JEE Main 2024 30Jan Shift 2 Question Paper (Available)- Download Solution PDF with Answer Key

Consider the system of linear equations:
x + y + z = 5, x + 2y + 2z = 9, x + 3y + λz = µ, where λ, µ ∈ R. Then, which of the following statements is NOT correct?
(1) System has infinite number of solutions if λ = 1 and µ = 13
(2) System is inconsistent if λ = 1 and µ ≠ 13
(3) System is consistent if λ ≠ 1 and µ = 13
(4) System has unique solution if λ = 1 and µ ≠ 13

For α, β ∈ (0, π/2), let 3 sin(α + β) = 2 sin(α − β), and a real number k be such that tanα = k tanβ. Then the value of k is equal to:
(1) 2/3
(2) -5
(3) 3/2
(4) 5

Let A(10, 0) and B(0, β) be points on the line 5x + 7y = 50. Let P divide AB in the ratio 7:3. Let 3x−25 = 0 be a directrix of the ellipse x²/a² + y²/b² = 1, and focus S such that a perpendicular from S passes through P. Find the length of the latus rectum:
(1) 25/3
(2) 32/9
(3) 25/9
(4) 32/5

Let a = i + αj + βk, where α, β ∈ R. Let b be a vector such that the angle between a and b is π/4 and |b| = 6. If |a × b| = 3√2, then the value of (α² + β²)|a × b|² is equal to:
(1) 90
(2) 75
(3) 95
(4) 85

Let f(x) = (x + 3)(x − 2)²(x + 1), x ∈ [-4, 4]. If M and m are the maximum and minimum values of f in [-4, 4], then the value of M - m is:
(1) 600
(2) 392
(3) 608
(4) 108

Let a and b be distinct positive real numbers. The 11th term of a GP (first term a, third term b) equals the pth term of another GP (first term a, fifth term b). Find p:
(1) 20
(2) 25
(3) 21
(4) 24

If x² − y² + 2hxy + 2gx + 2fy + c = 0 is the locus of a point that moves such that it is always equidistant from the lines x + 2y + 7 = 0 and 2x − y + 8 = 0, then the value of g + c + h − f equals:
(1) 14
(2) 6
(3) 8
(4) 29

Let a and b be two vectors such that |b| = 1 and |b × a| = 2. Then |(b × a) − b|² is equal to:
(1) 3
(2) 5
(3) 1
(4) 4

Let y = f(x) be a thrice differentiable function in (−5, 5). Let the tangents to the curve y = f(x) at (1, f(1)) and (3, f(3)) make angles π/6 and π/4, respectively, with the positive x-axis. If 2∫₁¹/√3((f′(t))² + 1)f′′(t) dt = α + β√3, where α and β are integers, then the value of α + β equals:
(1) -14
(2) 26
(3) -16
(4) 36

Let P be a point on the hyperbola H: x²/9 − y²/4 = 1, in the first quadrant such that the area of the triangle formed by P and the two foci of H is √13. Then, the square of the distance of P from the origin is:
(1) 18
(2) 26
(3) 22
(4) 24

Bag A contains 3 white and 7 red balls, and bag B contains 3 white and 2 red balls. One bag is selected at random, and a ball is drawn. The probability of drawing the ball from bag A, given the ball drawn is white, is:
(1) 1/4
(2) 1/9
(3) 1/3
(4) 3/10

Let f : R → R be defined by f(x) = ae²ˣ + beˣ + c. If f(0) = −1, f'(logₑ 2) = 21, and ∫[logₑ 4, 0] (f(x) − cx) dx = 39/2, then the value of |a + b + c| equals:
(1) 16
(2) 10
(3) 12
(4) 8

Let L₁: r = (ˆi − ˆj + 2ˆk) + λ(ˆi − ˆj + 2ˆk), λ ∈ R, L₂: r = (ˆj − ˆk) + μ(3ˆi + ˆj + pˆk), μ ∈ R, and L₃: r = δ(ˆi + mˆj − ˆk), δ ∈ R be three lines such that L₁ is perpendicular to L₂, and L₃ is perpendicular to both L₁ and L₂. Then the point which lies on L₃ is:
(1) (−1, 7, 4)
(2) (−1, −7, 4)
(3) (1, 7, 4)
(4) (1, −7, 4)

