url stringclasses 51
values | page_number int64 1 451 | extracted_answer_choices listlengths 1 20 | extracted_solution stringclasses 1
value | improved_question_solution stringlengths 26 9.11k | r1_distill_70b_response stringlengths 279 77.9k | __original_row_idx int64 0 5k |
|---|---|---|---|---|---|---|
https://ia801305.us.archive.org/8/items/ProblemsInCalculusOfOneVariableI.A.Maron/Problems%20in%20Calculus%20of%20One%20Variable%20-%20I.%20A.%20Maron.pdf | 205 | [
"\"I = (x³ + 1) sin x - 3I₁\"",
"\"I₁ = - x² cos x + 2I₂\"",
"\"I₂ = x sin x + cos x + C.\"",
"\"I = (x³ - 6x + 1) sin x + (3x² - 6) cos x + C.\""
] | NO ANSWER DETECTED | Let us put
u = x³ + 1; dv = cos x dx,
whence
du = 3x² dx; v = sin x.
I = (x³ + 1) sin x - 3 ∫ x² sin x dx = (x³ + 1) sin x - 3I₁,
where I₁ = ∫ x² sin x dx.
Integrating by parts again, we get
I₁ = - x² cos x + 2I₂,
where I₂ = ∫ x cos x dx.
Integrating by parts again, we obtain
I₂ = x sin x + cos x + ... | <think>
Okay, so I need to solve the integral I = ∫ (x³ + 1) cos x dx using integration by parts. Hmm, I remember that integration by parts is based on the formula ∫ u dv = uv - ∫ v du. So I need to choose which part of the integrand to set as u and which as dv.
Looking at the integrand (x³ + 1) cos x, I can either ch... | 1 |
https://ia801305.us.archive.org/8/items/ProblemsInCalculusOfOneVariableI.A.Maron/Problems%20in%20Calculus%20of%20One%20Variable%20-%20I.%20A.%20Maron.pdf | 262 | [
"\"free response\""
] | NO ANSWER DETECTED | If \( m(b - a) \leq \int f(x) dx \leq M(b - a) \), where \( m \) is the least value and \( M \) the greatest value of the function \( f(x) \) on the interval \([a, b]\), then this represents an estimation of the integral of the function \( f(x) \) over the interval from \( a \) to \( b \).
What is the estimation of t... | <think>
Okay, so I have this problem about estimating the integral of a function \( f(x) \) over an interval \([a, b]\). The statement given is that \( m(b - a) \leq \int f(x) dx \leq M(b - a) \), where \( m \) is the minimum value and \( M \) is the maximum value of \( f(x) \) on that interval. The question is asking ... | 8 |
https://jeeadv.ac.in/past_qps/2013_1.pdf | 3 | [
"(A) 0.3 × 10^-17 kg ms-1",
"(B) 1.0 × 10^-17 kg ms-1",
"(C) 3.0 × 10^-17 kg ms-1",
"(D) 9.0 × 10^-17 kg ms-1"
] | NO ANSWER DETECTED | A pulse of light of duration 100 ns is absorbed completely by a small object initially at rest. Power of the pulse is 30 mW and the speed of light is 3 × 10^8 ms-1. The final momentum of the object is:
(A) 0.3 × 10^-17 kg ms-1
(B) 1.0 × 10^-17 kg ms-1
(C) 3.0 × 10^-17 kg ms-1
(D) 9.0 × 10^-17 kg ms-1
What is ... | <think>
Okay, so I've got this physics problem here, and I need to figure out the final momentum of a small object after it completely absorbs a pulse of light. The pulse has a duration of 100 nanoseconds (ns), a power of 30 milliwatts (mW), and the speed of light is given as 3 × 10^8 meters per second (ms⁻¹). The opti... | 6 |
https://www.asi.edu.au/wp-content/uploads/2022/12/2017-asoe-chemistry-exam.pdf | 6 | [
"\"A: 1 mol\"",
"\"B: 2 mol\"",
"\"C: 4 mol\"",
"\"D: 8 mol\"",
"\"E: 16 mol\""
] | NO ANSWER DETECTED | Aqueous Fe2+ ions are readily oxidised to Fe3+ ions by oxygen gas in acidic solutions. Consider the following relevant reduction half equations:
Fe3+(aq) + e¯ → Fe2+(aq)
4H+(aq) + O2(g) + 4e¯ → 2H2O(l)
What chemical amount (in mol) of H2O would be produced from the reaction of 2 mol of Fe2+ with excess oxygen un... | <think>
Okay, so I have this chemistry problem here. It's about the oxidation of Fe²+ ions to Fe³+ ions using oxygen gas in an acidic solution. I need to find out how many moles of H2O are produced when 2 moles of Fe²+ react with excess oxygen. The options are from (a) 1 mol up to (e) 16 mol. Hmm, let's break this down... | 12 |
https://jeeadv.ac.in/past_qps/2017_1.pdf | 31 | [
"[A] (I) (iii) (P)",
"[B] (II) (iv) (Q)",
"[C] (III) (i) (R)",
"[D] (II) (iii) (P)"
] | NO ANSWER DETECTED | Here's the text extraction from the PDF, including the text within images:
**Page 1:**
* <bold>Answer Q.52, Q.53 and Q.54 by appropriately matching the information given in the three</bold>
<bold>columns of the following table.</bold>
* Let f (x) = x + loge x - x loge x, x ∈ (0,∞).
* • Column 1 contains inf... | <think>
Alright, let's tackle Q.54 step by step. So, the question is asking which combination is the only incorrect one. The options are A, B, C, and D, each pairing different statements from Columns 1, 2, and 3.
First, let me recall what each column represents:
- **Column 1** has statements about the zeros of f(x), ... | 15 |
https://ia801305.us.archive.org/8/items/ProblemsInCalculusOfOneVariableI.A.Maron/Problems%20in%20Calculus%20of%20One%20Variable%20-%20I.%20A.%20Maron.pdf | 238 | [
"NO CHOICES AVAILABLE"
] | NO ANSWER DETECTED | To evaluate the integral of the form I, we have:
I = ∫ dx / √(5 + 2x + x²).
We can rewrite the expression under the square root as follows: 5 + 2x + x² = 4 + (x + 1)².
Thus, we can substitute x + 1 = t, transforming the integral:
I = ∫ dt / √(4 + t²).
This leads to the substitution of t = 2 tan z.
What is the i... | <think>
Okay, so I have this integral I need to solve: I = ∫ dx / √(5 + 2x + x²). Hmm, it looks like a standard integral, but I'm not exactly sure how to approach it. Let me think.
First, I remember that when integrating expressions with square roots of quadratics, completing the square might be helpful. So maybe I s... | 0 |
https://ia801305.us.archive.org/8/items/ProblemsInCalculusOfOneVariableI.A.Maron/Problems%20in%20Calculus%20of%20One%20Variable%20-%20I.%20A.%20Maron.pdf | 342 | [
"NO CHOICES AVAILABLE"
] | NO ANSWER DETECTED | It is obvious that the abscissa of the point M equals 2a (the value of x at φ= 0), the abscissa of the point K being the minimum of the function x = a (1 + cos φ) cos φ. Let us find this minimum: dx = – a sin φ (1 + 2 cos φ) = 0, dφ φ₁ = 0; φ₂ = 2/3 π. At φ₁ = 0 we obtain xM = 2a, at φ₂ = 2/3 π, xK = –a/4. Find the min... | <think>
Okay, so I need to find the minimum value of the function \( x = a(1 + \cos \phi) \cos \phi \). Alright, let me think about how to approach this. I remember that to find the minimum or maximum of a function, we usually take its derivative and set it equal to zero. Then, we solve for the variable, which in this ... | 7 |
https://www.asi.edu.au/wp-content/uploads/2022/12/2014-asoe-chemistry-exam.pdf | 5 | [
"\"A: CO2\"",
"\"B: H2O2\"",
"\"C: H2S\"",
"\"D: NaCl\"",
"\"E: SO2\""
] | NO ANSWER DETECTED | A small spacecraft of capacity 10 m³ is connected to another of capacity 30 m³. Prior to connection, the pressure inside the smaller craft is 50 kPa and that inside the larger is 100 kPa. If all measurements are made at the same temperature, what is the pressure in the combined arrangement after connection?
Which one... | <think>
Okay, so I have two problems here. The first one is about connecting two spacecraft, and the second one is about identifying a substance with linear molecules under certain conditions. I'll tackle them one by one.
Starting with the spacecraft problem: There's a small spacecraft with a capacity of 10 m³ connect... | 2 |
https://ia801305.us.archive.org/8/items/ProblemsInCalculusOfOneVariableI.A.Maron/Problems%20in%20Calculus%20of%20One%20Variable%20-%20I.%20A.%20Maron.pdf | 159 | [
"\"free response\""
] | NO ANSWER DETECTED | As a result of n measurements of an unknown quantity x the numbers x₁, x₂, . . . , xₙ are obtained. It is required to find at what value of x the sum of the squares of the errors
f (x) = (x-x₁)² + (x - x₂)² +...+(x-xₙ)²
will be the least.
At what value of x will the sum of the squares of the errors be the least? | <think>
Alright, so I need to figure out at what value of x the sum of the squares of the errors is the least. The function given is f(x) = (x - x₁)² + (x - x₂)² + ... + (x - xₙ)². Hmm, okay, so this looks like a problem where I have to find the minimum of this function.
First, since this is a sum of squares, I remem... | 22 |
https://jeeadv.ac.in/past_qps/2019_2_English.pdf | 7 | [
"NO CHOICES AVAILABLE"
] | NO ANSWER DETECTED | A ball is thrown from ground at an angle Θ with horizontal and with an initial speed uo. For the resulting projectile motion, the magnitude of average velocity of the ball up to the point when it hits the ground for the first time is V₁. After hitting the ground, the ball rebounds at the same angle Θ but with a reduced... | <think>
Alright, let me see. So there's this problem about projectile motion. A ball is thrown upwards at an angle Θ with an initial speed u₀. It hits the ground, then rebounds with the same angle but a reduced speed u₀/α. I need to find α such that the average velocity over the entire duration is 0.8 V₁, where V₁ is t... | 20 |
https://ia801305.us.archive.org/8/items/ProblemsInCalculusOfOneVariableI.A.Maron/Problems%20in%20Calculus%20of%20One%20Variable%20-%20I.%20A.%20Maron.pdf | 166 | [
"NO CHOICES AVAILABLE"
] | NO ANSWER DETECTED | Find the intervals in which the graphs of the following functions are concave or convex and locate the points of inflection: (h) y = 2 - |x⁵ - 1|.
This function is part of a section discussing the convexity and concavity of curves, where it's stated that if f''(x) < 0 (or > 0) on an interval (a, b), then the curve y ... | <think>
Alright, so I need to figure out where the graph of y = 2 - |x⁵ - 1| is concave or convex, and also find the points of inflection. Hmm, okay. Let's start by understanding the function.
