The question asks about the essential property for a material to be used as a filament in an electric bulb. The primary function of a bulb's filament is to heat up and glow when current passes through it. We need to consider the electrical and thermal properties that enable this function efficiently and safely.
D) High resistivity
A material with high resistivity will offer significant resistance to the flow of electric current. According to Joule's law of heating (\(H = I^2 R t\)), this high resistance leads to a large amount of heat generation. This heat causes the filament to become incandescent and emit light. Tungsten, commonly used for filaments, has high resistivity and a very high melting point, allowing it to glow brightly without melting.
All 28 students of a class are standing in a straight row facing north. Jay is 14th from the right end, while Bela is 12th from the left end. How many students stand between Jay and Bela?
To find the number of students between Jay and Bela, we first need to determine their positions from a common reference point (e.g., the left end). We are given Jay's position from the right end and Bela's position from the left end. We will convert Jay's position to be from the left end and then calculate the number of students between them.
To find Jay's position from the left end, we use the formula:
\[ \text{Position from Left End} = \text{Total Students} - \text{Position from Right End} + 1 \]\[ \text{Jay's Position from Left End} = 28 - 14 + 1 = 15 \]Now we have Bela at the 12th position from the left and Jay at the 15th position from the left. Since both are facing North, their relative positions are straightforward.
The number of students between them is the absolute difference of their positions minus 1 (because we are counting students *between* them, not including them).
\[ \text{Students between} = \text{Jay's Position} - \text{Bela's Position} - 1 \]\[ \text{Students between} = 15 - 12 - 1 = 3 - 1 = 2 \]Therefore, there are 2 students standing between Jay and Bela.
A) 2 — As calculated, Jay is 15th from the left and Bela is 12th from the left. The students are at positions 12 (Bela), 13, 14, 15 (Jay). The students between them are at positions 13 and 14, which are 2 students.
The question asks to identify the Indian wrestler who won a bronze medal at the U23 Asian Wrestling Championships in 2022. This requires knowledge of recent sports achievements, specifically in wrestling.
Deepak Punia won a bronze medal in the 86kg category at the U23 Asian Wrestling Championships held in Bishkek, Kyrgyzstan, in 2022.
D) Deepak Punia — Deepak Punia secured a bronze medal in the 86kg freestyle category at the U23 Asian Wrestling Championships in 2022.
The question asks to identify the type of chemical reaction given the balanced equation: \(\text{Na}_2\text{SO}_4\text{(aq)} + \text{BaCl}_2\text{(aq)} \rightarrow \text{BaSO}_4\text{(s)} + 2\text{NaCl(aq)}\). We need to analyze the reactants and products, particularly their states, to classify the reaction.
D) precipitation reaction — The reaction \(\text{Na}_2\text{SO}_4\text{(aq)} + \text{BaCl}_2\text{(aq)} \rightarrow \text{BaSO}_4\text{(s)} + 2\text{NaCl(aq)}\) involves the formation of an insoluble solid, barium sulfate (\(\text{BaSO}_4\)), from the mixing of two aqueous solutions. This is the defining characteristic of a precipitation reaction.
This problem involves analyzing inequalities. We need to determine which of the given conclusions logically follows from the provided statement: \(A > S \geq D > F \leq G < H\). We will examine each option by tracing the relationship between the variables in the given statement.
A) \(S > F\) — As derived in step 3, from \(S \geq D\) and \(D > F\), we can logically conclude that \(S > F\).
To simplify the given algebraic expression, we will use substitution to make the expression easier to handle. We will substitute a variable for the common term \(x^2 + y^2\) and then factor the resulting quadratic-like expression. Finally, we will substitute back the original terms to get the simplified form.
Let the given expression be
\[ E = 2(x^2 + y^2)^2 - 3xy(x^2 + y^2) - 2x^2y^2 \]To simplify this, let's use a substitution. Let \(A = x^2 + y^2\) and \(B = xy\).
Substitute \(A\) and \(B\) into the expression:
\[ E = 2A^2 - 3AB - 2B^2 \]This is a quadratic expression in terms of \(A\) and \(B\).
Factor the quadratic expression \(2A^2 - 3AB - 2B^2\). We look for two numbers that multiply to \(2 \times (-2) = -4\) and add to \(-3\). These numbers are \(-4\) and \(1\).
\[ 2A^2 - 4AB + AB - 2B^2 \]Group the terms and factor by grouping:
\[ 2A(A - 2B) + B(A - 2B) \]Factor out the common term \((A - 2B)\):
\[ (A - 2B)(2A + B) \]Now, substitute back the original values for \(A\) and \(B\):
\[ A = x^2 + y^2 \]and
\[ B = xy \]Substitute these back into the factored expression:
\[ ( (x^2 + y^2) - 2(xy) ) ( 2(x^2 + y^2) + (xy) ) \]Simplify the terms:
\[ (x^2 + y^2 - 2xy)(2x^2 + 2y^2 + xy) \]Rearranging the terms in the first factor for better readability (though not strictly necessary):
\[ (x^2 - 2xy + y^2)(2x^2 + 2y^2 + xy) \]This can also be written as:
\[ (2x^2 + 2y^2 + xy)(x^2 + y^2 - 2xy) \]B) The simplified expression is \((2x^2 + 2y^2 + xy)(x^2 + y^2 - 2xy)\), which matches option B.
The question asks for the definition of a production function in economics. A production function describes the relationship between the inputs used in production and the resulting output.
Correct Option: C) output produced by the firm. The production function is a technical relationship that specifies the maximum output that can be produced from any given combination of inputs.
The question asks to identify the component in an electric motor that provides electrical contact between the commutator and the external battery terminals. We need to recall the basic construction and working principles of a DC electric motor.
Correct Option: D) carbon brushes — Carbon brushes are stationary conductors that make contact with the rotating commutator segments. They conduct current from the external power source (battery) to the armature coil through the commutator, and vice-versa. They are essential for the continuous operation of a DC motor.
The question asks to identify the type of reaction involved in the conversion of ethanol to acetic acid. We need to recall the definitions of different types of organic reactions, specifically focusing on what happens to the molecule during this transformation.
The overall reaction can be represented as:
\[ \text{CH}_3\text{CH}_2\text{OH} + \text{O}_2 \longrightarrow \text{CH}_3\text{COOH} + \text{H}_2\text{O} \]B) oxidation reaction — The conversion of ethanol to acetic acid involves the gain of oxygen and loss of hydrogen, which are characteristic features of an oxidation reaction in organic chemistry. The oxidation state of the carbon atom bonded to the functional group also increases.
The question asks for the correct explanation behind carbon's ability to form strong bonds with other elements. This property is primarily due to carbon's atomic structure, specifically its size and the resulting nuclear attraction to shared electrons.
Correct Option: B) A carbon nucleus holds the shared pairs of electrons strongly due to its small size.