Let a and b be real constants such that the function f defined by f(x) = { x² + 3x + a, x ≤ 1; bx + 2, x > 1 } is differentiable on R. Then, the value of ∫[2,−2] f(x) dx equals:
(1) 15
(2) 19/6
(3) 21
(4) 17

Let f : R − {0} → R be a function satisfying f(x/y) = f(x)/f(y) for all x, y with f(y) ≠ 0. If f'(1) = 2024, then:
(1) xf'(x) − 2024f(x) = 0
(2) xf(x) + 2024f(x) = 0
(3) f(x) + xf'(x) = 2024
(4) xf(x) − 2023f(x) = 0

If z is a complex number, then the number of common roots of the equations z¹⁹⁸⁵ + z¹⁰⁰ + 1 = 0 and z² + z + 1 = 0 is:
(1) 1
(2) 2
(3) 0
(4) 3

Suppose 2^−p, p, 2^−α, α are the coefficients of four consecutive terms in the expansion of (1 + x)ⁿ. Then the value of p² − α² + 6α + 2p equals:
(1) 4
(2) 10
(3) 8
(4) 6

If the domain of the function f(x) = logₑ(2x + 3 / 4x² + x − 3) + cos⁻¹(2x − 1 / x + 2) is (α, β], then the value of 5β − 4α is equal to:
(1) 10
(2) 12
(3) 11
(4) 9

Let f : R → R be a function defined by f(x) = x / (1 + x⁴)^1/4, and g(x) = f(f(f(x))). Then ∫[4√3, 8√3] x³g(x) dx equals:
(1) 33
(2) 36
(3) 42
(4) 39

Let R = diag(sinθ, sin(θ + 2π/3), sin(θ + 4π/3)) be a diagonal 3×3 matrix. For a square matrix M, let trace(M) denote the sum of all the diagonal entries of M. Then among the statements:
(I) Trace(R) = 0
(II) If trace(adj(adj(R))) = 0, then R has exactly one non-zero entry.
Which of the following is true?
(1) Both (I) and (II) are true
(2) Neither (I) nor (II) is true
(3) Only (II) is true
(4) Only (I) is true

Let Y = Y(X) be a curve lying in the first quadrant such that the area enclosed by the line Y − y = Y′(x)(X − x) and the coordinate axes, where (x, y) is any point on the curve, is always A = −y²/(2Y′(x)) + 1. If Y(1) = 1, then 12Y(2) equals:

Let a line passing through the point (−1, 2, 3) intersect the lines L₁: (x−1)/3 = (y−2)/2 = (z+1)/−2 and L₂: (x+2)/−3 = (y−2)/4 = (z−1)/−2 at points M(α, β, γ) and N(a, b, c), respectively. Then the value of (α + β + γ)² / (a + b + c) equals:

Consider two circles C₁: x² + y² = 25 and C₂: (x−α)² + y² = 16, where α ∈ (5, 9). Let the angle between the two radii (one to each circle) drawn from one of the intersection points of C₁ and C₂ be sin⁻¹(√63/8). If the length of the common chord of C₁ and C₂ is β, then the value of (αβ)² equals:

Let α = Σ C_n^k / (k + 1) and β = Σ (C_n^k C_n^k+1) / (k + 2). If 5α = 6, then n equals:

Let S_n be the sum of the first n terms of an arithmetic progression 3, 7, 11, ... . If (n(n + 1)) / ΣS_k < 42, then n equals:

In an examination of Mathematics paper, there are 20 questions of equal marks, and the question paper is divided into three sections: A, B, and C. A student is required to attempt a total of 15 questions, taking at least 4 questions from each section. If section A has 8 questions, section B has 6 questions, and section C has 6 questions, then the total number of ways a student can select 15 questions is:

The number of symmetric relations defined on the set {1, 2, 3, 4} which are not reflexive is:

The number of real solutions of the equation x(x² + 3x) + |x−1| + 6|k−2| = 0 is:

The area of the region enclosed by the parabola (y−2)² = x−1, the line x−2y+4 = 0, and the positive coordinate axes is:

The variance σ² of the data is:
x_i: 0, 1, 5, 6, 10, 12, 17
f_i: 3, 2, 3, 2, 6, 3, 3

If 50 Vernier divisions are equal to 49 main scale divisions of a traveling microscope and one smallest reading of the main scale is 0.5 mm, the Vernier constant of the traveling microscope is:

A block of mass 1 kg is pushed up a surface inclined to the horizontal at an angle of 60° by a force of 10 N parallel to the inclined surface. When the block is pushed up by 10 m along the inclined surface, the work done against the frictional force is:

For the photoelectric effect, the maximum kinetic energy (E_k) of the photoelectrons is plotted against the frequency (ν) of the incident photons. The slope of the graph gives:

A block of ice at −10°C is slowly heated and converted to steam at 100°C. Which of the following curves represents the phenomenon qualitatively?

In a nuclear fission reaction of an isotope of mass M, three similar daughter nuclei of the same mass are formed. The speed of a daughter nucleus in terms of mass defect ΔM will be:

Choose the correct statement for processes A & B shown in the figure:

An electron revolving in the nth Bohr orbit has a magnetic moment µ. If µₙ is the value of µ, the value of x is:

An alternating voltage V(t) = 220 sin 100t volt is applied to a purely resistive load of 50Ω. The time taken for the current to rise from half of the peak value to the peak value is:

A block of mass 1 kg is placed on a surface with a vertical cross-section given by y = x². If the coefficient of friction is 0.5, the maximum height above the ground at which the block can be placed without slipping is:

If the total energy transferred to a surface in time t is 6.48 × 10⁵ J, then the magnitude of the total momentum delivered to this surface for complete absorption is:

A beam of unpolarized light of intensity I₀ is passed through a polaroid A and then through another polaroid B which is oriented so that its principal plane makes an angle of 45° relative to that of A. The intensity of emergent light is:

• (1) I₀/4
• (2) I₀
• (3) I₀/2
• (4) I₀/8

The escape velocity of a body from Earth is 11.2 km/s. If the radius of a planet is one-third the radius of Earth and its mass is one-sixth that of Earth, the escape velocity from the planet is:

• (1) 11.2 km/s
• (2) 8.4 km/s
• (3) 4.2 km/s
• (4) 7.9 km/s

A particle of charge –q and mass m moves in a circle of radius r around an infinitely long line of charge having linear charge density +λ. The time period T is given by:

• (1) T² = (4πmr³)/(2kq)
• (2) T = 2πr √(m/(2kq))
• (3) T = (1/(2πr))√(m/(2kq))
• (4) T = 2kq/m

If mass is written as m = k c^p G^−1/2 h^1/2, then the value of p will be:

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

In the given circuit, the voltage across load resistance R_L is:

• (1) 8.75 V
• (2) 9.00 V
• (3) 13.50 V
• (4) 14.00 V

If three moles of monoatomic gas (γ = 5/3) is mixed with two moles of diatomic gas (γ = 7/5), the value of the adiabatic exponent γ for the mixture is:

• (1) 1.75
• (2) 1.40
• (3) 1.52
• (4) 1.35

Three blocks A, B, and C are pulled on a horizontal smooth surface by a force of 80 N. The tensions T₁ and T₂ in the string are respectively:

• (1) 40 N, 64 N
• (2) 60 N, 80 N
• (3) 88 N, 96 N
• (4) 80 N, 100 N

When a potential difference V is applied across a wire of resistance R, it dissipates energy at a rate W. If the wire is cut into two halves and these halves are connected mutually in parallel across the same supply, the energy dissipation rate will become:

• (1) W/4
• (2) W/2
• (3) 2W
• (4) 4W

Match List I with List II:
List I:
A. Gauss’s Law
B. Faraday’s Law
C. Lenz’s Law
D. Ampere’s Law

List II:
I. ∮ E · dA = Q / ε₀
II. ∮ B · dl = μ₀I
III. Induced emf opposes change
IV. ∮ E · dl = −dΦ/dt
 

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

Projectiles A and B are thrown at angles of 45° and 60° with the vertical respectively from the top of a 400 m high tower. If their ranges and times of flight are the same, the ratio of their speeds of projection v_A : v_B is:

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

A power transmission line feeds input power at 2.3 kV to a step-down transformer with its primary winding having 3000 turns. The output power is delivered at 230 V by the transformer. The current in the primary of the transformer is 5 A, and its efficiency is 90%. The winding of the transformer is made of copper. The output current of the transformer is:

• (1) 45 A
• (2) 50 A
• (3) 60 A
• (4) 55 A

A big drop is formed by coalescing 1000 small identical drops of water. If E₁ is the total surface energy of 1000 small drops and E₂ is the surface energy of the single big drop, then the ratio E₁:E₂ is x:1 where x equals:

• (1) 5
• (2) 8
• (3) 10
• (4) 15

Two discs with moments of inertia I₁ = 4 kg·m² and I₂ = 2 kg·m² about their central axes, rotating with angular speeds 10 rad/s and 4 rad/s, respectively, are brought into contact face-to-face. The loss in kinetic energy of the system is:

• (1) 20 J
• (2) 24 J
• (3) 30 J
• (4) 18 J

In an experiment to measure the focal length f of a convex lens, the magnitude of object distance x and image distance y are measured with reference to the focal point of the lens. The y-x plot is shown in the figure. The focal length of the lens is:

• (1) 15 cm
• (2) 18 cm
• (3) 20 cm
• (4) 25 cm

A vector has a magnitude equal to that of A = −3î + 4ĵ and is parallel to B = 4î + 3ĵ. The x and y components of this vector in the first quadrant are x and y, respectively. The value of x is:

• (1) 1
• (2) 2
• (3) 3
• (4) 4

The current of 5 A flows in a square loop of sides 1 m placed in air. The magnetic field at the center of the loop is X√2 × 10⁻⁷ T. The value of X is:

• (1) 10
• (2) 20
• (3) 30
• (4) 40

Two identical charged spheres are suspended by strings of equal lengths. The strings make an angle of 37° with each other. When suspended in a liquid of density 0.7 g/cm³, the angle remains the same. If the density of the material of the spheres is 1.4 g/cm³, the dielectric constant of the liquid is:

• (1) 1
• (2) 2
• (3) 3
• (4) 4

A wire is cut into two halves, and these halves are connected in parallel. The resistance of the wire before cutting was R. The equivalent resistance of the combination is:

• (1) R/2
• (2) R/4
• (3) R
• (4) 2R

A point source is emitting sound waves of intensity 16 × 10⁻⁸ W/m² at the origin. The difference in intensity (magnitude only) at two points located at distances of 2 m and 4 m from the origin, respectively, will be:

• (1) 2 × 10⁻⁸ W/m²
• (2) 3 × 10⁻⁸ W/m²
• (3) 4 × 10⁻⁸ W/m²
• (4) 5 × 10⁻⁸ W/m²

Two resistances of 100Ω and 200Ω are connected in series with a battery of 4V and negligible internal resistance. A voltmeter is used to measure voltage across the 100Ω resistance, which gives a reading of 1V. The resistance of the voltmeter must be:

• (1) 100 Ω
• (2) 200 Ω
• (3) 300 Ω
• (4) 400 Ω

Which among the following purification methods is based on the principle of “Solubility” in two different solvents?

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

Salicylaldehyde is synthesized from phenol, when reacted with:

• (1) HCl, NaOH
• (2) CO₂, NaOH
• (3) CCl₃, NaOH
• (4) HCl, NaOH

Given below are two statements:
Statement I: High concentration of strong nucleophilic reagent with secondary alkyl halides which do not have bulky substituents will follow SN2 mechanism.
Statement II: A secondary alkyl halide when treated with a large excess of ethanol follows SN1 mechanism.
In the light of the above statements, choose the most appropriate from the options given below:

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

m-Chlorobenzaldehyde on treatment with 50% KOH solution yields:

• (1) Benzyl alcohol
• (2) m-Chlorobenzoate and m-Chlorobenzyl alcohol
• (3) Benzoic acid
• (4) m-Chlorobenzoic acid

Given below are two statements: One is labelled as Assertion A and the other is labelled as Reason R.
Assertion A: H₂Te is more acidic than H₂S.
Reason R: Bond dissociation enthalpy of H₂Te is lower than H₂S.
In light of the above statements, choose the most appropriate from the options given below:

