Let the line L intersect the lines:

x − 2 = −y = z − 1, 2(x + 1) = 2(y − 1) = z + 1, and be parallel to the line: (x − 2)/3 = (y − 1)/1 = (z − 2)/2. Then which of the following points lies on L?

1. (1/3, -1, 1)
2. (-1/3, 1, -1)
3. (-1/3, -1, -1)
4. (-1/3, -1, 1)

Question 2:

The parabola y² = 4x divides the area of the circle x² + y² = 5 in two parts. The area of the smaller part is:

1. 2/3 + 5 sin⁻¹(2√5)
2. 1/3 + 5 sin⁻¹(2√5)
3. 1/3 + √5 sin⁻¹(2√5)
4. 2/3 + √5 sin⁻¹(2√5)

Question 3:

The solution curve of the differential equation 2y (dy/dx) + 3 = 5 (dy/dx), passing through the point (0, 1), is a conic whose vertex lies on the line:

1. 2x + 3y = 9
2. 2x + 3y = −9
3. 2x + 3y = −6
4. 2x + 3y = 6

Question 4:

A ray of light coming from P(1, 2) reflects from Q on the x-axis and passes through R(4, 3). If S(h, k) makes PQRS a parallelogram, then hk² equals:

1. 80
2. 90
3. 60
4. 70

Question 5:

For λ, μ ∈ R, if the system of equations 3x + 5y + λz = 3, 7x + 11y − 9z = 2, 97x + 155y − 189z = μ has infinitely many solutions, then μ + 2λ equals:

1. 25
2. 24
3. 27
4. 22

Question 6:

The coefficient of x⁷⁰ in x²(1 + x)⁹⁸ + x³(1 + x)⁹⁷ + ... + x⁵⁴(1 + x)⁴⁶ is (99Cp) − (46Cq). A possible value of p + q is:

1. 55
2. 61
3. 68
4. 83

Question 7:

If ∫ (2 − tanx)/(3 + tanx) dx = (1/2)(αx + loge|β sinx + γ cosx|) + C, then α + γ/β equals:

1. 3
2. 1
3. 4
4. 7

Question 8:

A variable line passes through (3, 5) and intersects the positive axes at A and B. The minimum area of triangle OAB is:

1. 30
2. 25
3. 40
4. 35

Question 9:

If |cosθ cos(60° − θ) cos(60° + θ)| ≤ 1/8, θ ∈ [0, 2π], then the sum of all θ where cos3θ attains its maximum value is:

1. 9π
2. 18π
3. 6π
4. 15π

Question 10:

Let OA = 2a, OB = 6a + 5b, and OC = 3b. If the area of the parallelogram with sides OA and OC is 15 sq. units, the area of quadrilateral OABC is:

1. 38
2. 40
3. 32
4. 35

Question 11:

If the domain of the function f(x) = sin⁻¹((x−1)/(2x+3)) is R−(α, β), then 12αβ is equal to:

1. 36
2. 24
3. 40
4. 32

Question 12:

If the sum of the series 1/(1 · (1 + d)) + 1/((1 + d)(1 + 2d)) + ... + 1/((1 + 9d)(1 + 10d)) is equal to 5, then 50d is equal to:

1. 20
2. 5
3. 15
4. 10

Question 13:

Let f(x) = ax³ + bx² + cx + 41 be such that f(1) = 40, f'(1) = 2, and f''(1) = 4. Then a² + b² + c² is equal to:

1. 62
2. 73
3. 54
4. 51

Question 14:

Let a circle passing through (2, 0) have its center at the point (h, k). Let (xc, yc) be the point of intersection of the lines 3x + 5y = 1 and (2 + c)x + 5c²y = 1. If h = lim c→1 xc and k = lim c→1 yc, then the equation of the circle is:

1. 25x² + 25y² − 20x + 2y − 60 = 0
2. 5x² + 5y² − 4x − 2y − 12 = 0
3. 25x² + 25y² − 2x + 2y − 60 = 0
4. 5x² + 5y² − 4x + 2y − 12 = 0

Question 15:

The shortest distance between the lines (x−3)/4 = (y+7)/−11 = (z−1)/5 and (x−5)/3 = (y−9)/−6 = (z+2)/1 is:

