## Questions and Answers

If A denotes the sum of all the coefficients in the expansion of (1 – 3x + 10x^2)^n and B denotes the sum of all the coefficients in the expansion of (1 + x^2)^n, then:

The number of common terms in the progressions 4, 9, 14, 19, ...... up to the 25th term and 3, 6, 9, 12, ...... up to 37th term is:

7

If the shortest distance of the parabola y^2 = 4x from the centre of the circle x^2 + y^2 – 4x – ______y + 64 = 0 is d, then d^2 is equal to:

16

If the shortest distance between the lines x − 4y + z = 0 and x − λy + z − 2 = 0 is trisected, then the sum of all possible values of λ is:

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If ∫(3 + x + 1/x + x^2) dx = a + b/2 + c/3, where a, b, c are rational numbers, then 2a + 3b – 4c is equal to:

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The intensity of the plane electromagnetic wave described by Ey = (200 Vm–1) sin[1.5 × 107t – 0.05 x] in the x-direction is:

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In the statements, which one is true?

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If a resistance of 4.5 Ω is connected on the left gap of a meter bridge, and the balance length is found to be at 60 cm from the left end, what is the value of the resistivity of the wire?

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The resultant resistance when a wire of resistance R and length L is cut into 5 equal parts and joined parallelly will be ____.

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At what temperature will the average kinetic energy of a monatomic molecule be 0.414 eV?

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Given the statements, which is the most appropriate answer?

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Then m + n is equal to

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Cyclohexene is what type of organic compound?

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The function f : N – {1} → N; defined by f(n) =

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What is the product formed when yellow compound of lead chromate gets dissolved in hot NaOH solution?

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Carbonate is basic.

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What is the least positive integral value of α for which the angle between the vectors αi − 2j + 2k and αi + 2αj − 2k is acute?

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Which statement is true about the viscosity of gases and surface tension of liquids?

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Salt of weak acid and weak base forming a solution can be acidic or basic.

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Calculate the magnitude and direction of the velocity for an ant moving in the Y-Z plane at t = 1s, given S = 2t^2j + 5k

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The mass of silver displaced by a quantity of electricity that displaces 5600 mL of O2 at S.T.P will be _____ g.

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What is the electronic configuration for Neodymium?

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If the refractive index of a prism material is given by cot(A/2), what is the angle of minimum deviation?

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Which circuit is reverse-biased?

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Match the following:

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What physical quantity cannot be measured using a spherometer?

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What is the mass of methane required to produce 22 g of CO2 after complete combustion?

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What is the change in internal energy when 0.08 kg of air is heated at constant volume through 5°C?

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If three moles of an ideal gas at 300 K expand against a constant opposing pressure of 80 kPa, then the amount of heat transferred is ______ J.

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What is the radius of the third stationary orbit of an electron for Bohr's atom if the radius of the fourth stationary orbit is R?

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## Study Notes

### JEE-Main Examination - January 2024

### Mathematics

- Section A:
- Question 1: 'k' values for Cr = (k^2 - 8)n Cr+1
- Question 2: Distance of a point from a line
- Question 3: Differential equations of x(t) and y(t)
- Question 4: Orthocentre of a triangle
- Question 5: Sum of coefficients in expansions of (1-3x+10x^2)^n and (1+x^2)^n
- Question 6: Number of common terms in two arithmetic progressions
- Question 7: Shortest distance of a parabola from a circle
- Question 8: Shortest distance between two lines
- Question 9: Value of 'd' in the equation ∫(x^2 + y^2) dx = a + b^2 + c^3
- Question 10: Properties of a relation R in a set M

- Section B:
- Question 11: Solution set of |z-i| = |z+i| = |z-1|
- Question 12: Circle passing through four points
- Question 13: Continuity of a function
- Question 14: Standard deviation of a set of observations
- Question 15: Length of a chord of an ellipse
- Question 16: Tangent of an angle in a triangle
- Question 17: Vector equation of a line
- Question 18: Limit of a function as x approaches 0
- Question 19: Properties of a matrix
- Question 20: Function f(n) = highest prime factor of n
- Question 21: Angle between two vectors
- Question 22: Solution of a differential equation
- Question 23: Solution of a differential equation
- Question 24: Area of a region bounded by curves
- Question 25: Value of 'p' in a geometric progression
- Question 26: Probability of getting a six in repeated tosses of a die
- Question 27: Solution of an equation in terms of 'p' and 'q'
- Question 28: Value of a series
- Question 29: Properties of a matrix
- Question 30: Solution of an equation in terms of 'A', 'B', and 'C'

