JEE Main 2024 31 Jan Shift 1 Question Paper (Available)- Download Solution PDF with Answer Key

JEE Main Question with Answer Key and Solution

Question 1:

For 0 < c < b < a, let (a + b − 2c)x² + (b + c − 2a)x + (c + a − 2b) = 0, and α = −1 be one of its roots. Which of the following statements is true?

• (1) Both (I) and (II) are true
• (2) Neither (I) nor (II) is true
• (3) Only (I) is true
• (4) Only (II) is true

Let a be the sum of all coefficients in the expansion of (1 − 2x + 2x²)²⁰²³(3 − 4x² + 2x³)²⁰²⁴. If the equations cx² + dx + e = 0 and 2bx² + ax + 4 = 0 have a common root, then c : d : e equals:

• (1) 2 : 1 : 4
• (2) 4 : 1 : 4
• (3) 1 : 2 : 4
• (4) 1 : 1 : 4

If the foci of a hyperbola are the same as that of the ellipse x²/9 + y²/25 = 1 and the eccentricity of the hyperbola is 15/8 times the eccentricity of the ellipse, then the smaller focal distance is:

• (1) 7
• (2) 14
• (3) 14
• (4) 7

If one of the diameters of the circle x² + y² − 10x + 4y + 13 = 0 is a chord of another circle C, whose center is the point of intersection of the lines 2x + 3y = 12 and 3x − 2y = 5, then the radius of circle C is:

• (1) √20
• (2) 4
• (3) 6
• (4) 3√5

The area of the region defined by y² ≤ 4x, x < 4, and xy(x − 1)(x − 2)(x − 3)(x − 4) > 0 is:

• (1) 16/3
• (2) 64/3
• (3) 8/3
• (4) 32/3

If f(x) = (4x + 3)/(6x − 4), with x ≠ 2/3, and (f ◦ f)(x) = g(x), where g: R − {2/3} → R − {2/3}, then (g ◦ g ◦ g)(4) is equal to:

• (1) 19/20
• (2) 19/20
• (3) −4
• (4) 4

Evaluate the limit:

lim (x → 0) [(e^(2|sin(x)|) - 2|sin(x)| - 1) / x²]

• (1) is equal to -1
• (2) does not exist
• (3) is equal to 1
• (4) is equal to 2

If the system of linear equations:

	x − 2y + z = −4  
	2x + alpha*y + 3z = 5  
	3x − y + beta*z = 3  
		

has infinitely many solutions, then 12*alpha + 13*beta is equal to:

• (1) 60
• (2) 64
• (3) 54
• (4) 58

The solution curve of the differential equation:

	y (dx/dy) = x [(ln(x)) − (ln(y)) + 1], with x > 0, y > 0, passing through the point (e, 1)
		

• (1) |(ln(y))/x| = x
• (2) |(ln(y))/x| = y²
• (3) |(ln(x))/y| = y
• (4) 2|(ln(x))/y| = y + 1

Let alpha, beta, gamma, delta ∈ Z and let A(alpha, beta), B(1, 0), C(gamma, delta), and D(1, 2) be the vertices of a parallelogram ABCD. If AB = sqrt(10) and the points A and C lie on the line 3y = 2x + 1, then 2(alpha + beta + gamma + delta) is equal to:

• (1) 10
• (2) 5
• (3) 12
• (4) 8

Let ⃗a = 3ˆi + ˆj − 2 ˆk, ⃗b = 4ˆi + ˆj + 7ˆk and ⃗c = ˆi − 3ˆj + 4ˆk be three vectors. If a vector ⃗p satisfies ⃗p ×⃗b = ⃗c ×⃗b and ⃗p · ⃗a = 0, then ⃗p · (ˆi − ˆj − ˆk) is equal to:

• (1) 24
• (2) 36
• (3) 28
• (4) 32

The sum of the series:

(1 / [1 - 3·(1²) + 1⁴]) + (2 / [1 - 3·(2²) + 2⁴]) + (3 / [1 - 3·(3²) + 3⁴]) + ... up to 10 terms

• (1) 45/109
• (2) -45/109
• (3) 55/109
• (4) -55/109

The distance of the point Q(0, 2, −2) from the line passing through the point P(5, −4, 3) and perpendicular to the lines ⃗r = (−3⃗i + 2⃗k) + λ(2⃗i + 3⃗j + 5⃗k), λ ∈ R and ⃗r = (⃗i − 2⃗j + ⃗k) + μ(−⃗i + 3⃗j + 2⃗k), μ ∈ R is:

• (1) √86
• (2) √20
• (3) √54
• (4) √74

For α, β, γ ≠ 0. If sin⁻¹(α) + sin⁻¹(β) + sin⁻¹(γ) = π and (α + β + γ)(α − γ + β) = 3αβ, then γ is equal to:

• (1) √3 / 2
• (2) √1 / 2
• (3) (√3 − 1) / 2√2
• (4) √3

Two marbles are drawn in succession from a box containing 10 red, 30 white, 20 blue, and 15 orange marbles, with replacement being made after each drawing. Then the probability that the first drawn marble is red and the second drawn marble is white is:

• (1) 2 / 25
• (2) 4 / 25
• (3) 2 / 3
• (4) 4 / 75

If f(x) = x³ + 2x² + 1 + 3x, then 2f(0) + f′(0) is equal to:

• (1) 48
• (2) 24
• (3) 42
• (4) 18

Three rotten apples are accidentally mixed with fifteen good apples. Assuming the random variable x to be the number of rotten apples in a draw of two apples, the variance of x is:

• (1) 37 / 153
• (2) 57 / 153
• (3) 47 / 153
• (4) 40 / 153

Let S be the set of positive integral values of a for which ax² + 2(a + 1)x + 9a + 4 / x² − 8x + 32 < 0, ∀x ∈ R.
Then, the number of elements in S is:

• (1) 1
• (2) 0
• (3) ∞
• (4) 3

If I = ∫ from 0 to π/2 of (5 sin²x cos^(11/2) x) / (1 + cos^(5/2) x)^(1/2) dx, then n in I = n√2 − 64 is:

• (1) 176
• (2) 150
• (3) 100
• (4) 80

If f(x) = x³ + 2x² + 1 + 3x, then 2f(0) + f′(0) is equal to:

• (1) 48
• (2) 24
• (3) 42
• (4) 18

Three rotten apples are accidentally mixed with fifteen good apples. Assuming the random variable x to be the number of rotten apples in a draw of two apples, the variance of x is:

• (1) 37 / 153
• (2) 57 / 153
• (3) 47 / 153
• (4) 40 / 153

Let S be the set of positive integral values of a for which ax² + 2(a + 1)x + 9a + 4 / x² − 8x + 32 < 0, ∀x ∈ R.
Then, the number of elements in S is:

• (1) 1
• (2) 0
• (3) ∞
• (4) 3

If I = ∫ from 0 to π/2 of (5 sin²x cos^(11/2) x) / (1 + cos^(5/2) x)^(1/2) dx, then n in I = n√2 − 64 is:

• (1) 176
• (2) 150
• (3) 100
• (4) 80

Let S = (−1, ∞) and f: S → R be defined as:
f(x) = ∫ from −1 to x of (e^t − 1)^(11) (2t − 1)^5 (t − 2)^7 (t − 3)^12 (2t − 10)^61 dt.
Let p be the sum of squares of the values of x where f(x) attains local maxima and q be the sum of the values of x where f(x) attains local minima. Then, the value of p² + 2q is:

• (1) 16
• (2) 27
• (3) 36
• (4) 40

The total number of words (with or without meaning) that can be formed out of the letters of the word 'DISTRIBUTION' taken four at a time is:

• (1) 3734
• (2) 4000
• (3) 3500
• (4) 4500

Let Q and R be the feet of perpendiculars from the point P(a, a, a) on the lines x = y, z = 1 and x = −y, z = −1 respectively. If ∠QPR is a right angle, then 12a² is equal to:

• (1) 12
• (2) 18
• (3) 24
• (4) 30

In the expansion of (1 + x)(1 − x²)^(1 + 3x + 3x² + 1x³), x ≠ 0, the sum of the coefficient of x² and x^−13 is equal to:

• (1) 118
• (2) 108
• (3) 125
• (4) 130

If α denotes the number of solutions of |1 − i|^x = 2^x and β = |z| arg(z), where z = −π/4 (1 + i)^4, 1 − √πi, √π + i, 1 + √πi, i = √−1, then the distance of the point (α, β) from the line 4x − 3y = 7 is:

• (1) 2
• (2) 3
• (3) 4
• (4) 5

Let the foci and length of the latus rectum of an ellipse x²/a² + y²/b² = 1, a > b be (±5, 0) and √50, respectively. Then, the square of the eccentricity of the hyperbola x²/b² − y²/a²b² = 1 equals:

• (1) 51
• (2) 48
• (3) 50
• (4) 45

Let ⃗a and ⃗b be two vectors such that |⃗a| = 1, |⃗b| = 4 and ⃗a · ⃗b = 2. If ⃗c = (2⃗a × ⃗b) − 3⃗b and the angle between ⃗b and ⃗c is α, then 192 sin²(α) is equal to:

• (1) 48
• (2) 54
• (3) 60
• (4) 72

Let A = {1, 2, 3, 4} and R = {(1, 2), (2, 3), (1, 4)} be a relation on A. Let S be the equivalence relation on A such that R ⊂ S and the number of elements in S is n. Then, the minimum value of n is:

• (1) 16
• (2) 18
• (3) 20
• (4) 24

Let f: R → R be a function defined by f(x) = 4x / (4x + 2) and M = ∫ f(1−a) to f(a) x sin⁴(x(1 − x)) dx, N = ∫ f(1−a) to f(a) sin⁴(x(1 − x)) dx; a ≠ 1/2.
If αM = βN, α, β ∈ N, then the least value of α² + β² is equal to:

• (1) 5
• (2) 10
• (3) 8
• (4) 7

The parameter that remains the same for molecules of all gases at a given temperature is:

• (1) Kinetic energy
• (2) Momentum
• (3) Mass
• (4) Speed

Identify the logic operation performed by the given circuit.

• (1) NAND
• (2) NOR
• (3) OR
• (4) AND

The relation between time t and distance x is t = αx² + βx, where α and β are constants. The relation between acceleration (a) and velocity (v) is:

• (1) a = −2αv³
• (2) a = −5αv³
• (3) a = −3αv²
• (4) a = −4αv³

The refractive index of a prism with apex angle A is cot(A/2). The angle of minimum deviation is:

• (1) δm = 180° − A
• (2) δm = 180° − 3A
• (3) δm = 180° − 4A
• (4) δm = 180° − 2A

A rigid wire consists of a semicircular portion of radius R and two straight sections. The wire is partially immersed in a perpendicular magnetic field B = B₀ ĵ. The magnetic force on the wire if it has a current i is:

• (1) −iBR ĵ
• (2) 2iBR ĵ
• (3) iBR ĵ
• (4) −2iBR ĵ

If the wavelength of the first member of the Lyman series of hydrogen is λ, the wavelength of the second member will be:

• (1) (27/32)λ
• (2) (32/27)λ
• (3) (27/5)λ
• (4) (5/27)λ

Four identical particles of mass m are kept at the four corners of a square. If the gravitational force exerted on one of the masses by the other masses is (2√2 + 1) Gm² / L², the length of the sides of the square is:

• (1) L/2
• (2) 4L
• (3) 3L
• (4) 2L

The given figure represents two isobaric processes for the same mass of an ideal gas. Then:

• (1) P₂ ≥ P₁
• (2) P₂ > P₁
• (3) P₁ = P₂
• (4) P₁ > P₂

If the percentage errors in measuring the length and the diameter of a wire are 0.1% each, the percentage error in measuring its resistance will be:

• (1) 0.2%
• (2) 0.3%
• (3) 0.1%
• (4) 0.144%

In a plane electromagnetic wave, the electric field oscillates sinusoidally at a frequency of 5 × 10¹⁰ Hz and an amplitude of 50 V/m. The total average energy density of the electromagnetic field of the wave is:

• (1) 1.106 × 10⁻⁸ J/m³
• (2) 4.425 × 10⁻⁸ J/m³
• (3) 2.212 × 10⁻⁸ J/m³
• (4) 2.212 × 10⁻¹⁰ J/m³

A force is represented by F = ax² + bt¹/² where x = distance and t = time. The dimensions of b² / a are:

• (1) [ML³T⁻³]
• (2) [MLT⁻²]
• (3) [ML²T⁻¹]
• (4) [MLT²]

Two charges q and 3q are separated by a distance r in air. At a distance x from charge q, the resultant electric field is zero. The value of x is:

• (1) (1 + √3) r / 3
• (2) r / 3 (1 + √3)
• (3) r (1 + √3)
• (4) r (1 + √3) / 3

In the given arrangement of a doubly inclined plane, two blocks of masses M and m are placed. The blocks are connected by a light string passing over an ideal pulley as shown. The coefficient of friction between the surface of the plane and the blocks is 0.25. The value of m, for which M = 10 kg will move down with an acceleration of 2 m/s², is:

• (1) 9 kg
• (2) 4.5 kg
• (3) 6.5 kg
• (4) 2.25 kg

A coil is placed perpendicular to a magnetic field of 5000 T. When the field is changed to 3000 T in 2s, an induced emf of 22 V is produced in the coil. If the diameter of the coil is 0.02 m, then the number of turns in the coil is:

• (1) 7
• (2) 70
• (3) 35
• (4) 140

The fundamental frequency of a closed organ pipe is equal to the first overtone frequency of an open organ pipe. If the length of the open pipe is 60 cm, the length of the closed pipe will be:

• (1) 60 cm
• (2) 45 cm
• (3) 30 cm
• (4) 15 cm

A small steel ball is dropped into a long cylinder containing glycerine. Which one of the following is the correct representation of the velocity-time graph for the transit of the ball?

• (1) Linear
• (2) Exponential
• (3) Parabolic
• (4) Constant

A coin is placed on a disc. The coefficient of friction between the coin and the disc is μ. If the distance of the coin from the center of the disc is r, the maximum angular velocity which can be given to the disc, so that the coin does not slip away, is:

• (1) μg / r
• (2) √r μg
• (3) π μg / r
• (4) μ √rg

The depth below the surface of the sea to which a rubber ball can be taken so as to decrease its volume by 0.02% is:

• (1) 18 m
• (2) 20 m
• (3) 25 m
• (4) 30 m

A particle performs simple harmonic motion with amplitude A. Its speed is increased to three times at an instant when its displacement is 2A/3. The new amplitude of motion is nA/3. The value of n is:

• (1) 7
• (2) 6
• (3) 5
• (4) 4

A capacitor of capacitance 2 μF is connected across a 100 V battery. It is then disconnected and connected in parallel with another uncharged capacitor of capacitance 6 μF. The common potential across the capacitors is:

• (1) 20 V
• (2) 25 V
• (3) 30 V
• (4) 40 V

A thin lens made of material of refractive index 1.5 has focal length f in air. Its focal length in a medium of refractive index 1.3 will be:

• (1) f × 0.5
• (2) f × 1.5
• (3) f × 1.3
• (4) f × 2.5

A projectile is fired from the ground with an initial speed of 50 m/s at an angle of 30° with the horizontal. The maximum height attained by the projectile is:

• (1) 31.25 m
• (2) 25 m
• (3) 50 m
• (4) 37.5 m

A wire of length L and radius r has resistance R. The resistance of another wire of the same material with length 2L and radius 2r will be:

• (1) R / 2
• (2) R / 4
• (3) R
• (4) R / 8

The depth below the surface of the sea to which a rubber ball can be taken so as to decrease its volume by 0.02% is:

• (1) 18 m
• (2) 20 m
• (3) 25 m
• (4) 30 m

A particle performs simple harmonic motion with amplitude A. Its speed is increased to three times at an instant when its displacement is 2A/3. The new amplitude of motion is nA/3. The value of n is:

• (1) 7
• (2) 6
• (3) 5
• (4) 4

The mass defect in a particular reaction is 0.4 g. The amount of energy liberated is n × 10^7 kWh, where n =:

• (1) 1
• (2) 2
• (3) 3
• (4) 4

Given below are two statements:
Statement-I: Noble gases have very high boiling points.
Statement-II: Noble gases are monoatomic gases. They are held together by strong dispersion forces. Because of this, they are liquefied at very low temperature. Hence, they have very high boiling points.

In the light of the above statements, choose the correct answer:

• (1) Statement I is false but Statement II is true.
• (2) Both Statement I and Statement II are true.
• (3) Statement I is true but Statement II is false.
• (4) Both Statement I and Statement II are false.