1. 187√563
2. 178√563
3. 185√563
4. 179√563

Question 16:

The frequency distribution of the age of students in a class of 40 students is given below:

If the mean deviation about the median is 1.25, then 4x + 5y is equal to:

1. 43
2. 44
3. 47
4. 46

Question 17:

The solution of the differential equation (x² + y²)dx − 5xy dy = 0, y(1) = 0, is:

1. |x² − 4y²|⁵ = x²
2. |x² − 2y²|⁶ = x
3. |x² − 4y²|⁶ = x
4. |x² − 2y²|⁵ = x²

Question 18:

Let three vectors a = αî + 4ĵ + 2k̂, b = 5î + 3ĵ + 4k̂, c = xî + yĵ + zk̂, form a triangle such that c = a − b and the area of the triangle is 5√6. If α is a positive real number, then |c|² is:

1. 16
2. 14
3. 12
4. 10

Question 19:

Let α, β be the roots of the equation x² + 2√2x − 1 = 0. The quadratic equation whose roots are α⁴ + β⁴ and 1/10(α⁶ + β⁶) is:

1. x² − 190x + 9466 = 0
2. x² − 195x + 9466 = 0
3. x² − 195x + 9506 = 0
4. x² − 180x + 9506 = 0

Question 20:

Let f(x) = x² + 9, g(x) = x/(x − 9), and a = f(g(10)), b = g(f(3)). If e and ℓ denote the eccentricity and the length of the latus rectum of the ellipse x²/a² + y²/b² = 1, then 8e² + ℓ² is equal to:

1. 16
2. 8
3. 6
4. 12

Question 21:

Let a, b, c denote the outcomes of three independent rolls of a fair tetrahedral die, whose four faces are marked 1, 2, 3, 4. If the probability that ax² + bx + c = 0 has all real roots is m/n, where gcd(m, n) = 1, then m + n is equal to:

Question 22:

The sum of the square of the modulus of the elements in the set: {z = a + ib : a, b ∈ Z, z ∈ C, |z − 1| ≤ 1, |z − 5| ≤ |z − 5i|} is:

Question 23:

Let the set of all positive values of λ, for which the point of local minimum of the function:
f(x) = (1 + x(λ² − x²)) satisfies x² + x + 2 / x² + 5x + 6 < 0, be (α, β). Then α² + β² is equal to:

Question 24:

Let the following limit be equal to π/k, where k is an integer. Then k² is equal to:
Given:
lim n→∞ [n√(n⁴ + 1) − 2n(n² + 1)√(n⁴ + 1) + n√(n⁴ + 16) + ...]

Question 25:

The remainder when 428²⁰²⁴ is divided by 21 is:

Question 26:

Let f : (0, π) → R be a function given by:
f(x) =
8/7 * tan(8x) / tan(7x), 0 < x < π/2 a − 8, x = π/2 (1 + |cot(x)|) * (b/a) * tan(|x|), π/2 < x < π
where a, b ∈ Z. If f is continuous at x = π/2, find a² + b².

Question 27:

Let A be a non-singular matrix of order 3. If:
det(3adj(2adj((detA)A))) = 3⁻¹³ · 2⁻¹⁰, and:
det(3adj(2A)) = 2^m · 3^n, then |3m + 2n| is equal to:

Question 28:

Let the center of a circle, passing through the points (0, 0), (1, 0), and touching the circle x² + y² = 9, be (h, k). Then for all possible values of the coordinates of the center (h, k), 4(h² + k²) is equal to:

Question 29:

If a function f satisfies f(m + n) = f(m) + f(n) for all m, n ∈ N, and f(1) = 1, then the largest natural number λ such that:
Σ_k=1²⁰²² f(λ + k) ≤ (2022)², is equal to:

Question 30:

Let A = {2, 3, 6, 7} and B = {4, 5, 6, 8}. Let R be a relation defined on A × B by:
(a₁, b₁) R (a₂, b₂) ⇔ a₁ + a₂ = b₁ + b₂. Then the number of elements in R is:

Question 31:

A proton, an electron, and an alpha particle have the same energies. Their de-Broglie wavelengths will be compared as:

1. λe > λα > λp
2. λα < λp < λe
3. λp < λe < λα
4. λp > λe > λα

Question 32:

A particle moving in a straight line covers half the distance with speed 6 m/s. The other half is covered in two equal time intervals with speeds 9 m/s and 15 m/s, respectively. The average speed of the particle during the motion is:

1. 8.8 m/s
2. 10 m/s
3. 9.2 m/s
4. 8 m/s

Question 33:

A plane EM wave is propagating along the x-direction. It has a wavelength of 4 mm. If the electric field is in the y-direction with the maximum magnitude of 60 V/m, the equation for the magnetic field is:

1. Bz = 60 sin[π/2(x − 3 × 10⁸t)] k̂ T
2. Bz = 2 × 10⁻⁷ sin[π/2 × 10³(x − 3 × 10⁸t)] k̂ T
3. Bx = 60 sin[π/2(x − 3 × 10⁸t)] î T
4. Bz = 2 × 10⁻⁷ sin[π/2(x − 3 × 10⁸t)] k̂ T

Question 34:

Given below are two statements:

Statement (I): When currents vary with time, Newton’s third law is valid only if momentum carried by the electromagnetic field is taken into account.
Statement (II): Ampere’s circuital law does not depend on Biot-Savart’s law.

Choose the correct answer:

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

Question 35:

A light-emitting diode (LED) is fabricated using GaAs semiconducting material whose band gap is 1.42 eV. The wavelength of light emitted from the LED is:

1. 650 nm
2. 1243 nm
3. 875 nm
4. 1400 nm

Question 36:

A sphere of relative density σ and diameter D has a concentric cavity of diameter d. The ratio of D/d, if it just floats on water in a tank, is:

1. (σ / (σ − 1))^(1/3)
2. ((σ + 1) / (σ − 1))^(1/3)
3. ((σ − 1) / σ)^(1/3)
4. ((σ − 2) / (σ + 2))^(1/3)

Question 37:

A capacitor is made of a flat plate of area A and a second plate having a stair-like structure as shown in the figure. If the area of each stair is A/3 and the height is d, the capacitance of the arrangement is:

1. (11ϵ₀A) / (18d)
2. (13ϵ₀A) / (17d)
3. (11ϵ₀A) / (20d)
4. (18ϵ₀A) / (11d)

Question 38:

A light, unstretchable string passing over a smooth light pulley connects two blocks of masses m₁ and m₂. If the acceleration of the system is g/8, then the ratio of the masses m₂/m₁ is:

1. 9 : 7
2. 4 : 3
3. 5 : 3
4. 8 : 1

Question 39:

The dimensional formula of latent heat is:

1. [M₀L T⁻²]
2. [MLT⁻²]
3. [M₀L²T⁻²]
4. [ML²T²]

Question 40:

The volume of an ideal gas (γ = 1.5) is changed adiabatically from 5 litres to 4 litres. The ratio of initial pressure to final pressure is:

1. 4/5
2. 16/25
3. 8/5√5
4. √2/5

Question 41:

The energy equivalent of 1 g of substance is:

1. 11.2 × 10²⁴ MeV
2. 5.6 × 10¹² MeV
3. 5.6 eV
4. 5.6 × 10⁶ MeV

Question 42:

An astronaut takes a ball of mass m from Earth to space. He throws the ball into a circular orbit about Earth at an altitude of 318.5 km. From Earth’s surface to the orbit, the change in total mechanical energy of the ball is xGMem / 21Re. The value of x is:

1. 11
2. 9
3. 12
4. 10

Question 43:

Given below are two statements:

Statement (I): When currents vary with time, Newton’s third law is valid only if momentum carried by the electromagnetic field is taken into account.
Statement (II): Ampere’s circuital law does not depend on Biot-Savart’s law.