- Section A (continued):
- Question 31: Position of an ant moving in the Y-Z plane
- Question 32: Viscosity of gases and surface tension of liquids
- Question 33: Refractive index of a prism
- Question 34: Force on a proton in an electric and magnetic field
- Question 35: Acceleration due to gravity on the surface of the earth
- Question 36: Height of a rail to negotiate a curve
- Question 37: Reverse-biased circuit
- Question 38: (Not provided)
- Question 39: (Not provided)
- Question 40: (Not provided)

### Physics

- Question 34: Electric and magnetic fields
- Question 35: Acceleration due to gravity on the surface of the earth
- Question 36: Height of a rail to negotiate a curve
- Question 37: Reverse-biased circuit
- Question 42: Magnetic field and a rectangular loopHere are the study notes for the text:

### Physics

- A body of mass 1000 kg is moving horizontally with a velocity of 6 m/s. If 200 kg extra mass is added, the final velocity is [4 options].
- A plane electromagnetic wave propagating in the x-direction is described by Ey = (200 V/m) sin[1.5 x 10^7t - 0.05x]. The intensity of the wave is [4 options].
- A thin metallic wire having a cross-sectional area of 10^-4 m^2 is used to make a ring of radius 30 cm. A positive charge of 2π C is uniformly distributed over the ring, while another positive charge of 30 pC is kept at the center of the ring. The tension in the ring is [answer].
- A wire of length 10 cm and radius 7 x 10^-4 m is connected across the right gap of a meter bridge. When a resistance of 4.5 Ω is connected on the left gap by using a resistance box, the balance length is found to be at 60 cm from the left end. If the resistivity of the wire is R x 10^-7 Ωm, then the value of R is [4 options].

### Chemistry

- Element not showing variable oxidation state is [4 options].
- Highest enol content will be shown by [4 options].
- A solution of two miscible liquids showing negative deviation from Raoult's law will have [4 options].
- A complex ion has the highest magnetic moment if it has [4 options].
- Choose the polar molecule from the following: [4 options].
- The ascending order of acidity of –OH group in the following compounds is [4 options].
- Statement I: The 4f and 5f-series of elements are placed separately in the Periodic table top reserve the principle of classification. Statement II: S-block elements can be found in pure form in nature. [4 options].

### Miscellaneous

- A wire of resistance R and length L is cut into 5 equal parts. If these parts are joined in parallel, then the resultant resistance will be [4 options].
- The average kinetic energy of a monatomic molecule is 0.414 eV at a temperature of [4 options].
- Two bodies of mass 4 g and 25 g are moving with equal kinetic energies. The ratio of the magnitude of their linear momentum is [4 options].
- A convex lens of focal length 40 cm forms an image of an extended source of light on a photoelectric cell. A current I is produced. The lens is replaced by another convex lens having the same diameter but focal length 20 cm. The photoelectric current now is [4 options].
- An electric charge 10^-6 µC is placed at the origin of an X-Y co-ordinate system. Two points P and Q are situated at (3, 3) m and (6, 0) m respectively. The potential difference between the points P and Q will be [4 options].

Let me know if you want me to clarify anything!### Acidic/Basic Nature of Salt

- The acidic/basic nature of a salt depends on the Ka and Kb values of the acid and base forming it.
- A salt of a weak acid and weak base can have an acidic or basic nature.

### SN1 and SN2 Reactions

- Racemisation occurs in SN1 reactions.
- Inversion occurs in SN2 reactions.

### Electronic Configuration of Neodymium

- The atomic number of Neodymium is 60.
- The electronic configuration of Neodymium is [Xe] 4f4 6s2.

### Displacement of Oxygen

- The mass of silver displaced by a quantity of electricity that displaces 5600 mL of O2 at S.T.P. is 11 g.

### Reaction Kinetics

- The order of the reaction 2HI(g) → H2(g) + I2(g) is determined by the rate of reaction at different concentrations of HI.

### Combustion of Methane

- The mass of methane required to produce 22 g of CO2 after complete combustion is dependent on the molar masses of C, H, and O.

### Thermodynamic Processes

- Three moles of an ideal gas at 300 K expand isothermally from 30 dm3 to 45 dm3 against a constant opposing pressure of 80 kPa.
- The amount of heat transferred in this process is dependent on the initial and final volumes of the gas.

### Organic Compounds

- 3-Methylhex-2-ene reacts with HBr in the presence of peroxide to form an addition product.
- The number of possible stereoisomers for the product is dependent on the structure of 3-Methylhex-2-ene.

### Bond Order

- The sum of bond order of CO and NO+ is a specific value.

### Oxidation State of Sulphur

- The number of compounds with +4 oxidation state of Sulphur from the given list (SO3, H2SO3, SOCl2, SF4, BaSO4, H2S2O7) is specific.

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## Description

Solve this JEE Main mathematics test paper from January 2024. Questions cover various math topics.