The function is y = 2 - |x⁵ - 1|. That means it's a transformation of the absolute value function applied to x⁵ - 1, and then ... | 13 |
https://ia801305.us.archive.org/8/items/ProblemsInCalculusOfOneVariableI.A.Maron/Problems%20in%20Calculus%20of%20One%20Variable%20-%20I.%20A.%20Maron.pdf | 342 | [
"NO CHOICES AVAILABLE"
] | NO ANSWER DETECTED | The relevant text states:
```text
7.6.18. Compute the volume of the solid generated by revolving the figure bounded by the following lines:
(a) xy = 4, x=1, x = 4, y=0 about the x-axis;
(b) y=2x-x², y=0 about the x-axis;
```
Compute the volume of the solid generated by revolving the figure bounded by the following lin... | <think>
Alright, so I have two calculus problems here where I need to compute the volume of solids of revolution. Let's take them one at a time, starting with part (a).
Problem (a) is bounded by the curves xy = 4, x=1, x=4, and y=0, revolved around the x-axis. Hmm, okay. So, let's visualize this region. The curve xy =... | 21 |
https://ia801305.us.archive.org/8/items/ProblemsInCalculusOfOneVariableI.A.Maron/Problems%20in%20Calculus%20of%20One%20Variable%20-%20I.%20A.%20Maron.pdf | 49 | [
"NO CHOICES AVAILABLE"
] | NO ANSWER DETECTED | Find lim x, if x = n(-1)^n / (1 - 2n) n² + 1. | <think>
Okay, so I need to find the limit of x as n approaches something. Wait, actually, looking at the problem again, it says "Find lim x, if x = n(-1)^n / (1 - 2n) n² + 1." Hmm, this might be a bit confusing. Is it x as n approaches infinity? I think so, because usually, limits like this are about n approaching infi... | 31 |
https://www.asi.edu.au/wp-content/uploads/2022/12/2012-asoe-chemistry-exam.pdf | 5 | [
"\"4.53\"",
"\"5.53\"",
"\"7.00\"",
"\"8.47\"",
"\"9.47\""
] | NO ANSWER DETECTED | A certain buffer solution contains equal concentration of weak acid (HX) and its conjugate base (X¯). Ka for HX is 2.9 × 10¯5. What is the pH of the buffer?
a. 4.53
b. 5.53
c. 7.00
d. 8.47
e. 9.47 | <think>
Okay, so I have this buffer solution problem here, and I need to figure out the pH. Let me see. The problem says it's a buffer with equal concentrations of a weak acid, HX, and its conjugate base, X⁻. The Ka for HX is 2.9 × 10⁻⁵. The options are a through e, with pH values ranging from around 4.5 to 9.5. Hmm, b... | 3 |
https://www.asi.edu.au/wp-content/uploads/2022/12/2014-asoe-chemistry-exam.pdf | 5 | [
"\"A: 0.8%\"",
"\"B: 8.0%\"",
"\"C: 20%\"",
"\"D: 80%\"",
"\"E: 92%\""
] | NO ANSWER DETECTED | The relative atomic mass of boron, which consists of the isotopes 10B and 11B is 10.8. What is the percentage of 11B atoms in the isotopic mixture?
(a) 0.8% (b) 8.0% (c) 20% (d) 80% (e) 92% | <think>
Okay, so I have this problem here about the relative atomic mass of boron, which is made up of two isotopes: 10B and 11B. The relative atomic mass is given as 10.8, and I need to find the percentage of 11B atoms in the mixture. The options are (a) 0.8%, (b) 8.0%, (c) 20%, (d) 80%, and (e) 92%. Hmm, alright.
Fi... | 24 |
https://ia801305.us.archive.org/8/items/ProblemsInCalculusOfOneVariableI.A.Maron/Problems%20in%20Calculus%20of%20One%20Variable%20-%20I.%20A.%20Maron.pdf | 49 | [
"NO CHOICES AVAILABLE"
] | NO ANSWER DETECTED | Find lim x, if x = Vn / n. | <think>
</think>
To find the limit of \( x \) as \( n \) approaches infinity, where \( x = \frac{V_n}{n} \), I need more information about \( V_n \). Could you clarify or provide the context or expression for \( V_n \)? This will help me determine how to proceed with the calculation. | 19 |
https://www.asi.edu.au/wp-content/uploads/2022/12/2012-asoe-chemistry-exam.pdf | 3 | [
"\"a. A minimum of 1.21 volts is applied to the cell and electrons move from the silver electrode to the iron electrode.\"",
"\"b. A minimum of 1.21 volts is applied to the cell and electrons move from the iron electrode to the silver electrode.\"",
"\"c. A minimum of 0.39 volts is applied to the cell and elect... | NO ANSWER DETECTED | A working galvanic cell is constructed using an iron electrode in an iron(II) nitrate solution and a silver electrode in a silver(I) nitrate solution. When the cell runs down, it can be charged up again. The standard electrode potentials are given as E°(Ag+(aq)/Ag(s) = +0.80 V and E°(Fe2+(aq)/Fe(s) = -0.41 V). Which of... | <think>
Okay, so I need to figure out what happens during the charging process of this galvanic cell. The cell uses an iron electrode in iron(II) nitrate and a silver electrode in silver(I) nitrate. I remember that when a cell is discharged, it's just operating normally as a galvanic cell, but when it's charged, it's b... | 23 |
https://jeeadv.ac.in/past_qps/2015_2.pdf | 14 | [
"\"3\""
] | NO ANSWER DETECTED | The molar conductivity of a solution of a weak acid HX (0.01 M) is 10 times smaller than the molar conductivity of a solution of a weak acid HY (0.10 M). If the degree of ionization of both acids is considered to be much less than 1, what is the difference in their pKa values, pKa (HX) - pKa (HY)? | <think>
Okay, so I have this problem about molar conductivity of weak acids, HX and HY. Let me try to figure it out step by step. Hmm, the problem says that HX is 0.01 M and its molar conductivity is 10 times smaller than HY, which is 0.10 M. Both are weak acids, so their degree of ionization is much less than 1. I nee... | 14 |
https://ia801305.us.archive.org/8/items/ProblemsInCalculusOfOneVariableI.A.Maron/Problems%20in%20Calculus%20of%20One%20Variable%20-%20I.%20A.%20Maron.pdf | 175 | [
"\"x₁= -1",
"x2=0",
"x₃ = 1\""
] | NO ANSWER DETECTED | Here's the text extraction from the provided PDF images, with formatting indicated:
**Page 1**
<bold>§ 3.11. Investigating Functions and Sketching Graphs</bold>
<highlighted>175</highlighted>
<highlighted>3. Test the function for continuity, find out the discontinuities</highlighted>
<highlighted>and their character.... | <think>
To determine the critical points of the function \( y = x^6 - 3x^4 + 3x^2 - 5 \), I'll follow these steps:
First, I need to find the derivative of the function with respect to \( x \). The derivative will help identify where the function has horizontal tangents or doesn't change direction, which are potential ... | 81 |
https://www.asi.edu.au/wp-content/uploads/2022/12/2017-asoe-chemistry-exam.pdf | 7 | [
"\"A: Covalent bonding\"",
"\"B: Hydrogen bonding\"",
"\"C: Ionic bonding\"",
"\"D: Intermolecular forces\"",
"\"E: Metallic bonding\""
] | NO ANSWER DETECTED | Solid carbon dioxide, also known as dry ice, sublimes to form gaseous carbon dioxide. What type of bonding is significantly weakened because of this phase change?
(a) Covalent bonding
(b) Hydrogen bonding
(c) Ionic bonding
(d) Intermolecular forces
(e) Metallic bonding | <think>
Okay, so I've got this question about dry ice and what happens when it sublimes. Let me try to work through this step by step.
First, I know that dry ice is solid carbon dioxide. I've seen it before; it's that stuff that looks like ice but smokes a lot because it turns straight into gas. So, when it sublimes, ... | 65 |
https://ia801305.us.archive.org/8/items/ProblemsInCalculusOfOneVariableI.A.Maron/Problems%20in%20Calculus%20of%20One%20Variable%20-%20I.%20A.%20Maron.pdf | 221 | [
"\"√ax^2 + bx + c = t + x√a\"",
"\"√ax^2 + bx + c = tx - √c\"",
"\"√ax^2 + bx + c = (x - α) t\""
] | NO ANSWER DETECTED | Integrals of the form ∫ R(x, √ax² + bx + c) dx are calculated with the aid of one of the three Euler substitutions:
(1) √ax² + bx + c = t + x√a if a > 0;
(2) √ax² + bx + c = tx - √c if c > 0;
(3) √ax² + bx + c = (x - α)t if ax² + bx + c = a(x - α)(x - β), i.e. if α is a real root of the trinomial ax² + bx + c.
... | <think>
Alright, so I need to figure out what the third Euler substitution is used for when dealing with integrals of the form ∫ R(x, √(ax² + bx + c)) dx, specifically for quadratic expressions that have a real root. Hmm, I remember Euler substitutions are techniques to simplify integrals involving square roots of quad... | 16 |
https://www.asi.edu.au/wp-content/uploads/2022/12/2009-asoe-chemistry-exam.pdf | 16 | [
"NO CHOICES AVAILABLE"
] | NO ANSWER DETECTED | To obtain a single product, sometimes “protections" are employed to “mask” certain functional groups to prevent them from taking part in a reaction. Some of these protections include converting reactive amines, alcohols, aldehydes and carboxylic acids into relatively unreactive esters, ethers and amides. These protecti... | <think>
Okay, so I'm trying to figure out the answer to the question about protections used to mask functional groups in organic chemistry. I remember that in synthesis, sometimes certain groups are too reactive, so they need to be protected to prevent them from interfering in the reaction. The user mentioned that Tabl... | 74 |
https://jeeadv.ac.in/past_qps/2012_2.pdf | 1 | [
"\"A: a²Ik\"",
"\"B: (π/2 + 1)a²Ik\"",
"\"C: - (π/2 + 1)a²Ik\"",
"\"D: (2π+1)a²Ik\""
] | NO ANSWER DETECTED | A loop carrying current I lies in the x-y plane as shown in the figure. The unit vector k is coming out of the plane of the paper. The magnetic moment of the current loop is:
(A) a²Ik
(B) (π/2 + 1)a²Ik
(C) - (π/2 + 1)a²Ik
(D) (2π+1)a²Ik
What is the magnetic moment of the current loop carrying current I that lie... | <think>
Okay, so I have this problem about finding the magnetic moment of a current loop. The loop lies in the x-y plane, and the unit vector k is coming out of the paper, which I think means it's pointing in the positive z-direction. The multiple-choice options are given, so I need to figure out which one is correct. ... | 29 |
https://ia801305.us.archive.org/8/items/ProblemsInCalculusOfOneVariableI.A.Maron/Problems%20in%20Calculus%20of%20One%20Variable%20-%20I.%20A.%20Maron.pdf | 59 | [
"\"1\""
] | NO ANSWER DETECTED | Using the sequences of the roots of the equations sin(1/x) = 1 and sin(1/x) = -1, show that the function f(x) = sin(1/x) has no limit as x approaches 0.
