The question asks for the definition of resistance in the context of electrical properties of a material. We need to recall the fundamental concept of electrical resistance.
Correct Option: B) opposes the flow of current
The question asks for a specific date related to the eligibility criteria for citizenship under the Citizenship Amendment Act (CAA) of 2019. To answer this, one needs to recall the key provisions of the CAA, particularly the cut-off date for entry into India for the specified communities from the mentioned countries.
A) 31 December 2014 — This is the correct cut-off date as stipulated by the Citizenship Amendment Act of 2019 for individuals belonging to the specified communities from Pakistan, Afghanistan, or Bangladesh to be eligible for Indian citizenship.
To find the original number, we can set up an algebraic equation. If a number is increased by 50%, it means the new number is 100% of the original number plus 50% of the original number, which totals 150% of the original number. We can then solve for the original number.
Let the unknown number be \(x\).
When the number is increased by 50%, it means we are adding 50% of \(x\) to \(x\). Mathematically, this can be written as:
\[ x + 50\% \text{ of } x \]Convert the percentage to a decimal or fraction:
\[ 50\% = \frac{50}{100} = 0.5 \]Substitute this into the expression:
\[ x + 0.5x \]Combine the terms:
\[ 1x + 0.5x = 1.5x \]According to the problem, this increased number is 2910. So, we set up the equation:
\[ 1.5x = 2910 \]To find \(x\), divide both sides by 1.5:
\[ x = \frac{2910}{1.5} \]Perform the division:
\[ x = \frac{2910}{\frac{3}{2}} = 2910 \times \frac{2}{3} \]Calculate the value:
\[ x = \frac{5820}{3} = 1940 \]Thus, the original number is 1940.
Correct Option: B) 1940
To expand the given expression \((4a + 6b + 9c)^2\), we will use the algebraic identity for the square of a trinomial: \((x + y + z)^2 = x^2 + y^2 + z^2 + 2xy + 2yz + 2zx\).
In our expression \((4a + 6b + 9c)^2\), we can identify:
Substitute these values into the identity \((x + y + z)^2 = x^2 + y^2 + z^2 + 2xy + 2yz + 2zx\):
\[ (4a + 6b + 9c)^2 = (4a)^2 + (6b)^2 + (9c)^2 + 2(4a)(6b) + 2(6b)(9c) + 2(9c)(4a) \]Add all the calculated terms together:
\[ (4a + 6b + 9c)^2 = 16a^2 + 36b^2 + 81c^2 + 48ab + 108bc + 72ac \]Correct Option: D) \(16a^2 + 36b^2 + 81c^2 + 48ab + 108bc + 72ac\)
A cylindrical rod has an outer curved surface area of 4500 cm². If the length of the rod is 39 cm, then the outer radius (in cm) of the rod, correct to two places of decimal, is:
(Take π =\( \frac{22}{7} \))
The problem asks us to find the outer radius of a cylindrical rod given its outer curved surface area and length. We will use the formula for the curved surface area of a cylinder and substitute the given values to solve for the radius.
The curved surface area of a cylinder is given by:
\[ A = 2 \pi r h \]where \(r\) is the radius and \(h\) is the height (or length) of the cylinder.Rearrange the equation to isolate \(r\):
\[ r = \frac{4500 \times 7}{2 \times 22 \times 39} \]\[ r = \frac{31500}{1716} \]Rounding \(18.35664\) to two decimal places gives \(18.36\).
Thus, the outer radius of the rod is approximately \(18.36 \text{ cm}\).
A) 18.36 — This matches our calculated value after rounding to two decimal places.
The question asks why a compass needle deflects when brought near a bar magnet. This phenomenon is a fundamental concept in magnetism, involving the interaction between two magnetic fields.
C) The compass needle is a small bar magnet. This is the correct reason. A compass needle is a small, freely pivoting magnet that interacts with external magnetic fields, causing it to align with those fields, hence deflecting.
To determine why covalent molecules have low melting and boiling points, we need to understand the nature of forces present within and between molecules. Melting and boiling involve overcoming intermolecular forces, not intramolecular bonds.
Correct Option: B) they have weak intermolecular forces
Covalent molecules have low melting and boiling points because the energy required to overcome the weak intermolecular forces between individual molecules is relatively low. The covalent bonds within the molecules are strong, but these bonds are not broken during melting or boiling.
The question asks about the location where Swachh Vayu Diwas was celebrated in India in 2024 to combat air pollution. This requires knowledge of recent environmental initiatives and events in India.
B) Jaipur: The national celebration of Swachh Vayu Diwas (International Day of Clean Air for blue skies) in 2024 was held in Jaipur, Rajasthan. This event is organized by the Ministry of Environment, Forest and Climate Change (MoEFCC) to raise awareness and promote actions for clean air.
The question asks about the six accounts involved in the economic classification of the budget. This is a specific framework used in public finance to categorize government transactions. We need to identify the correct set of accounts and the nature of transactions they cover.
Correct Option: B) Accounts I to VI: Transaction in commodities, revenue, and capital. This option accurately describes the six accounts and the broad categories of transactions they encompass within the economic classification of the budget.
This is a logical reasoning problem involving the ranking of marks of five people (B, C, D, F, H). We need to deduce the relative order of their scores based on the given clues and then determine how many people scored less than C.
This means the arrangement could be D _ B or B _ D. There is one person in between them.
Since there are a total of five people, this clue is crucial. If there are three people between H and B, it implies H and B are at the extreme ends of the ranking. For example, H _ _ _ B or B _ _ _ H. This means H and B are the 1st and 5th (or 5th and 1st) highest scorers.
If B is at one end (say, 5th position), and there's one person between B and D, then D must be in the 3rd position (B _ D). This contradicts the fact that there are 3 people between H and B, as it would mean H is 1st, then 3 people, then B is 5th. Let's list the positions from highest to lowest (1st to 5th).
Case 1: B is the highest scorer (1st position).
Case 2: H is the highest scorer (1st position).
This means F and B are adjacent, and F is immediately higher than B. So, F B is a block.
Let's re-evaluate the cases from step 3:
If B is 1st (Case 1: B _ _ _ H), then F cannot be immediately higher than B. So, Case 1 is invalid.
Therefore, H must be the highest scorer, and B must be the lowest scorer (5th position).
So, the arrangement is H _ _ _ B.
From clue 1, "Only one person has scored between B and D." Since B is 5th, D must be 3rd. So, the arrangement becomes H _ D _ B.
From clue 3, "No one has scored between F and B and F's score is more than B's score." This means F is immediately before B. So, F is 4th. The arrangement becomes H _ D F B.
The people are B, C, D, F, H. The remaining person is C. The vacant position is 2nd. So, C must be in the 2nd position.
The final arrangement from highest to lowest is: H C D F B.
Looking at the final arrangement H C D F B, the people who scored less than C are D, F, and B. There are three people.