For the given reaction, choose the correct expression of Kc from the following:
Fe^3+ (aq) + SCN^- (aq) ⇌ (FeSCN)^2+ (aq)

• (1) Kc = [FeSCN^2+] / [Fe^3+][SCN^-]
• (2) Kc = [Fe^3+][SCN^-] / [FeSCN^2+]
• (3) Kc = [FeSCN^2+]^2 / [Fe^3+][SCN^-]
• (4) Kc = [FeSCN^2+] / [Fe^3+]^2[SCN^-]

Identify the mixture that shows positive deviations from Raoult’s Law:

• (1) (CH3)2CO + C6H5NH2
• (2) CHCl3 + C6H6
• (3) CHCl3 + (CH3)2CO
• (4) (CH3)2CO + CS2

The compound that is white in color is:

• (1) Ammonium sulphide
• (2) Lead sulphate
• (3) Lead iodide
• (4) Ammonium arsnomolybdate

The metals that are employed in the battery industries are:

• A. Fe
• B. Mn
• C. Ni
• D. Cr
• E. Cd

Choose the correct answer from the options given below:

• (1) B, C and E only
• (2) A, B, C, D and E
• (3) A, B, C and D only
• (4) B, D and E only

A species having carbon with a sextet of electrons and can act as an electrophile is called:

• (1) Carbon free radical
• (2) Carbanion
• (3) Carbocation
• (4) Pentavalent carbon

Identify the factor from the following that does not affect electrolytic conductance of a solution:

• (1) The nature of the electrolyte added
• (2) The nature of the electrode used
• (3) Concentration of the electrolyte
• (4) The nature of solvent used

The product (C) in the below-mentioned reaction is:

CH3−CH2−CH2−Br (KOH aqueous, heat) → A → (HBr) → B → (KOH alcoholic, heat) → C

• (1) Propan-1-ol
• (2) Propene
• (3) Propyne
• (4) Propan-2-ol

Given below are two statements: One is labelled as Assertion A and the other as Reason R:

Assertion A: Alcohols react both as nucleophiles and electrophiles.

Reason R: Alcohols react with active metals such as sodium, potassium, and aluminum to yield corresponding alkoxides and liberate hydrogen.

Choose the correct answer from the options given below:

• (1) A is false but R is true
• (2) A is true but R is false
• (3) Both A and R are true and R is the correct explanation of A
• (4) Both A and R are true but R is NOT the correct explanation of A

The correct sequence of electron gain enthalpy of the elements listed below is:

• A. Ar
• B. Br
• C. F
• D. S

Choose the most appropriate from the options given below:

• (1) C > B > D > A
• (2) A > D > B > C
• (3) A > D > C > B
• (4) D > C > B > A

Identify correct statements from below:

• A. The chromate ion is square planar
• B. Dichromates are generally prepared from chromates
• C. The green manganate ion is diamagnetic
• D. Dark green coloured K2MnO4 disproportionates in a neutral or acidic medium to give permanganate
• E. With increasing oxidation number of transition metal, ionic character of the oxides decreases

Choose the correct answer from the options given below:

• (1) B, C, D only
• (2) A, D, E only
• (3) A, B, C only
• (4) B, D, E only

'Adsorption' principle is used for which of the following purification methods?

• (1) Extraction
• (2) Chromatography
• (3) Distillation
• (4) Sublimation

Integrated rate law equation for a first order gas phase reaction is given by (where Pi is initial pressure and Pt is total pressure at time t):

• (1) k = 2.303 / t × log (Pi / (2Pi − Pt))
• (2) k = 2.303 / t × log (2Pi / (2Pi − Pt))
• (3) k = 2.303 / t × log ((2Pi − Pt) / Pi)
• (4) k = 2.303 / t × (Pi / (2Pi − Pt))

Given below are two statements: One is labelled as Assertion (A) and the other is labelled as Reason (R):

Assertion A: pKa value of phenol is 10.0 while that of ethanol is 15.9.

Reason R: Ethanol is stronger acid than phenol.

Choose the correct answer from the options given below:

• (1) A is true but R is false.
• (2) A is false but R is true.
• (3) Both A and R are true and R is the correct explanation of A.
• (4) Both A and R are true but R is NOT the correct explanation of A.

Given below are two statements:

Statement I: IUPAC name of HO–CH2–(CH2)3–CH2–COCH3 is 7-hydroxyheptan-2-one.

Statement II: 2-oxoheptan-7-ol is the correct IUPAC name for the above compound.

Choose the most appropriate answer from the options given below:

• (1) Statement I is correct but Statement II is incorrect.
• (2) Both Statement I and Statement II are incorrect.
• (3) Both Statement I and Statement II are correct.
• (4) Statement I is incorrect but Statement II is correct.