What is lim sin x as x approaches 0? | <think>
Alright, so I have this problem here where I need to show that the function f(x) = sin(1/x) doesn't have a limit as x approaches 0. Hmm, okay. I remember that for a function to have a limit as x approaches a certain point, it needs to approach a specific value from both sides. So if I can show that as x approac... | 61 |
https://www.asi.edu.au/wp-content/uploads/2022/12/2017-asoe-chemistry-exam.pdf | 7 | [
"NO CHOICES AVAILABLE"
] | NO ANSWER DETECTED | To determine the percentage by mass of oxygen gas in air, an excess of copper is added to a sealed 25.00 L container filled with air. This is heated and the oxygen reacts with the copper to form copper(II) oxide. Write a balanced chemical equation for this reaction. | <think>
Okay, so I need to figure out the balanced chemical equation for the reaction where copper reacts with oxygen to form copper(II) oxide. Hmm, I remember from my chemistry class that when metals react with oxygen, they form metal oxides. Copper is a metal, and oxygen is a diatomic gas, O₂. The product here is cop... | 73 |
https://ia801305.us.archive.org/8/items/ProblemsInCalculusOfOneVariableI.A.Maron/Problems%20in%20Calculus%20of%20One%20Variable%20-%20I.%20A.%20Maron.pdf | 262 | [
"\"free response\""
] | NO ANSWER DETECTED | The integrand \( f(x) = \sin x \) decreases on the interval \([ \frac{\pi}{4}, \frac{\pi}{3} ]\) since its derivative \( f'(x) = \cos x - \sin x \) is less than 0. Therefore, the least value of the function is \( f(\frac{\pi}{3}) = \frac{\sqrt{3}}{2} \) and its greatest value is \( f(\frac{\pi}{4}) = \frac{\sqrt{2}}{2}... | <think>
Okay, so I need to figure out the least and greatest values of the function \( f(x) = \sin x \) on the interval \([ \frac{\pi}{4}, \frac{\pi}{3} ]\). I remember that since the function is decreasing on an interval, its least value should be at the right endpoint and its greatest value at the left endpoint. Let ... | 10 |
https://www.asi.edu.au/wp-content/uploads/2022/12/2014-asoe-chemistry-exam.pdf | 5 | [
"\"A: 75.0 kPa\"",
"\"B: 87.5 kPa\"",
"\"C: 100 kPa\"",
"\"D: 125 kPa\"",
"\"E: 150 kPa\""
] | NO ANSWER DETECTED | A small spacecraft of capacity 10 m³ is connected to another of capacity 30 m³. Prior to connection, the pressure inside the smaller craft is 50 kPa and that inside the larger is 100 kPa. If all measurements are made at the same temperature, what is the pressure in the combined arrangement after connection?
(a) 75.0 k... | <think>
Okay, so I'm trying to figure out this problem where there are two spacecraft connected together. One has a capacity of 10 m³, and the other is bigger, 30 m³. Before they connect, the smaller one has a pressure of 50 kPa and the larger one has 100 kPa. The question is, after connecting them, what's the pressure... | 70 |
https://www.asi.edu.au/wp-content/uploads/2022/12/2014-asoe-chemistry-exam.pdf | 5 | [
"\"A: chemical reactivity\"",
"\"B: first ionisation energy\"",
"\"C: number of electrons in the outer shell\"",
"\"D: number of protons in the nucleus of its atom\"",
"\"E: relative atomic mass\""
] | NO ANSWER DETECTED | The order of elements in the Periodic Table is described in relation to various properties including chemical reactivity, first ionisation energy, number of electrons in the outer shell, number of protons in the nucleus of its atom, and relative atomic mass. Which one of the following determines the order of elements i... | <think>
Okay, so I have this question about the Periodic Table and what determines the order of elements there. Let me try to break this down step by step.
First, I remember that the Periodic Table is organized in a specific way, and the order isn't random. I think it's related to some property of the elements. The qu... | 99 |
https://ia801305.us.archive.org/8/items/ProblemsInCalculusOfOneVariableI.A.Maron/Problems%20in%20Calculus%20of%20One%20Variable%20-%20I.%20A.%20Maron.pdf | 49 | [
"NO CHOICES AVAILABLE"
] | NO ANSWER DETECTED | 1.7.4. Find lim x, if
(c) x_n = 1 - n³ + n;
Find lim x, if x = 1 - n³ + n. | <think>
Okay, so I've got this limit problem to solve. It says to find the limit of x as n approaches something, right? But wait, the problem is a bit unclear. It says "Find lim x, if x_n = 1 - n³ + n" and then again "Find lim x, if x = 1 - n³ + n." Hmm, I think maybe it's asking for the limit as n approaches infinity ... | 60 |
https://ia801305.us.archive.org/8/items/ProblemsInCalculusOfOneVariableI.A.Maron/Problems%20in%20Calculus%20of%20One%20Variable%20-%20I.%20A.%20Maron.pdf | 45 | [
"NO CHOICES AVAILABLE"
] | NO ANSWER DETECTED | Prove that the sequence with the general term Xn = 1/n^k (k > 0) is an infinitely small sequence. To prove that the sequence Xn is infinitely small is to prove that lim Xn = 0. Take an arbitrary ε > 0. Since |Xn| = 1/n^k, we have to solve the inequality 1/n^k < ε, whence n > 1/ε. Hence N may be expressed as the integra... | <think>
Okay, so I need to prove that the sequence \( X_n = \frac{1}{n^k} \) where \( k > 0 \) is an infinitely small sequence. I remember that an infinitely small sequence is one where the limit as \( n \) approaches infinity is zero. So, essentially, I need to show that \( \lim_{n \to \infty} \frac{1}{n^k} = 0 \).
H... | 18 |
https://ia801305.us.archive.org/8/items/ProblemsInCalculusOfOneVariableI.A.Maron/Problems%20in%20Calculus%20of%20One%20Variable%20-%20I.%20A.%20Maron.pdf | 120 | [
"NO CHOICES AVAILABLE"
] | NO ANSWER DETECTED | The law of rectilinear motion of a body with a mass of 100 kg is s = 2t^2 + 3t + 1. Determine the kinetic energy (mv^2/2) of the body 5 seconds after the start.
What is the kinetic energy (mv^2/2) of a body with a mass of 100 kg at 5 seconds after the start if its law of rectilinear motion is s = 2t^2 + 3t + 1? | <think>
Okay, so I need to find the kinetic energy of a body after 5 seconds. The body has a mass of 100 kg, and its motion is described by the equation s = 2t² + 3t + 1. Hmm, kinetic energy, right? I remember that kinetic energy is given by the formula KE = (1/2)mv², where m is mass and v is velocity.
Wait, so I hav... | 25 |
https://ia801305.us.archive.org/8/items/ProblemsInCalculusOfOneVariableI.A.Maron/Problems%20in%20Calculus%20of%20One%20Variable%20-%20I.%20A.%20Maron.pdf | 49 | [
"NO CHOICES AVAILABLE"
] | NO ANSWER DETECTED | lim x, if x = 1 / (3n cos(n³)/(6n + 1)).
Find lim x, if x = 1 / (3n cos(n³)/(6n + 1)). | <think>
Okay, so I have this limit problem to solve: the limit as n approaches infinity of x, where x is equal to 1 divided by (3n multiplied by cos(n³ divided by (6n + 1))). Hmm, let me write that down to make sure I get it right.
So, x = 1 / [3n * cos(n³ / (6n + 1))]. And we're looking for lim as n approaches infini... | 68 |
https://ia801305.us.archive.org/8/items/ProblemsInCalculusOfOneVariableI.A.Maron/Problems%20in%20Calculus%20of%20One%20Variable%20-%20I.%20A.%20Maron.pdf | 120 | [
"NO CHOICES AVAILABLE"
] | NO ANSWER DETECTED | A body of mass 6g is in rectilinear motion according to the law s=-1+ln (t+1)+(t+1)^3 (s is in centimetres and t, in seconds). The velocity of motion is equal to the time derivative of the distance. Find the kinetic energy (mv^2/2) of the body one second after it begins to move. What is the kinetic energy (mv^2/2) of t... | <think>
Alright, let me try to figure out how to solve this problem. So, we have a body with a mass of 6 grams moving in a straight line, and its position as a function of time is given by the equation s = -1 + ln(t + 1) + (t + 1)^3. They want to find the kinetic energy of the body one second after it starts moving. Ki... | 48 |
https://jeeadv.ac.in/past_qps/2021_2_English.pdf | 26 | [
"\"A) 198\"",
"\"B) 199\"",
"\"C) 200\"",
"\"D) 201\""
] | NO ANSWER DETECTED | Let M = {(x, y) ∈ R x R : x² + y² ≤ r²}, where r > 0. Consider the geometric progression aₙ = 2ⁿ⁻¹, n = 1, 2, 3, ... . Let S₀ = 0 and, for n ≥ 1, let Sₙ denote the sum of the first n terms of this progression. For n ≥ 1, let Cₙ denote the circle with center (Sₙ₋₁, 0) and radius aₙ, and Dₙ denote the circle with center ... | <think>
Alright, let's tackle this problem step by step. It's a bit involved, but if I break it down, it should make sense. So, first, let me parse the question and understand each component.
We have a set M defined as all points (x, y) in the real plane such that x² + y² ≤ r², where r is given as (2¹⁹⁹ - 1)√2. So, M ... | 67 |
https://jeeadv.ac.in/past_qps/2010_1.pdf | 5 | [
"A) FeO",
"B) FeS",
"C) Fe₂O₃",
"D) FeSiO3"
] | NO ANSWER DETECTED | The extraction of copper from chalcopyrite involves partial roasting, removal of iron, and self-reduction. The ore chalcopyrite (CuFeS₂) contains both copper and iron, and during the extraction process, iron is removed as a specific compound.
Iron is removed from chalcopyrite as:
A) FeO
B) FeS
C) Fe₂O₃
D) FeSiO3... | <think>
Okay, so I have this chemistry question about extracting copper from chalcopyrite. Hmm, I remember chalcopyrite is a sulfide mineral with the formula CuFeS₂. The question is about how iron is removed during the extraction process. The options are FeO, FeS, Fe₂O₃, and FeSiO₃.
I think extraction of copper from ... | 86 |
https://jeeadv.ac.in/past_qps/2014_2.pdf | 2 | [
"\"A) 60 ± 0.15Ω\"",
"\"B) 135 ± 0.56Ω\"",
"\"C) 60 ± 0.25Ω\"",
"\"D) 135 ± 0.23Ω\""
] | NO ANSWER DETECTED | During an experiment with a metre bridge, the galvanometer shows a null point when the jockey is pressed at 40.0 cm using a standard resistance of 90 Ω, as shown in the figure. The least count of the scale used in the metre bridge is 1 mm. The unknown resistance is
(A) 60 ± 0.15 Ω
(B) 135 ± 0.56 Ω
(C) 60 ± 0.25 Ω... | <think>
Alright, so I've got this problem about a meter bridge experiment. Hmm, I remember that a meter bridge, also known as a resistance bridge, is used to measure unknown resistances. The basic principle is that it’s a Wheatstone bridge circuit, right? The null point indicates balance, meaning the currents in both a... | 57 |
https://ia801305.us.archive.org/8/items/ProblemsInCalculusOfOneVariableI.A.Maron/Problems%20in%20Calculus%20of%20One%20Variable%20-%20I.%20A.%20Maron.pdf | 49 | [
"NO CHOICES AVAILABLE"
] | NO ANSWER DETECTED | 1.7.4. Find lim x, if x = 1 / (Vn² + 1 + V4n² - 1).
