some number and adding/subtracting another.
If we multiply 13 by 10, we get 130. \(166 - 130 = 36\). This doesn't seem straightforward.
Let's try multiplying 13 by 12: \(13 \times 12 = 156\). Then \(156 + 10 = 166\).
So, the pattern could be \((A - C) \times 12 + 10 = B\).
Here, \(A = 49\), \(B = 230\), \(C = 17\).
Using the derived pattern: \((A - C) \times 12 + 10\)
\[ (49 - 17) \times 12 + 10 \] \[ 32 \times 12 + 10 \] \[ 384 + 10 \] \[ 394 \]This does not match \(B = 230\). So, the pattern \((A - C) \times 12 + 10 = B\) is incorrect.
Let's try a different approach. What if we use \(A\) and \(C\) directly?
Consider \(A \times X + C \times Y = B\).
Let's try multiplying the first number by a constant and the third number by a constant and adding them.
If we try \(A \times 4 + C \times 2\):
\[ 32 \times 4 + 19 \times 2 \] \[ 128 + 38 \] \[ 166 \]This matches \(B = 166\)! So, the pattern is \(A \times 4 + C \times 2 = B\).
Here, \(A = 49\), \(B = 230\), \(C = 17\).
Using the pattern: \(A \times 4 + C \times 2\)
\[ 49 \times 4 + 17 \times 2 \] \[ 196 + 34 \] \[ 230 \]This matches \(B = 230\)! So, the pattern is confirmed: (First number \(\times\) 4) + (Third number \(\times\) 2) = Second number.
A) (36, 186, 21) \[ 36 \times 4 + 21 \times 2 \] \[ 144 + 42 \] \[ 186 \]
This matches the second number, 186. So, option A is the correct answer.
Correct Option: A) (36, 186, 21)
Applying the pattern: \(37 \times 4 + 21 \times 2 = 148 + 42 = 190\). This is not equal to 186.
Applying the pattern: \(36 \times 4 + 20 \times 2 = 144 + 40 = 184\). This is not equal to 186.
Applying the pattern: \(36 \times 4 + 21 \times 2 = 144 + 42 = 186\). This is not equal to 187.
This question asks about the fundamental differences in how two common protozoa, Amoeba and Paramecium, ingest food. Understanding their cellular structures and feeding mechanisms is key to answering this question.
Correct Option: A) Amoeba can take up food from entire cell surface. Paramecium only through specific spot.
The question asks for the alternative name for the Indian Councils Act of 1909. This requires knowledge of key historical acts and movements during British rule in India.
Correct Option: A) Morley–Minto Reforms
The Indian Councils Act of 1909 is famously known as the Morley–Minto Reforms. This act introduced a limited measure of self-governance to India by expanding the legislative councils and allowing for the election of Indians to these councils, though the British retained ultimate control. It also introduced separate electorates for Muslims, which was a significant and controversial provision.
A, B, C, D, E, F, G, and H live on eight different floors of the same building. The lowermost floor in the building is numbered 1, the floor above it, number 2 and so on till the topmost floor is numbered 8.
D lives on an even numbered floor but does not live on floor number 4 or 2. Only five persons live between D and A. C lives immediately above A. H lives on floor number 1. Only B lives between the floors of F and D. E does not live on an even numbered floor. How many people live above F’s floor?
This is a logical reasoning problem involving arrangement. We need to deduce the floor on which each person lives based on the given clues. We will create a table for the floors and fill in the residents step-by-step.
Floors: There are 8 floors, numbered 1 to 8.
Floor 8: Floor 7: Floor 6: Floor 5: Floor 4: Floor 3: Floor 2: Floor 1:
Clue 1: H lives on floor number 1.
Floor 8: Floor 7: Floor 6: Floor 5: Floor 4: Floor 3: Floor 2: Floor 1: H
Clue 2: D lives on an even numbered floor but does not live on floor number 4 or 2.
Possible floors for D: 6 or 8.
Clue 3: Only five persons live between D and A.
If D is on floor 6, then A would be on floor \(6 - 5 - 1 = 0\), which is not possible. So, D must be on floor 8.
If D is on floor 8, then A is on floor \(8 - 5 - 1 = 2\).
Floor 8: D Floor 7: Floor 6: Floor 5: Floor 4: Floor 3: Floor 2: A Floor 1: H
Clue 4: C lives immediately above A.
Since A is on floor 2, C must be on floor 3.
Floor 8: D Floor 7: Floor 6: Floor 5: Floor 4: Floor 3: C Floor 2: A Floor 1: H
Clue 5: Only B lives between the floors of F and D.
D is on floor 8. This means B must be on floor 7, and F must be on floor 6.
Floor 8: D Floor 7: B Floor 6: F Floor 5: Floor 4: Floor 3: C Floor 2: A Floor 1: H
Clue 6: E does not live on an even numbered floor.
The remaining empty floors are 4 and 5. E cannot live on an even floor (4), so E must live on floor 5. The last remaining person, G, must live on floor 4.
Floor 8: D Floor 7: B Floor 6: F Floor 5: E Floor 4: G Floor 3: C Floor 2: A Floor 1: H
Final Question: How many people live above F's floor?
F lives on floor 6. The people living above F are on floors 7 and 8. These are B and D. So, 2 people live above F's floor.
C) 2