Choose the correct answer:

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

Question 44:

A particle of mass m moves on a straight line with its velocity increasing with distance according to the equation v = α√x, where α is a constant. The total work done by all the forces applied on the particle during its displacement from x = 0 to x = d, will be:

1. m / 2α²d
2. md / 2α²
3. mα²d / 2
4. 2mα²d

Question 45:

A galvanometer has a coil of resistance 200Ω with a full-scale deflection at 20µA. The value of resistance to be added to use it as an ammeter of range 0−20mA is:

1. 0.40Ω
2. 0.20Ω
3. 0.50Ω
4. 0.10Ω

Question 46:

A heavy iron bar, of weight W, is having its one end on the ground and the other on the shoulder of a person. The bar makes an angle θ with the horizontal. The weight experienced by the person is:

1. W/2
2. W
3. W cos θ
4. W sin θ

Question 47:

One main scale division of a vernier caliper is equal to m units. If nth division of the main scale coincides with (n+1)th division of the vernier scale, the least count of the vernier caliper is:

1. n / (n+1)
2. m / (n+1)
3. 1 / (n+1)
4. m / n(n+1)

Question 48:

A bulb and a capacitor are connected in series across an AC supply. A dielectric is then placed between the plates of the capacitor. The glow of the bulb:

1. increases
2. remains same
3. becomes zero
4. decreases

Question 49:

The equivalent resistance between A and B is:

1. 18Ω
2. 25Ω
3. 27Ω
4. 19Ω

Question 50:

A sample of 1 mole gas at temperature T is adiabatically expanded to double its volume. If the adiabatic constant for the gas is γ = 3/2, then the work done by the gas in the process is:

1. RT [2 − √2]
2. R T [2 − √2]
3. RT [2 + √2]
4. T R [2 + √2]

Question 51:

If vec a and vec b make an angle cos⁻¹(5/9) with each other, then |vec a + vec b| = √2|vec a − vec b| for |vec a| = n|vec b|. The integer value of n is:

1. 2
2. 3
3. 4
4. 5

Question 52:

At the center of a half-ring of radius R = 10 cm and linear charge density 4 nC/m, the potential is xπV. The value of x is:

1. 4
2. 2
3. 1
4. 3

Question 53:

A star has 100% helium composition. It starts to convert three 4He into 12C via the triple alpha process as: 4He + 4He + 4He → 12C + Q. The mass of the star is 2.0 × 10³² kg and it generates energy at the rate of 5.808 × 10³⁰ W. The rate of converting these 4He to 12C is n × 10⁴² s⁻¹, where n is:

1. 10
2. 20
3. 15
4. 25

Question 54:

In a Young’s double-slit experiment, the intensity at a point is 1/4 of the maximum intensity. The minimum distance of the point from the central maximum is x μm. (Given: λ = 600 nm, d = 1.0 mm, D = 1.0 m)

1. 100
2. 200
3. 300
4. 400

Question 55:

A string is wrapped around the rim of a wheel of moment of inertia 0.40 kgm² and radius 10 cm. The wheel is free to rotate about its axis. Initially, the wheel is at rest. The string is now pulled by a force of 40N. The angular velocity of the wheel after 10 s is x rad/s, where x is:

1. 50
2. 75
3. 100
4. 150

Question 56:

A square loop of edge length 2m carrying a current of 2A is placed with its edges parallel to the x-y-axis. A magnetic field is passing through the x-y-plane and is expressed as: B = B₀(1 + 4x)k̂, where B₀ = 5T. The net magnetic force experienced by the loop is x N.

1. 120
2. 160
3. 180
4. 200

Question 57:

Two persons pull a wire towards themselves. Each person exerts a force of 200 N on the wire. The Young's modulus of the material of the wire is 1 × 10¹¹ N/m². The original length of the wire is 2 m, and the area of the cross-section is 2 cm². The wire will extend in length by ........ µm.

Question 58:

When a coil is connected across a 20 V DC supply, it draws a current of 5 A. When it is connected across a 20 V, 50 Hz AC supply, it draws a current of 4 A. The self-inductance of the coil is ...... mH. (π = 3)

Question 59:

The position, velocity, and acceleration of a particle executing simple harmonic motion are found to have magnitudes of 4 m, 2 m/s, and 16 m/s² at a certain instant. The amplitude of the motion is √x m, where x is ........

Question 60:

The current flowing through the 1 Ω resistor is n/10. The value of n is ........

Diagram:

Question 61:

The molar conductivity for electrolytes A and B are plotted against √C. Electrolytes A and B respectively are:

Graph:

1. Weak electrolyte, Weak electrolyte
2. Strong electrolyte, Strong electrolyte
3. Weak electrolyte, Strong electrolyte
4. Strong electrolyte, Weak electrolyte

Question 62:

Methods used for purification of organic compounds are based on:

1. Neither on nature of compound nor on the impurity present.
2. Nature of compound only.
3. Nature of compound and presence of impurity.
4. Presence of impurity only.