Find lim x, if x = 1 / (Vn² + 1 + V4n² - 1). | <think>
Alright, so I need to find the limit of x as n approaches infinity, where x is defined as 1 over the square root of (n squared plus 1) plus the square root of (4n squared minus 1). Hmm, okay, let me write this out more clearly.
So, x = 1 / (√(n² + 1) + √(4n² - 1)). I need to compute the limit of x as n approac... | 103 |
https://www.asi.edu.au/wp-content/uploads/2022/12/2015-asoe-chemistry-exam.pdf | 3 | [
"\"A: 0.110 mol L¯¹\"",
"\"B: 0.138 mol L¯¹\"",
"\"C: 0.220 mol L¯¹\"",
"\"D: 0.275 mol L¯¹\"",
"\"E: 0.550 mol L¯¹\""
] | NO ANSWER DETECTED | 250.0 mL of 0.550 mol L¯¹ Na2SO4 is diluted to 1250 mL. The concentration of Na⁺ ions in the resulting solution can be calculated based on this dilution. What is the concentration (in mol L¯¹) of Na⁺ ions in a solution prepared by diluting 250.0 mL of 0.550 mol L¯¹ Na2SO4 to 1250 mL?
(a) 0.110 mol L¯¹
(b) 0.138 mol... | <think>
Okay, so I have this problem where I need to find the concentration of Na⁺ ions after diluting a sodium sulfate solution. Let me try to think through this step by step.
First, the problem says that we have 250.0 mL of a 0.550 mol/L Na2SO4 solution. We're diluting this to 1250 mL, and we need to find out the c... | 88 |
https://jeeadv.ac.in/past_qps/2013_1.pdf | 21 | [
"\"A: P>Q>R>S",
"B: S>P>R>Q",
"C: P>R>Q>S",
"D: R>P>S>Q\""
] | NO ANSWER DETECTED | KI in acetone undergoes S2 reaction with each of P, Q, R, and S. The rates of the reaction vary as follows:
- H3C-Cl (P)
- -Cl (Q)
- R
- Cl (S)
(A) P>Q>R>S
(B) S>P>R>Q
(C) P>R>Q>S
(D) R>P>S>Q
The rates of the reaction vary as? | <think>
Okay, so I've got this S_N2 reaction problem here, and I'm trying to figure out the correct order of reaction rates for P, Q, R, and S with KI in acetone. Let me break this down step by step.
First, I remember that S_N2 reactions are bimolecular nucleophilic substitutions. The rate of the reaction depends on b... | 28 |
https://ia801305.us.archive.org/8/items/ProblemsInCalculusOfOneVariableI.A.Maron/Problems%20in%20Calculus%20of%20One%20Variable%20-%20I.%20A.%20Maron.pdf | 49 | [
"NO CHOICES AVAILABLE"
] | NO ANSWER DETECTED | Find lim x, if x = 2n + 3 - Vn - 1.
Note: The context indicates that we are evaluating the limit of sequences in the section regarding limits. | <think>
Okay, so I need to find the limit of x as n approaches something? Hmm, the question is a bit unclear. It says, "Find lim x, if x = 2n + 3 - Vn - 1." Wait, what does "Vn" mean here? Is that a typo or some function? In the context of limits and sequences, it's possible that "Vn" could be the square root of n, bec... | 71 |
https://www.asi.edu.au/wp-content/uploads/2022/12/2017-asoe-chemistry-exam.pdf | 7 | [
"NO CHOICES AVAILABLE"
] | NO ANSWER DETECTED | A 500.0 L container filled with air weighs 23.888 kg. When the container is completely evacuated of all air, it weighs 21.702 kg. Find the density of the air (in g L¯¹). | <think>
Okay, so here's this problem: I have a 500.0 L container filled with air, and it weighs 23.888 kg. When the container is completely evacuated of all air, it weighs 21.702 kg. I need to find the density of the air in grams per liter. Hmm, okay, let me think.
First, density is mass over volume, right? So, if I c... | 55 |
https://ia801305.us.archive.org/8/items/ProblemsInCalculusOfOneVariableI.A.Maron/Problems%20in%20Calculus%20of%20One%20Variable%20-%20I.%20A.%20Maron.pdf | 82 | [
"\"free response\""
] | NO ANSWER DETECTED | 1.14.9. Redefine the following functions at the point x=0 so as to make them continuous: (a) f (x) = (tan x)/x.
Redefine the following functions at the point x=0 so as to make them continuous: (a) f (x) = (tan x)/x. | <think>
Alright, so I have this function f(x) = (tan x)/x, and I need to redefine it at x=0 to make it continuous there. Hmm, okay. I remember that for a function to be continuous at a point, the limit as x approaches that point should exist and be equal to the function's value at that point. Right now, if I plug in x=... | 101 |
https://jeeadv.ac.in/past_qps/2020_1_English.pdf | 8 | [
"\"A: the force causing the molecules to move across the tube is AnkBTS\"",
"\"B: force balance implies n₁ẞνι = ΔηkBT\"",
"\"C: total number of molecules going across the tube per sec is ()()s\"",
"\"D: rate of molecules getting transferred through the tube does not change with time\""
] | NO ANSWER DETECTED | Here's the extracted text with formatting indications:
**Page 1**
* <bold>JEE (Advanced) 2020</bold> <bold>Paper 1</bold>
* <bold>Q.12</bold> As shown schematically in the figure, two vessels contain water solutions (at temperature T) of potassium permanganate (KMnO₄) of different concentrations n₁ and n₂ (n₁ > ... | <think>
Okay, so I've got this question here about diffusion in two connected vessels with potassium permanganate solutions. Let me try to unpack this step by step. The problem mentions that n₁ is greater than n₂, and Δn is much smaller than n₁. So we're dealing with a situation where the concentration difference is sm... | 77 |
https://ia801305.us.archive.org/8/items/ProblemsInCalculusOfOneVariableI.A.Maron/Problems%20in%20Calculus%20of%20One%20Variable%20-%20I.%20A.%20Maron.pdf | 59 | [
"NO CHOICES AVAILABLE"
] | NO ANSWER DETECTED | Proceeding from Cauchy's definition of the limit of a function, prove that for any \( K > 0 \) there exists \( M > 0 \) such that from the inequality \( x > M \) there always follows the inequality \( \log_a x > K \).
Using this approach, prove that
\[
\lim_{x \to +\infty} \log_a x = +\infty.
\]
Finally, prove tha... | <think>
Alright, so I've been given this problem to prove using Cauchy's definition of the limit for functions. The first part is about showing that for any \( K > 0 \), there exists an \( M > 0 \) such that whenever \( x > M \), it follows that \( \log_a x > K \). Then, I need to use this result to show that the limit... | 58 |
https://www.asi.edu.au/wp-content/uploads/2022/12/2012-asoe-chemistry-exam.pdf | 7 | [
"\"a. 0.100 mol kg¯¹\"",
"\"b. 0.128 mol kg¯¹\"",
"\"c. 0.160 mol kg¯¹\"",
"\"d. 0.201 mol kg¯¹\"",
"\"e. 0.252 mol kg¯¹\""
] | NO ANSWER DETECTED | One way to measure the concentration of a substance is through molality. A 1 molal solution is defined as 1 mol of substance per 1 kg of the solvent used to make up the solution. What is the molality of a solution made by dissolving 100 g of bromothymol blue (C27H28Br2O5S) in 1.00 L of ethanol at 10°C? The density of e... | <think>
Okay, so I have this problem about calculating the molality of a solution. Hmm, I remember molality is a measure of concentration based on moles per kilogram of solvent. It's different from molarity, which is moles per liter of solution. Since the question asks for molality, I need to focus on the mass of the s... | 43 |
https://ia801305.us.archive.org/8/items/ProblemsInCalculusOfOneVariableI.A.Maron/Problems%20in%20Calculus%20of%20One%20Variable%20-%20I.%20A.%20Maron.pdf | 120 | [
"NO CHOICES AVAILABLE"
] | NO ANSWER DETECTED | A raft is pulled to the bank by means of a rope which is wound on a drum, at a rate of 3 m/min. Determine the speed of the raft at the moment when it is 25 m distant from the bank if the drum is situated on the bank 4 m above water level. What is the speed of the raft at the moment when it is 25 m distant from the bank... | <think>
Alright, so I've got this problem about a raft being pulled towards the bank with a rope wound on a drum. The drum is situated 4 meters above the water level, and the rope is being pulled at a rate of 3 meters per minute. I need to find the speed of the raft when it's 25 meters away from the bank. Hmm, okay, le... | 79 |
https://ia801305.us.archive.org/8/items/ProblemsInCalculusOfOneVariableI.A.Maron/Problems%20in%20Calculus%20of%20One%20Variable%20-%20I.%20A.%20Maron.pdf | 220 | [
"\"(ax+b)/(cx+d) = t^m\"",
"\"m has the same sense as above\""
] | NO ANSWER DETECTED | If the integrand is a rational function of <bold>x</bold> and fractional powers of a linear fractional function of the form <bold>(ax+b)/(cx+d)</bold>, then rationalization of the integral is effected by the substitution <bold>(ax+b)/(cx+d) = t^m</bold>, where <bold>m</bold> has the same sense as above. Define <bold>m<... | <think>
Okay, so I'm trying to understand how to rationalize an integral when the integrand is a rational function of x and also involves fractional powers of a linear fractional function. The given form is (ax + b)/(cx + d), and the substitution suggested is to let (ax + b)/(cx + d) = t^m. The question is asking me to... | 92 |
https://jeeadv.ac.in/past_qps/2018_1.pdf | 18 | [
"NO CHOICES AVAILABLE"
] | NO ANSWER DETECTED | Liquids A and B form ideal solution over the entire range of composition. At temperature T, equimolar binary solution of liquids A and B has vapour pressure 45 Torr. At the same temperature, a new solution of A and B having mole fractions \(x_A\) and \(x_B\), respectively, has vapour pressure of 22.5 Torr. The vapour p... | <think>
Okay, so I have this problem about ideal solutions and vapor pressure. Let me try to make sense of it step by step. I'm not super confident about all the concepts, but I'll try to work through it logically.
First, let me read the problem again carefully:
"Liquids A and B form ideal solution over the entire ra... | 90 |
https://jeeadv.ac.in/past_qps/2011_1.pdf | 4 | [
"\"A: Adsorption is always exothermic.\"",
"\"B: Physisorption may transform into chemisorption at high temperature.\"",
"\"C: Physisorption increases with increasing temperature but chemisorption decreases with increasing temperature.\"",
"\"D: Chemisorption is more exothermic than physisorption, however it ... | NO ANSWER DETECTED | The correct statement(s) pertaining to the adsorption of a gas on a solid surface is (are):
(A) Adsorption is always exothermic.
(B) Physisorption may transform into chemisorption at high temperature.
(C) Physisorption increases with increasing temperature but chemisorption decreases with increasing temperature.