The correct statements from the following are:

• A. The strength of anionic ligands can be explained by crystal field theory.
• B. Valence bond theory does not give a quantitative interpretation of kinetic stability of coordination compounds.
• C. The hybridization involved in the formation of [Ni(CN)4]2− complex is dsp2.
• D. The number of possible isomer(s) of cis-[PtCl2(en)2]2+ is one.

Choose the correct answer from the options given below:

• (1) A, D only
• (2) A, C only
• (3) B, D only
• (4) B, C only

The linear combination of atomic orbitals to form molecular orbitals takes place only when the combining atomic orbitals:

• A. have the same energy
• B. have the minimum overlap
• C. have the same symmetry about the molecular axis
• D. have different symmetry about the molecular axis

Choose the most appropriate answer from the options given below:

• (1) A, B, C only
• (2) A and C only
• (3) B, C, D only
• (4) B and D only

Match List I with List II:

List I:

• A. Glucose/NaHCO3/Δ
• B. Glucose/HNO3
• C. Glucose/HI/Δ
• D. Glucose/Bromine water

List II:

• I. Gluconic acid
• II. No reaction
• III. n-hexane
• IV. Saccharic acid

Choose the correct answer from the options given below:

• (1) A-IV, B-I, C-III, D-II
• (2) A-II, B-IV, C-III, D-I
• (3) A-III, B-II, C-I, D-IV
• (4) A-I, B-IV, C-III, D-II

Consider the oxides of group 14 elements SiO2, GeO2, SnO2, PbO2, CO, and GeO.

The amphoteric oxides are:

• (1) GeO, GeO2
• (2) SiO2, GeO2
• (3) SnO2, PbO2
• (4) SiO2, CO

Match List I with List II:

List I (Technique):

• A. Distillation
• B. Fractional distillation
• C. Steam distillation
• D. Distillation under reduced pressure

List II (Application):

• I. Separation of glycerol from spent-lye
• II. Aniline - Water mixture
• III. Separation of crude oil fractions
• IV. Chloroform - Aniline

Choose the correct answer from the options given below:

• (1) A-IV, B-I, C-II, D-III
• (2) A-IV, B-III, C-II, D-I
• (3) A-I, B-II, C-IV, D-III
• (4) A-II, B-III, C-I, D-IV

Molar mass of the salt from NaBr, NaNO3, KI, and CaF2 which does not evolve colored vapours on heating with concentrated H2SO4 is:

• (1) 78 g/mol
• (2) 88 g/mol
• (3) 98 g/mol
• (4) 108 g/mol

The 'Spin only' Magnetic moment for [Ni(NH3)6]2+ is × 10⁻¹ BM. (given Atomic number of Ni: 28)

• (1) 28
• (2) 30
• (3) 32
• (4) 34

The product of the following reaction is P.
CH₃–CH₂–CH₂–Br (KOH(aq), Δ) → A
HBr → B
KOH(alc), Δ → C

• (1) Propan-1-ol
• (2) Propene
• (3) Propyne
• (4) Propan-2-ol

The number of species from the following in which the central atom uses sp³ hybrid orbitals in its bonding is:
NH₃, SO₂, SiO₂, BeCl₂, CO₂, H₂O, CH₄, BF₃

• (1) 4
• (2) 3
• (3) 5
• (4) 6

The total number of hydrogen atoms in Product A and Product B is:

• (1) 8
• (2) 9
• (3) 10
• (4) 11

Number of alkanes obtained on electrolysis of a mixture of CH₃COONa and C₂H₅COONa is:

• (1) 2
• (2) 3
• (3) 4
• (4) 5

Consider the following reaction at 298 K:
3/2 O₂(g) → O₃(g), Kp = 2.47 × 10⁻²⁹.
ΔG° for the reaction is kJ. (Given R = 8.314 J K⁻¹ mol⁻¹)

• (1) 150
• (2) 163
• (3) 175
• (4) 190

The ionization energy of sodium in kJ/mol. If electromagnetic radiation of wavelength 242 nm is just sufficient to ionize sodium atom, what is the ionization energy?

• (1) 450
• (2) 470
• (3) 494
• (4) 510

One Faraday of electricity liberates x × 10⁻¹ gram atom of copper from copper sulphate, x is:

• (1) 4
• (2) 5
• (3) 6
• (4) 7