Question 63:

In the following sequence of reaction, the major products B and C respectively are:

Reaction:

Question 64:

The correct order of basic strength of Pyrrole, Pyridine, and Piperidine is:

1. Piperidine > Pyridine > Pyrrole
2. Pyrrole > Pyridine > Piperidine
3. Pyridine > Piperidine > Pyrrole
4. Pyrrole > Piperidine > Pyridine

Question 65:

In which one of the following pairs do the central atoms exhibit sp² hybridization?

1. BF₃ and NO₂⁻
2. NH₂⁻ and H₂O
3. H₂O and NO₂
4. NH₂⁻ and BF₃

Question 66:

The F⁻ ions make the enamel on teeth much harder by converting hydroxyapatite (the enamel on the surface of teeth) into much harder fluoroapatite having the formula:

1. [3(Ca₃(PO₄)₂ ⋅ CaF₂)]
2. [3(Ca₂(PO₄)₂ ⋅ Ca(OH)₂)]
3. [3(Ca₃(PO₄)₃ ⋅ CaF₂)]
4. [3(Ca₃(PO₄)₂ ⋅ Ca(OH)₂)]

Question 67:

The relative stability of the contributing structures is:

1. (I) > (III) > (II)
2. (I) > (II) > (III)
3. (II) > (I) > (III)
4. (III) > (II) > (I)

Question 68:

Given below are two statements:
• Statement (I): The oxidation state of an element in a particular compound is the charge acquired by its atom on the basis of electron gain enthalpy consideration from other atoms in the molecule.
• Statement (II): pπ–pπ bond formation is more prevalent in second-period elements over other periods.
In the light of the above statements, choose the most appropriate answer from the options given below:

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

Question 69:

Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R):
• Assertion (A): SN2 reaction of C₆H₅CH₂Br occurs more readily than the SN2 reaction of CH₃CH₂Br.
• Reason (R): The partially bonded unhybridized p-orbital that develops in the trigonal bipyramidal transition state is stabilized by conjugation with the phenyl ring.
In the light of the above statements, choose the most appropriate answer from the options given below:

1. (A) is not correct but (R) is correct.
2. Both (A) and (R) are correct but (R) is not the correct explanation of (A).
3. Both (A) and (R) are correct and (R) is the correct explanation of (A).
4. (A) is correct but (R) is not correct.

Question 70:

For the given compounds, the correct order of increasing pKa value is:

1. (E) < (D) < (C) < (B) < (A)
2. (D) < (E) < (C) < (B) < (A)
3. (E) < (D) < (B) < (A) < (C)
4. (B) < (D) < (A) < (C) < (E)

Question 71:

Assertion (A): Both rhombic and monoclinic sulphur exist as S₈, while oxygen exists as O₂.
Reason (R): Oxygen forms pπ–pπ multiple bonds with itself and other elements having small size and high electronegativity like C, N, which is not possible for sulphur.
In the light of the above statements, choose the most appropriate answer from the options given below:

1. Both (A) and (R) are correct and (R) is the correct explanation of (A).
2. Both (A) and (R) are correct but (R) is not the correct explanation of (A).
3. (A) is correct but (R) is not correct.
4. (A) is not correct but (R) is correct.

Question 72:

Assertion (A): The total number of geometrical isomers shown by [Co(en)₂Cl₂]⁺ complex ion is three.
Reason (R): [Co(en)₂Cl₂]⁺ complex ion has an octahedral geometry.
In the light of the above statements, choose the most appropriate answer from the options given below:

1. Both (A) and (R) are correct and (R) is the correct explanation of (A).
2. Both (A) and (R) are correct but (R) is not the correct explanation of (A).
3. (A) is correct but (R) is not correct.
4. (A) is not correct but (R) is correct.

Question 73:

The electronic configuration of Cu(II) is 3d⁹, whereas that of Cu(I) is 3d¹⁰. Which of the following is correct?

1. Cu(II) is less stable.
2. Stability of Cu(I) and Cu(II) depends on the nature of copper salts.
3. Cu(II) is more stable.
4. Cu(I) and Cu(II) are equally stable.