(D) Ch... | <think>
Okay, I'm going to try to figure out the correct statements about adsorption. Hmm, so the question is asking which of the options (A) through (D) are correct regarding the adsorption of a gas on a solid surface. I remember that adsorption is different from absorption. Adsorption is when gas molecules stick to a... | 91 |
https://www.asi.edu.au/wp-content/uploads/2022/12/2007-asoe-chemistry-exam.pdf | 1 | [
"\"15 minutes\""
] | NO ANSWER DETECTED | Reading Time: 15 minutes. Examination Time: 120 minutes. What is the time allowed for the Reading Time in the 2007 National Qualifying Examination? | <think>
First, I'll identify the given information: the Reading Time is 15 minutes and the Examination Time is 120 minutes.
Next, I'll analyze the problem. The question asks for the Reading Time allowed in the 2007 National Qualifying Examination, which is already provided as 15 minutes.
Since the Reading Time is dir... | 146 |
https://jeeadv.ac.in/past_qps/2010_1.pdf | 5 | [
"A) S",
"B) O2-",
"C) S2-",
"D) SO₂"
] | NO ANSWER DETECTED | In self-reduction, the reducing species is:
A) S
B) O2-
C) S2-
D) SO₂
In self-reduction, the reducing species is? | <think>
Okay, so I have this question about self-reduction and which species acts as the reducing agent. The options are S, O2-, S2-, and SO2. Hmm, I need to figure out which one is the correct answer.
First, I should recall what self-reduction means. From what I remember, self-reduction is a process where a species i... | 44 |
https://ia801305.us.archive.org/8/items/ProblemsInCalculusOfOneVariableI.A.Maron/Problems%20in%20Calculus%20of%20One%20Variable%20-%20I.%20A.%20Maron.pdf | 253 | [
"NO CHOICES AVAILABLE"
] | NO ANSWER DETECTED | Here is the extracted text from the PDF, with formatting as indicated.
==Page 1==
<bold>§ 6.1. The Lower and Upper Integral Sums</bold> <highlighted>253</highlighted>
Form an integral sum:
n-1
<bold>I<sub>n</sub> = Σ Δx<sub>i</sub> = Σamq<sup>(i+1)</sup> maq<sup>i</sup>(q — 1) =</bold>
i=0
i=0
<bold>= am+1 (q-1) q<sup... | <think>
Okay, let me try to figure out the result of the integral \( \int_a^b x^m \, dx \). From the text, I see that it's related to computing the integral using the definition with integral sums. The process starts by forming an integral sum \( I_n \), which is a summation involving terms like \( \Delta x_i \), and t... | 141 |
https://ia801305.us.archive.org/8/items/ProblemsInCalculusOfOneVariableI.A.Maron/Problems%20in%20Calculus%20of%20One%20Variable%20-%20I.%20A.%20Maron.pdf | 120 | [
"NO CHOICES AVAILABLE"
] | NO ANSWER DETECTED | A point is in motion along a cubic parabola 12y = x^3. Differentiating both members of the given equation with respect to t gives the relation between the rates of change of the coordinates. Hence, at -2 < x < 2, the rate of change of the ordinate is less than that of the abscissa; at x = ±2, the rates of change of the... | <think>
Okay, so I have this problem where a point is moving along a cubic parabola given by the equation 12y = x³. The question is about figuring out which coordinate, x or y, changes faster as the point moves along this curve. The problem mentions something about differentiating both sides with respect to time, t, to... | 69 |
https://ia801305.us.archive.org/8/items/ProblemsInCalculusOfOneVariableI.A.Maron/Problems%20in%20Calculus%20of%20One%20Variable%20-%20I.%20A.%20Maron.pdf | 178 | [
"\"0\"",
"\"2\"",
"\"∞\""
] | NO ANSWER DETECTED | Here's the extracted text with formatting:
==Page 1==
<bold>178</bold>
<bold>Ch. 111. Differential Calculus: Investigation of Funct's</bold>
(c) <highlighted>The function is defined and continuous over the entire axis
except at the points x = ± 2. The function is odd, its graph is
symmetrical about the origin, therefo... | <think>
To determine the value of \( b \) in the inclined asymptote \( y = 2x + b \) as \( x \) approaches infinity, we analyze the function \( y = \frac{2x^3}{x^2 - 4} \).
First, we find the limit of \( y \) divided by \( x \) as \( x \) becomes very large:
\[
k = \lim_{x \to +\infty} \frac{y}{x} = \lim_{x \to +\inft... | 140 |
https://jeeadv.ac.in/past_qps/2011_2.pdf | 18 | [
"\"A: 5 √2",
"B: 3 √2",
"C: √2",
"D: √3\""
] | NO ANSWER DETECTED | Let P(6,3) be a point on the hyperbola \( x^2 y^2 = a^2 b^2 \). If the normal at the point P intersects the x-axis at (9,0), then the eccentricity of the hyperbola is:
(A) \( 5\sqrt{2} \)
(B) \( 3\sqrt{2} \)
(C) \( \sqrt{2} \)
(D) \( \sqrt{3} \)
If the normal at the point P intersects the x-axis at (9,0), then ... | <think>
Okay, so I have this hyperbola equation \( x^2 y^2 = a^2 b^2 \). Hmm, let me make sure I understand that correctly. Is that the standard form of a hyperbola? I remember that hyperbola equations are usually in the form \( \frac{x^2}{a^2} - \frac{y^2}{b^2} = 1 \) or \( \frac{y^2}{b^2} - \frac{x^2}{a^2} = 1 \). Bu... | 52 |
https://jeeadv.ac.in/past_qps/2014_1.pdf | 24 | [
"\"3\""
] | NO ANSWER DETECTED | Let f: R → R and g: R → R be respectively given by f(x) = |x| + 1 and g(x) = x² + 1. Define h: R → R by h(x) = {max {f(x), g(x)} if x ≤ 0, min {f(x), g(x)} if x > 0. The number of points at which h(x) is not differentiable is: | <think>
Okay, so I have this problem where two functions f(x) and g(x) are defined, and then h(x) is defined piecewise as the max or min of these two functions depending on whether x is less than or equal to zero or greater than zero. I need to figure out how many points h(x) isn't differentiable at. Hmm, let me break ... | 27 |
https://www.asi.edu.au/wp-content/uploads/2022/12/2009-asoe-chemistry-exam.pdf | 16 | [
"NO CHOICES AVAILABLE"
] | NO ANSWER DETECTED | In the reaction below for the production of compound C, all functional groups on the starting material have been protected. Circle the functional groups which need to be deprotected in order for this reaction to proceed to give the product on the right. Label with a P the protections which need to remain on during the ... | <think>
Okay, so I have this chemistry problem here about protecting and deprotecting functional groups. Hmm, I remember that in organic synthesis, often certain functional groups need to be protected to prevent them from reacting when you’re trying to do something else. Then, after the reaction, you deprotect them to ... | 89 |
https://jeeadv.ac.in/past_qps/2019_2_English.pdf | 7 | [
"NO CHOICES AVAILABLE"
] | NO ANSWER DETECTED | A 10 cm long perfectly conducting wire PQ is moving with a velocity 1 cm/s on a pair of horizontal rails of zero resistance. One side of the rails is connected to an inductor L = 1 mH and a resistance R = 1 Ω. The horizontal rails, L, and R lie in the same plane with a uniform magnetic field B = 1 T perpendicular to th... | <think>
Okay, so I have this physics problem here about a conducting wire moving on rails with some inductor and resistance in the circuit. It's kind of an electromagnetism problem, probably involving induced EMF or something like that. Let me read the problem again and try to break it down step by step.
We have a 10 ... | 5 |
https://jeeadv.ac.in/past_qps/2018_2.pdf | 18 | [
"NO CHOICES AVAILABLE"
] | NO ANSWER DETECTED | Consider the following reversible reaction, A(g) + B(g) = AB(g). The activation energy of the backward reaction exceeds that of the forward reaction by 2RT (in J mol¯¹). If the pre-exponential factor for the forward reaction is 4 times that of the reverse reaction, the absolute value of ∆G® (in J mol¯¹) for the reactio... | <think>
Okay, let me try to figure out how to solve this problem. It's about a reversible reaction where A gas and B gas form AB gas. The question is asking for the absolute value of the standard Gibbs energy change, ΔG°, for the reaction at 300 K.
First, let me recall what I know about activation energy and pre-expo... | 49 |
https://ia801305.us.archive.org/8/items/ProblemsInCalculusOfOneVariableI.A.Maron/Problems%20in%20Calculus%20of%20One%20Variable%20-%20I.%20A.%20Maron.pdf | 49 | [
"NO CHOICES AVAILABLE"
] | NO ANSWER DETECTED | 1.7.4. Find lim x, if
(g) xₙ = 1 - 2 + 3 - 4 + 5 - 6 + ... - 2n.
Find lim x, if x = 1 - 2 + 3 - 4 + 5 - 6 + ... - 2n. | <think>
Okay, so I have this problem where I need to find the limit of the sequence xₙ, which is defined as 1 - 2 + 3 - 4 + 5 - 6 + ... - 2n. Hmm, let me write that out to make sure I understand it correctly.
The sequence starts at 1, subtracts 2, adds 3, subtracts 4, adds 5, subtracts 6, and so on, alternating betwee... | 96 |
https://jeeadv.ac.in/past_qps/2012_2.pdf | 3 | [
"\"14.0 cm\"",
"\"15.2 cm\"",
"\"16.4 cm\"",
"\"17.6 cm\""
] | NO ANSWER DETECTED | A student is performing the experiment of Resonance Column. The diameter of the column tube is 4 cm. The frequency of the tuning fork is 512 Hz. The air temperature is 38°C in which the speed of sound is 336 m/s. The zero of the meter scale coincides with the top end of the Resonance Column tube. When the first resonan... | <think>
Okay, so I have this physics problem about resonance columns. Hmm, resonance columns are those tubes where you can create different resonant lengths by changing the water level. I remember that when the tuning fork is struck and held over the tube, it creates a column of air that resonates when its length is ju... | 39 |
https://ia801305.us.archive.org/8/items/ProblemsInCalculusOfOneVariableI.A.Maron/Problems%20in%20Calculus%20of%20One%20Variable%20-%20I.%20A.%20Maron.pdf | 120 | [
"NO CHOICES AVAILABLE"
] | NO ANSWER DETECTED | 2.5.10. f (x) = 3x<highlighted>5</highlighted> - 15x<highlighted>3</highlighted> + 5x - 7. Find out at which of the points x the rate of change of the function is minimal. The rate of change of a function at a certain point is equal to the derivative of the function at this point f'(x) = 15x<highlighted>4</highlighted>... | <think>
Okay, let me try to figure out where the rate of change of the function \( f(x) = 3x^5 - 15x^3 + 5x - 7 \) is minimal. Hmm, the rate of change at a point is given by the derivative of the function at that point. So first, I need to find the derivative \( f'(x) \).
Alright, taking the derivative of each term:
... | 137 |
https://ia801305.us.archive.org/8/items/ProblemsInCalculusOfOneVariableI.A.Maron/Problems%20in%20Calculus%20of%20One%20Variable%20-%20I.%20A.%20Maron.pdf | 451 | [
"NO CHOICES AVAILABLE"
] | NO ANSWER DETECTED | Here's the text extracted from the PDF:
In the section discussing integration techniques, it states that through a substitution of \( x = t \), one can reduce the given integral to the form \( \int \sin t dt \), where \( \alpha = 1 - t^2 \). The text also notes that it is vital to consider the conditions under which t... | <think>
Okay, so I have this problem here about integrating something, and they mention using a substitution \( x = t \), which seems a bit confusing because usually substitutions are like \( u = something \). Wait, maybe they mean substituting \( t = x \) or \( t = 1 - x^2 \)? Hmm, not sure. It says the integral can b... | 17 |
https://jeeadv.ac.in/past_qps/2019_1_English.pdf | 13 | [
"\"A: The central atom in X is sp³ hybridized\"",
"\"B: There is a coordinate bond in Y\"",
"\"C: The oxidation state of the central atom in Z is +2\"",
"\"D: The central atom in Z has one lone pair of electrons\""
] | NO ANSWER DETECTED | A tin chloride Q undergoes the following reactions (not balanced): Q + Cl → X, Q + Me3N → Y, Q + CuCl2 → Z + CuCl. X is a monoanion having pyramidal geometry. Both Y and Z are neutral compounds. Choose the correct option(s):
(A) The central atom in X is sp³ hybridized
(B) There is a coordinate bond in Y
(C) The o... | <think>
Alright, so I'm trying to solve this chemistry problem where a tin chloride Q is reacting in three different ways. The reactions aren't balanced, so I have to figure out the possible products and their structures based on the given clues. Then, I need to determine which of the statements A, B, C, D are correct.... | 94 |
https://ia801305.us.archive.org/8/items/ProblemsInCalculusOfOneVariableI.A.Maron/Problems%20in%20Calculus%20of%20One%20Variable%20-%20I.%20A.%20Maron.pdf | 180 | [
"\"x = 1/2\"",
"\"x = 0\"",
"\"x = 1\"",
"\"x = 2\""
] | NO ANSWER DETECTED | Let us find the extrema of the function, for which purpose we evaluate the derivative: y' = 2xe/xe1/x = 2e1/x (x - 1/2), whence we find the only critical point x = 1/2. Since for x≠0, y" (x) = 2e1/x 2e1/x2 el/x +-el/x 1 = X2 x² e1/x (2x²-2x+1) > 0. What critical point is found when evaluating the derivative? | <think>
Alright, let me try to figure out what this problem is asking. It mentions finding the extrema of a function by evaluating the derivative. From what I remember, extrema are the maximum and minimum points of a function, and to find them, we take the derivative and set it equal to zero. So, critical points are wh... | 36 |
https://ia801305.us.archive.org/8/items/ProblemsInCalculusOfOneVariableI.A.Maron/Problems%20in%20Calculus%20of%20One%20Variable%20-%20I.%20A.%20Maron.pdf | 120 | [
"NO CHOICES AVAILABLE"
] | NO ANSWER DETECTED | Find the slope of the tangent to the cubic parabola y = x^3 at the point x = √3/3. Write the equations of the tangents to the curve y = 1/(1 + x^2) at the points of its intersection with the hyperbola y = 1/(x + 1). Write the equation of the normal to the parabola y = x^2 + 4x + 1 that is perpendicular to the line join... | <think>
Alright, so I have these four calculus problems to solve. Let me try to tackle them one by one.
First problem: Find the slope of the tangent to the cubic parabola \( y = x^3 \) at the point \( x = \sqrt{3}/3 \).
Okay, finding the slope of the tangent line at a specific point. I remember that the slope of the ... | 54 |
https://jeeadv.ac.in/past_qps/2008_2.pdf | 8 | [
"\"5!\"",
"\"2 × 5!\"",
"\"7×5!\"",
"\"21 x 5!\""
] | NO ANSWER DETECTED | Consider all possible permutations of the letters of the word ENDEANOEL. The number of permutations in which the letter E occurs in the first and the last positions is
(A) 5!
(B) 2 × 5!
(C) 7×5!
(D) 21 x 5!
What is the number of permutations in which the letter E occurs in the first and the last positions? | <think>
Okay, so I have this problem here: I need to find the number of permutations of the letters in the word ENDEANOEL where the letter E is in the first and last positions. The options given are (A) 5!, (B) 2 × 5!, (C) 7×5!, and (D) 21 x 5!. Hmm, let's break this down step by step.
First, I recall that ENDEANOEL i... | 118 |
https://www.asi.edu.au/wp-content/uploads/2022/12/2015-asoe-chemistry-exam.pdf | 8 | [
"NO CHOICES AVAILABLE"
] | NO ANSWER DETECTED | 0.1292 g iron(III) oxide is dissolved in nitric acid and made up to 250.0 mL in a volumetric flask. It is normal in AAS to express solution concentrations in terms of the concentration of metal ions present. The concentration range used in iron AAS is typically 2-10 mg of iron per litre. Dilutions were performed as nec... | <think>
Alright, so I have this problem here about iron analysis using Atomic Absorption Spectroscopy (AAS). Hmm, okay, let's piece this together step by step. I might be a bit rusty on some of these concepts, but I'll try to work through it.
First, let me read the problem again and jot down the key details:
- **0.12... | 95 |
https://jeeadv.ac.in/past_qps/2018_1.pdf | 4 | [
"\"free response\""
] | NO ANSWER DETECTED | Two men are walking along a horizontal straight line in the same direction. The man in front walks at a speed of 1.0 m s¯¹ and the man behind walks at a speed of 2.0 m s¯¹. A third man is standing at a height of 12 m above the same horizontal line such that all three men are in a vertical plane. The two walking men are... | <think>
Alright, let me try to figure out this problem step by step. It's about the Doppler effect, I think. So, here's what I understand.
We have two men walking along a horizontal straight line in the same direction. The one in front is walking at 1.0 m/s, and the one behind is walking at 2.0 m/s. There's also a thi... | 56 |
https://ia801305.us.archive.org/8/items/ProblemsInCalculusOfOneVariableI.A.Maron/Problems%20in%20Calculus%20of%20One%20Variable%20-%20I.%20A.%20Maron.pdf | 261 | [
"\"free response\""
] | NO ANSWER DETECTED | Here is the extracted text from the PDF, with the formatting as requested:
<bold>6.2.10. Evaluate the integrals:</bold>
(a) I = ∫(-1 over -2) dx/(11+5x)^3;
(b) I = ∫(-2 over -3) dx/x^2 -1;
(c) I = ∫(π over -π) sin^2 (x/2) dx;
(d) I = ∫(2 over 0) x^2/(x^2+1) dx;
(e) I = ∫(1 over e) e^x dx/x ln x;
(f) I = ∫(π over 1) si... | <think>
Alright, so I have this integral to evaluate: I = ∫ from -1 to -2 of dx/(11 + 5x)^3. Hmm, seems like a definite integral, right? Let me break it down step by step because I want to make sure I don't make any mistakes.
First, I notice that the integrand is 1 over (11 + 5x) cubed. That suggests to me that perhap... | 123 |
https://jeeadv.ac.in/past_qps/2014_2.pdf | 3 | [
"\"A) 3.7 eV\"",
"\"B) 3.2 eV\"",
"\"C) 2.8 eV\"",
"\"D) 2.5 eV\""
] | NO ANSWER DETECTED | A metal surface is illuminated by light of two different wavelengths 248 nm and 310 nm. The maximum speeds of the photoelectrons corresponding to these wavelengths are u₁ and u₂, respectively. If the ratio u₁: u₂ = 2: 1 and hc = 1240 eV nm, the work function of the metal is nearly what?
(A) 3.7 eV
(B) 3.2 eV
(C) ... | <think>
Alright, so here I am trying to figure out this physics problem about the photoelectric effect. Okay, let's see. The problem says that a metal surface is illuminated by light of two different wavelengths: 248 nm and 310 nm. The maximum speeds of the photoelectrons corresponding to these wavelengths are u₁ and u... | 100 |
https://jeeadv.ac.in/past_qps/2013_1.pdf | 31 | [
"\"A) 4(√2-1)\"",
"\"B) 2√2 (√2-1)\"",
"\"C) 2(√2+1)\"",
"\"D) 2√2 (√2+1)\""
] | NO ANSWER DETECTED | Here's the extracted text with formatting indications:
==Page 1==
<bold>MATHEMATICS</bold>
45. The area enclosed by the curves <bold>y = sin x + cos x</bold> and <bold>y = |cos x - sin x|</bold> over the interval [0, π/2] is
(A) 4(√2-1)
(B) 2√2 (√2-1)
(C) 2(√2+1)
(D) 2√2 (√2+1)
अंतराल [0, π/2] पर वक्रों <bold>y = sin ... | <think>
Okay, so I have this problem here where I need to find the area enclosed by two curves: y = sin x + cos x and y = |cos x - sin x| over the interval [0, π/2]. The options are given, so probably after solving, my answer should match one of them.
First, I should sketch these curves to visualize the area I'm deal... | 85 |
https://ia801305.us.archive.org/8/items/ProblemsInCalculusOfOneVariableI.A.Maron/Problems%20in%20Calculus%20of%20One%20Variable%20-%20I.%20A.%20Maron.pdf | 82 | [
"\"free response\""
] | NO ANSWER DETECTED | Here is the extracted text, formatted as requested:
==Start of extracted text==
<bold>§ 1.14. Continuity of a Function. Points of Discontinuity</bold>
<bold>83</bold>
<bold>1.14.7. Test the following functions for continuity</bold>
<bold>(a) f(x)=e^(x)-1;</bold>
<bold>(b) f (x) = { (e^(x)-1)/x for x≠0,</bold... | <think>
Alright, so I have this problem set in front of me, and it's all about testing the continuity of different functions. Let me try to work through each one step by step. I'm a bit nervous because continuity can sometimes be tricky, especially with all these different functions. But I'll take it one at a time.
St... | 87 |
https://ia801305.us.archive.org/8/items/ProblemsInCalculusOfOneVariableI.A.Maron/Problems%20in%20Calculus%20of%20One%20Variable%20-%20I.%20A.%20Maron.pdf | 262 | [
"\"free response\""
] | NO ANSWER DETECTED | Since the function \( f(x) = \sqrt{3} + x^3 \) increases monotonically on the interval [1, 3], the minimum value \( m = 2 \) and the maximum value \( M = \sqrt{30} \). The estimation of the integral has the form \( 2 \leq \int (\sqrt{3} + x^3) dx \leq 2\sqrt{30} \approx 10.95 \).
Estimate the following integral: \( I ... | <think>
Okay, so I have this integral I need to estimate: \( I = \int_{1}^{3} (\sqrt{3} + x^3) dx \). Hmm, the problem already mentions something about the function increasing monotonically on the interval [1, 3], so I think that should help in setting up the bounds for the estimation.