Question 74:

What is the structure of C?

1. Linear
2. Bent
3. Trigonal Planar
4. Tetrahedral

Question 75:

Compare the energies of the following sets of quantum numbers for a multielectron system:

(A) n = 4, l = 1
(B) n = 4, l = 2
(C) n = 3, l = 1
(D) n = 3, l = 2
(E) n = 4, l = 0
Choose the correct order of energies:

1. (B) > (A) > (C) > (E) > (D)
2. (E) > (C) < (D) < (A) < (B)
3. (E) > (C) > (A) > (D) > (B)
4. (C) < (E) < (D) < (A) < (B)

Question 76:

The correct order of basic strength of Pyrrole, Pyridine, and Piperidine is:

1. Piperidine > Pyridine > Pyrrole
2. Pyrrole > Pyridine > Piperidine
3. Pyridine > Piperidine > Pyrrole
4. Pyrrole > Piperidine > Pyridine

Question 77:

The molar conductivity for electrolytes A and B are plotted against C^1/2. Electrolytes A and B respectively are:

1. Weak electrolyte, Weak electrolyte
2. Strong electrolyte, Strong electrolyte
3. Weak electrolyte, Strong electrolyte
4. Strong electrolyte, Weak electrolyte

Question 78:

Methods used for purification of organic compounds are based on:

1. Neither on nature of compound nor on the impurity present
2. Nature of compound only
3. Nature of compound and presence of impurity
4. Presence of impurity only

Question 79:

In the following sequence of reactions, the major products B and C respectively are:

1. Wurtz reaction, Grignard reagent
2. Substitution, Elimination
3. Hydrolysis, Oxidation
4. Halogenation, Nitration

Question 80:

The total number of species from the following in which one unpaired electron is present, is:

N₂, O₂, C⁻₂, O⁻₂, H⁺₂, CN⁻, He⁺₂

1. 3
2. 4
3. 5
4. 6

Question 81:

Number of ambidentate ligands among the following is:

NO⁻₂, SCN⁻, C₂O²⁻₄, NH₃, CN⁻, SO²⁻₄, H₂O

1. 2
2. 3
3. 4
4. 5

Question 82:

Total number of essential amino acids among the given list of amino acids is:

Arginine, Phenylalanine, Aspartic acid, Cysteine, Histidine, Valine, Proline

1. 3
2. 4
3. 5
4. 6

Question 83:

Number of colourless lanthanoid ions among the following is:

Eu³⁺, Lu³⁺, Nd³⁺, La³⁺, Sm³⁺

1. 1
2. 2
3. 3
4. 4

Question 84:

The correct order of increasing pKa value is:

1. (E) < (D) < (C) < (B) < (A)
2. (D) < (E) < (C) < (B) < (A)
3. (E) < (D) < (B) < (A) < (C)
4. (B) < (D) < (A) < (C) < (E)

Question 85:

For the given compounds, the correct order of increasing stability of their resonance structures is:

1. (III) < (II) < (I)
2. (I) < (II) < (III)
3. (III) > (I) > (II)
4. (I) < (III) < (II)

Question 86:

The correct order of hybridization in the following molecules is:

NH₃, H₂O, BF₃, and CO₂

1. sp > sp² > sp³
2. sp³ > sp² > sp
3. sp > sp³ > sp²
4. sp² > sp > sp³

Question 87:

The total number of species from the following in which one unpaired electron is present, is:

N₂, O₂, C^-2, O^-2, H⁺², CN^-, He⁺²

1. 3
2. 4
3. 5
4. 6

Question 88:

Number of ambidentate ligands among the following is:

NO^-2, SCN^-, C₂O₄^2-, NH₃, CN^-, SO₄^2-, H₂O

1. 2
2. 3
3. 4
4. 5

Question 89:

Total number of essential amino acids among the given list of amino acids is:

Arginine, Phenylalanine, Aspartic acid, Cysteine, Histidine, Valine, Proline

1. 3
2. 4
3. 5
4. 6

Question 90:

Number of colourless lanthanoid ions among the following is:

Eu³⁺, Lu³⁺, Nd³⁺, La³⁺, Sm³⁺

1. 1
2. 2
3. 3
4. 4