First off, I remember that when ... | 4 |
https://www.asi.edu.au/wp-content/uploads/2022/12/2007-asoe-chemistry-exam.pdf | 1 | [
"\"ANY THREE (3)\""
] | NO ANSWER DETECTED | Section B: Apportion your time equally on the questions in this section. Answer ANY THREE (3) of Questions 16, 17, 18 or 19. How many of Questions 16, 17, 18 or 19 should you answer in Section B of the 2007 National Qualifying Examination? | <think>
Okay, so I've got this question here about the 2007 National Qualifying Examination. It says in Section B, I should apportion my time equally on the questions in this section. Then it tells me to answer ANY THREE (3) of Questions 16, 17, 18, or 19. Hmm, the question is asking me: How many of Questions 16, 17, 1... | 169 |
https://www.asi.edu.au/wp-content/uploads/2022/12/2009-asoe-chemistry-exam.pdf | 8 | [
"\"A HSO4-, K+, Na+, HCO3\"",
"\"B K+, CO32-, Cl-, Al3+\"",
"\"C K+, Ba2+, NO3, OH-\"",
"\"D Na+, Ba2+, H+, SO42-\"",
"\"E Ca2+, K+, CO32-, Cl-\""
] | NO ANSWER DETECTED | <bold>Australian Science Olympiads</bold> <highlighted>2009 Chemistry National Qualifying Examination</highlighted>
<bold>Q11</bold>
Which of the following groups of ions can coexist in significant quantities in aqueous solution
without reacting with each other?
A <highlighted>HSO4</highlighted>-, K+, Na+, HCO3
B <... | <think>
Okay, so I have this chemistry problem here about ions coexisting in aqueous solution without reacting. There are five options, A to E, each with a different set of ions. I need to figure out which group can exist together without any reactions happening. Hmm, I remember that in solution, ions can react in vari... | 130 |
https://jeeadv.ac.in/past_qps/2015_1.pdf | 13 | [
"\"free response\""
] | NO ANSWER DETECTED | All the energy released from the reaction X → Y, ΔGº = -193 kJ mol-1 is used for oxidizing M⁺ as M⁺ → M³+ + 2e, E° = -0.25V. Under standard conditions, the number of moles of M⁺ oxidized when one mole of X is converted to Y is? | <think>
Alright, so I have this problem here about energy released from a reaction being used to oxidize a metal ion. Hmm, okay. Let me try to parse this step by step.
The reaction given is X → Y, with a standard Gibbs free energy change (ΔGº) of -193 kJ per mole. That means this reaction is spontaneous, right? Since ... | 9 |
https://www.asi.edu.au/wp-content/uploads/2022/12/2008-asoe-chemistry-exam.pdf | 18 | [
"NO CHOICES AVAILABLE"
] | NO ANSWER DETECTED | A solution of a mixture of glucagon and an unknown protein is provided. The unknown protein consists of 129 amino acids, of which 3 are phenylalanine, 3 are tyrosine, and 6 are tryptophan. Using a glucagon-specific analysis, the mass concentration of glucagon is calculated to be 0.24 g L¯¹. The absorption of a solution... | <think>
Okay, so I have this problem where I have a mixture of glucagon and an unknown protein. The unknown protein has 129 amino acids, with 3 phenylalanine, 3 tyrosine, and 6 tryptophan. I need to find the concentration of this unknown protein in mol/L, given some information about the absorbance of the mixture and t... | 64 |
https://ia801305.us.archive.org/8/items/ProblemsInCalculusOfOneVariableI.A.Maron/Problems%20in%20Calculus%20of%20One%20Variable%20-%20I.%20A.%20Maron.pdf | 153 | [
"\"A: Critical points at x = -1, (3-17)/4, (3 + 117)/4, 3\"",
"\"B: No critical points\""
] | NO ANSWER DETECTED | Let \( f(x) = (x + 1)^2 + (x - 3)^2 \). To find the critical points using the first derivative, we need to compute \( f'(x) \) and determine where this derivative equals zero.
Using the first derivative, what critical points can be found for the function \( f(x) = (x + 1)^2 + (x - 3)^2 \)? | <think>
Okay, so I need to find the critical points of the function \( f(x) = (x + 1)^2 + (x - 3)^2 \) using the first derivative. Hmm, critical points occur where the derivative is zero or undefined, right? Since this function is a polynomial, its derivative should be defined everywhere, so I just need to find where t... | 107 |
https://jeeadv.ac.in/past_qps/2018_1.pdf | 14 | [
"\"A) Bi2O5 is more basic than N2O5\"",
"\"B) NF3 is more covalent than BiF3\"",
"\"C) PH3 boils at lower temperature than NH3\"",
"\"D) The N-N single bond is stronger than the P-P single bond\""
] | NO ANSWER DETECTED | Based on the compounds of group 15 elements, the correct statement(s) is (are):
(A) Bi2O5 is more basic than N2O5
(B) NF3 is more covalent than BiF3
(C) PH3 boils at lower temperature than NH3
(D) The N-N single bond is stronger than the P-P single bond
Based on the compounds of group 15 elements, which stateme... | <think>
Okay, so I have this chemistry question here about group 15 elements, which are also known as the nitrogen group. The question gives me four statements, labeled (A) through (D), and asks which ones are correct. Let me try to break this down step by step.
First, I need to remember the general trends in group 15... | 138 |
https://jeeadv.ac.in/past_qps/2014_2.pdf | 37 | [
"\"A: 3",
"B: 1",
"C: 4",
"D: 2\""
] | NO ANSWER DETECTED | Let \( f_1: \mathbb{R} \to \mathbb{R}, f_2: [0,\infty) \to \mathbb{R}, f_3: \mathbb{R} \to \mathbb{R} \) and \( f_4: \mathbb{R} \to [0,\infty) \) be defined by
\[
f_1(x) =
\begin{cases}
|x| & \text{if } x < 0 \\
e^x & \text{if } x \geq 0
\end{cases},
\]
\[
f_2(x) = x^2,
\]
\[
f_3(x) =
\begin{cases}
\sin x & \text{... | <think>
Okay, let's try to figure out the classification of \( f_2 \). So, \( f_2 \) is defined from \([0, \infty)\) to \(\mathbb{R}\) and it's given by \( f_2(x) = x^2 \). I remember that classification usually involves determining properties like continuity, differentiability, whether it's one-one (injective), onto, ... | 139 |
https://ia801305.us.archive.org/8/items/ProblemsInCalculusOfOneVariableI.A.Maron/Problems%20in%20Calculus%20of%20One%20Variable%20-%20I.%20A.%20Maron.pdf | 307 | [
"NO CHOICES AVAILABLE"
] | NO ANSWER DETECTED | Given the function
f (x) = {1-x at 0<x<1, 0 at 1<x<2, (2-x)² at 2<x<3.
Check directly that the function
F(x) = ∫f(t) dt
is continuous on the interval [0, 3] and that its derivative at each interior point of this interval exists and is equal to f (x).
**§ 6.8. Additional Problems**
**6.8.1.** Given the func... | <think>
Alright, so I've got this problem where I need to show that the function F(x), which is the integral of f(t) from t=0 to t=x, is continuous on [0,3] and that its derivative at each interior point is equal to f(x). The function f(x) is piecewise defined: it's 1 - x from 0 to 1, 0 from 1 to 2, and (2 - x)² from 2... | 150 |
https://jeeadv.ac.in/past_qps/2011_2.pdf | 18 | [
"\"A: p and t",
"B: p and s",
"C: q and s",
"D: q and r\""
] | NO ANSWER DETECTED | Column I shows four systems, each of the same length L, for producing standing waves. The lowest possible natural frequency of a system is called its fundamental frequency, whose wavelength is denoted as λf.
**Column I**
(A) Pipe closed at one end
(B) Pipe open at both ends
(C) Stretched wire clamped at both ends... | <think>
Okay, so I have this matching problem where I need to pair four systems from Column I with the correct statements in Column II. Column I includes a pipe closed at one end, a pipe open at both ends, a stretched wire clamped at both ends, and a stretched wire clamped at both ends and at the midpoint. Column II de... | 157 |
https://ia801305.us.archive.org/8/items/ProblemsInCalculusOfOneVariableI.A.Maron/Problems%20in%20Calculus%20of%20One%20Variable%20-%20I.%20A.%20Maron.pdf | 59 | [
"\"lim u (x) / lim v (x)\""
] | NO ANSWER DETECTED | If the limits lim u (x) and lim v(x) exist, then according to theorems regarding limits, if lim v(x) ≠ 0, it is established that:
<bold>lim</bold> <bold>u(x) / v(x) = lim u(x) / lim v(x).</bold>
What is lim (u(x)/(v(x)) if lim v(x) ≠ 0? | <think>
Okay, so I’ve got this limit problem to solve. The question is about finding the limit of u(x) divided by v(x) as x approaches some value, and they mentioned that both lim u(x) and lim v(x) exist. Also, it's given that lim v(x) is not equal to zero. Hmm, I remember that there are some rules about limits of quot... | 171 |
https://jeeadv.ac.in/past_qps/2008_2.pdf | 14 | [
"\"independent of a\"",
"\"directly proportional to a\"",
"\"directly proportional to a^2\"",
"\"inversely proportional to a\""
] | NO ANSWER DETECTED | The nuclear charge (Ze) is non-uniformly distributed within a nucleus of radius R. The charge density p(r) [charge per unit volume] is dependent only on the radial distance r from the centre of the nucleus as shown in figure. The electric field is only along the radial direction. The electric field at r = R is related ... | <think>
Okay, so I have this physics problem here about nuclear charge distribution and electric field. Hmm, I remember that electric field inside a charged sphere depends on whether the charge is uniformly distributed or not. In this problem, it says the nuclear charge is non-uniformly distributed, and the charge dens... | 42 |
https://ia801305.us.archive.org/8/items/ProblemsInCalculusOfOneVariableI.A.Maron/Problems%20in%20Calculus%20of%20One%20Variable%20-%20I.%20A.%20Maron.pdf | 49 | [
"NO CHOICES AVAILABLE"
] | NO ANSWER DETECTED | Find lim x, if x = 1 - n³ + n.
Extracted Text: <bold>§ 1.7. Evaluation of Limits of Sequences</bold>
<bold>1.7.5. Find limx, if</bold>
<bold>(c) xn=1-n³+n;</bold> | <think>
Okay, so I have this problem here: Find the limit of xn as n approaches something, but wait, the question says "Find lim x, if x = 1 - n³ + n." Hmm, that's a bit confusing. Let me try to parse it. It seems like it might be a translation issue or maybe I misread it. Looking back, I see it's from section 1.7.5 wh... | 173 |
https://jeeadv.ac.in/past_qps/2023_2_English.pdf | 29 | [
"NO CHOICES AVAILABLE"
] | NO ANSWER DETECTED | The entropy versus temperature plot for phases α and β at 1 bar pressure is given. ST and S0 are entropies of the phases at temperatures T and 0 K, respectively. The transition temperature for α to β phase change is 600 K and Cp,β - Cp,α = 1 J mol−1 K−1. Assume (Cp,β - Cp,α) is independent of temperature in the range o... | <think>
Alright, let me try to figure out how to solve this entropy change problem. So, we have two phases, α and β, and we're given a plot of their entropy versus temperature at 1 bar pressure. The key points here are:
1. The transition temperature from α to β is 600 K.
2. The difference in heat capacities, Cp,β - Cp... | 72 |
https://ia801305.us.archive.org/8/items/ProblemsInCalculusOfOneVariableI.A.Maron/Problems%20in%20Calculus%20of%20One%20Variable%20-%20I.%20A.%20Maron.pdf | 95 | [
"NO CHOICES AVAILABLE"
] | NO ANSWER DETECTED | Find the constants a and b from the condition: (a) lim (x → 8) (ax+b) = 0; (b) lim (x → 0) (x²- x + 1-ax-b) = 0. | <think>
Okay, so I have to find the constants a and b based on these two limit conditions. Let me first read and understand the problem again.
Part (a) says: The limit as x approaches 8 of (ax + b) is 0. So that gives me one equation involving a and b.
Part (b) says: The limit as x approaches 0 of (x² - x + 1 - ax - ... | 168 |
https://jeeadv.ac.in/past_qps/2018_1.pdf | 18 | [
"NO CHOICES AVAILABLE"
] | NO ANSWER DETECTED | The standard emf of the electrochemical cell, Mg(s) | Mg<sub>2+</sub> (aq, 1 M) || Cu<sub>2+</sub> (aq, 1 M) | Cu(s) is 2.70 V at 300 K. When the concentration of Mg<sub>2+</sub> is changed to x M, the cell potential changes to 2.67 V at 300 K. Given that <bold>F/R</bold> = 11500 K V<bold>-1</bold>, where <bold>F</bold... | <think>
Alright, so I have this problem about an electrochemical cell. The cell is Mg(s) | Mg²+ (aq, 1 M) || Cu²+ (aq, 1 M) | Cu(s), and it has a standard emf of 2.70 V at 300 K. Then, the concentration of Mg²+ is changed to x M, and the cell potential drops to 2.67 V. I need to find x. The problem also gives me F/R = ... | 75 |
https://ia801305.us.archive.org/8/items/ProblemsInCalculusOfOneVariableI.A.Maron/Problems%20in%20Calculus%20of%20One%20Variable%20-%20I.%20A.%20Maron.pdf | 421 | [
"\"1\""
] | NO ANSWER DETECTED | <bold>Answers and Hints to Ch. I</bold>
<bold>1.10.1.</bold> <highlighted>(d) </highlighted> <highlighted>5</highlighted> <highlighted>; (e) </highlighted> <highlighted>1</highlighted> <highlighted>; (f) </highlighted> <highlighted>-</highlighted> <highlighted>1</highlighted> <highlighted>.</highlighted> <highlighted>H... | <think>
Alright, so I've got this question here from Problem 1.10.1, specifically part (e). The answer is given as 1, but I need to figure out how that makes sense. Let me go through my thought process step by step.
First off, I don't have the exact problem statement for part (e). It must be one of those where without... | 128 |
https://jeeadv.ac.in/past_qps/2021_1_English.pdf | 1 | [
"\"50\"",
"\"75\"",
"\"350\"",
"\"525\""
] | NO ANSWER DETECTED | A heavy nucleus Q of half-life 20 minutes undergoes alpha-decay with a probability of 60% and beta-decay with probability of 40%. Initially, the number of Q nuclei is 1000. How many alpha-decays of the heavy nucleus Q occur in the first one hour, given that its half-life is 20 minutes and it undergoes alpha-decay with ... | <think>
Okay, so I'm trying to figure out how many alpha-decays of the heavy nucleus Q occur in the first hour. The problem gives me a few pieces of information: the half-life is 20 minutes, it can decay either by alpha or beta, with probabilities 60% and 40% respectively. Initially, there are 1000 nuclei.
First, I ne... | 104 |
https://jeeadv.ac.in/past_qps/2013_1.pdf | 25 | [
"\"A: 1 × 10-4\"",
"\"B: 1 × 10-5\"",
"\"C: 1 × 10-6\"",
"\"D: 1 × 10-3\""
] | NO ANSWER DETECTED | The initial rate of hydrolysis of methyl acetate (1M) by a weak acid (HA, 1M) is 1/100th of that of a strong acid (HX, 1M), at 25 °C. The K of HA is given as multiple choice options.
(A) 1 × 10-4
(B) 1 × 10-5
(C) 1 × 10-6
(D) 1 × 10-3
The initial rate of hydrolysis of methyl acetate (1M) by a weak acid (HA, 1... | <think>
Alright, let me try to work through this problem step by step. So, we're dealing with the hydrolysis of methyl acetate catalyzed by both a weak acid (HA) and a strong acid (HX). The initial rate with HA is 1/100th of that with HX. We need to find the K (acid dissociation constant) of HA from the given options.
... | 154 |
https://www.asi.edu.au/wp-content/uploads/2022/12/2015-asoe-chemistry-exam.pdf | 3 | [
"\"A: Tb2SO4\"",
"\"B: TbSO4\"",
"\"C: Tb2(SO4)3\"",
"\"D: Tb(SO4)2\"",
"\"E: Tb3(SO4)2\""
] | NO ANSWER DETECTED | The formula for terbium phosphate is TbPO4. Terbium sulfate is derived from the sulfate ion (SO4) and terbium. Determine what the correct formula would be given the common oxidation states of terbium and the sulfate ion. What is the formula for terbium sulfate?
(a) Tb2SO4
(b) TbSO4
(c) Tb2(SO4)3
(d) Tb(SO4)2
... | <think>
Okay, so I need to figure out the correct formula for terbium sulfate. I know that sulfate is the ion, and terbium is the metal here. Let me start by recalling some basic chemistry concepts about how ionic compounds are formed.
First, I remember that ionic compounds are made of positive ions (cations) and neg... | 122 |
https://jeeadv.ac.in/past_qps/2014_2.pdf | 3 | [
"\"A) 330 K\"",
"\"B) 660 K\"",
"\"C) 990 K\"",
"\"D) 1550 K\""
] | NO ANSWER DETECTED | Parallel rays of light of intensity I = 912 Wm¯² are incident on a spherical black body kept in surroundings of temperature 300 K. Take Stefan-Boltzmann constant σ = 5.7 × 10−8 Wm−2K−4 and assume that the energy exchange with the surroundings is only through radiation. The final steady state temperature of the black bo... | <think>
Alright, let's try to figure out this problem step by step. So, we have a spherical black body that's being illuminated by parallel rays of light with an intensity of 912 W/m². It's kept in surroundings at 300 K, and we need to find its final steady-state temperature. The options are given, so I can check if my... | 82 |
https://ia801305.us.archive.org/8/items/ProblemsInCalculusOfOneVariableI.A.Maron/Problems%20in%20Calculus%20of%20One%20Variable%20-%20I.%20A.%20Maron.pdf | 113 | [
"\"a) x+√xy+y=a\"",
"\"b) arc tan (y/x) = ln x² + y²\"",
"\"c) ex sin y-e-y cos x = 0\"",
"\"d) ey + xy = e; find yx at the point (0, 1)\""
] | NO ANSWER DETECTED | Find yx for the following implicit functions: (a) x+√xy+y=a; (b) arc tan (y/x) = ln x² + y²; (c) ex sin y-e-y cos x = 0; (d) ey + xy = e; find yx at the point (0, 1). | <think>
Alright, so I have to find yx for four different implicit functions. Hmm, I remember that yx usually denotes the derivative dy/dx, right? So, I need to use implicit differentiation for each of these equations. Let me try to take them one by one.
Starting with part (a): x + sqrt(xy) + y = a.
First, let me rewr... | 46 |
https://jeeadv.ac.in/past_qps/2014_1.pdf | 3 | [
"NO CHOICES AVAILABLE"
] | NO ANSWER DETECTED | A parallel plate capacitor has a dielectric slab of dielectric constant K between its plates that covers 1/3 of the area of its plates, as shown in the figure. The total capacitance of the capacitor is C while that of the portion with dielectric in between is C₁. When the capacitor is charged, the plate area covered by... | <think>
Alright, so I've got this problem about a parallel plate capacitor with a dielectric slab. Hmm, let me try to visualize it. The capacitor has two plates, and between them, there's a dielectric material covering only a portion of the area—specifically, one-third of the plate area. The rest is just air or vacuum,... | 102 |
https://www.asi.edu.au/wp-content/uploads/2022/12/2009-asoe-chemistry-exam.pdf | 8 | [
"\"A 1:1\"",
"\"B 1:2\"",
"\"C 2:1\"",
"\"D 1:4\"",
"\"E 4:1\""
] | NO ANSWER DETECTED | A gaseous mixture containing ethane and methane underwent complete combustion to produce 5.28 g of carbon dioxide and 3.78 g of water. What is the volume ratio of ethane to methane in the original mixture?
A 1:1
B 1:2
C 2:1
D 1:4
E 4:1 | <think>
Alright, so I have this problem where a gaseous mixture of ethane and methane undergoes complete combustion, producing some carbon dioxide and water. I'm given the masses of those products and need to find the volume ratio of ethane to methane in the original mixture. The options are A through E, with various r... | 134 |
https://jeeadv.ac.in/past_qps/2011_1.pdf | 20 | [
"\"3\""
] | NO ANSWER DETECTED | Four point charges, each of +q, are rigidly fixed at the four corners of a square planar soap film of side 'a'. The surface tension of the soap film is y. The system of charges and planar film are in equilibrium, and a = k / N² where 'k' is a constant. Then N is...
Then N is... | <think>
Alright, so I have this problem where four point charges, each of charge +q, are fixed at the four corners of a square soap film. The soap film has a surface tension y and side length a. The system is in equilibrium, and it's given that a equals k divided by N squared, where k is a constant. I need to find what... | 50 |
https://ia801305.us.archive.org/8/items/ProblemsInCalculusOfOneVariableI.A.Maron/Problems%20in%20Calculus%20of%20One%20Variable%20-%20I.%20A.%20Maron.pdf | 287 | [
"NO CHOICES AVAILABLE"
] | NO ANSWER DETECTED | Prove the equality
\[
\int_{-a}^{a} f(x) \, dx = \int_{0}^{a} [f(x) + f(-x)] \, dx
\]
for any continuous function \( f(x) \).
Consider the integral
\[
\int_{-a}^{a} f(x) \, dx = \int_{0}^{a} [f(x) + f(-x)] \, dx
\]
for any continuous function \( f(x) \). | <think>
Okay, so I need to prove that the integral from -a to a of f(x) dx is equal to the integral from 0 to a of [f(x) + f(-x)] dx for any continuous function f(x). Hmm, interesting. I remember that integrals have some properties related to symmetry, especially when dealing with even and odd functions, but I don't kn... | 142 |
https://ia801305.us.archive.org/8/items/ProblemsInCalculusOfOneVariableI.A.Maron/Problems%20in%20Calculus%20of%20One%20Variable%20-%20I.%20A.%20Maron.pdf | 287 | [
"NO CHOICES AVAILABLE"
] | NO ANSWER DETECTED | The integrand \( x^4 \sin x \) is being considered over the interval \([-7, 7]\). It is important to note that \( x^4 \) is an even function, while \( \sin x \) is an odd function. Thus, the product \( x^4 \sin x \) results in an odd function overall when integrating over a symmetric interval around zero.
Compute the ... | <think>
Okay, so I've got this integral to compute: the integral from -7 to 7 of x^4 times sin x dx. Hmm, that sounds a bit tricky, but maybe I can figure it out by thinking about the properties of the functions involved.
First off, I remember that integrating over symmetric intervals can sometimes be easier if the fu... | 172 |
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