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

Product A and B formed in the following set of reactions are:
1. Benzene + HNO₃ + H₂SO₄ → A
2. A + Sn/HCl → B

• (1) A = C₆H₅NO₂, B = C₆H₅NH₂
• (2) A = C₆H₆, B = C₆H₅NH₂
• (3) A = C₆H₅NO₂, B = C₆H₆
• (4) A = C₆H₅NH₂, B = C₆H₅NO₂

IUPAC name of the following compound is:
CH₃—CH—CH₂—CN
NH₂

• (1) 2-Aminopentanitrile
• (2) 2-Aminobutanitrile
• (3) 3-Aminobutanenitrile
• (4) 3-Aminopropanenitrile

The products A and B formed in the following reaction scheme are respectively:
1. Benzene + HNO₃ + H₂SO₄ → A
2. A + Sn/HCl → B

• (1) A = C₆H₅NO₂, B = C₆H₅NH₂
• (2) A = C₆H₆, B = C₆H₅NH₂
• (3) A = C₆H₅NO₂, B = C₆H₆
• (4) A = C₆H₅NH₂, B = C₆H₅NO₂

The molecule/ion with square pyramidal shape is:

• (1) [Ni(CN)₆]²⁻
• (2) PCl₅
• (3) BrF₅
• (4) PF₅

The orange color of K₂Cr₂O₇ and purple color of KMnO₄ is due to:

• (1) Charge transfer transition in both.
• (2) d → d transition in KMnO₄ and charge transfer transitions in K₂Cr₂O₇.
• (3) d → d transition in K₂Cr₂O₇ and charge transfer transitions in KMnO₄.
• (4) d → d transition in both.

Alkaline oxidative fusion of MnO₂ gives “A” which on electrolytic oxidation in alkaline solution produces B. A and B respectively are:

• (1) Mn₂O₇ and MnO₄⁻
• (2) MnO₂ and MnO₄⁻
• (3) Mn₂O₇ and MnO₂⁻
• (4) MnO₂⁻ and Mn₂O₇

If a substance ‘A’ dissolves in a solution of a mixture of ‘B’ and ‘C’ with their respective number of moles as nₐ, nᵦ, and nₖ, the mole fraction of C in the solution is:

• (1) Option 1
• (2) Option 2
• (3) Option 3
• (4) Option 4

Given below are two statements:
Statement I: Along the period, the chemical reactivity of the element gradually increases from group 1 to group 18.
Statement II: The nature of oxides formed by group 1 elements is basic, while that of group 17 elements is acidic.
In the light of the above statements, choose the most appropriate from the questions given below:

• (1) Both Statement I and Statement II are true.
• (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 false.

The coordination geometry around the manganese in decacarbonylmanganese(0) is:

• (1) Octahedral
• (2) Trigonal bipyramidal
• (3) Square pyramidal
• (4) Square planar

Given below are two statements:
Statement I: Since fluorine is more electronegative than nitrogen, the net dipole moment of NF₃ is greater than NH₃.
Statement II: In NH₃, the orbital dipole due to lone pair and the dipole moment of NH bonds are in opposite directions, but in NF₃, the orbital dipole due to lone pair and dipole moments of N − F bonds are in the same direction.
In light of the above statements, choose the most appropriate from the options given below:

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

The correct stability order of carbocations is:

• (1) C₃⁺ > CH₃⁺ > (CH₂)₂CH⁺ > (CH₃)₂CH₂⁺
• (2) CH₃⁺ > (CH₂)₂CH⁺ > (CH₃)₂CH₂⁺ > C₃⁺
• (3) (CH₃)₂CH⁺ > (CH₂)₂CH⁺ > C₃⁺ > (CH₃)₂CH⁺
• (4) (CH₃)₂CH₂⁺ > (CH₂)₂CH⁺ > CH₃⁺ > C₃⁺

The solution from the following with the highest depression in freezing point/lowest freezing point is:

• (1) 180 g of acetic acid dissolved in water
• (2) 180 g of acetic acid dissolved in benzene
• (3) 180 g of benzoic acid dissolved in benzene
• (4) 180 g of glucose dissolved in water

A and B formed in the following reactions are:
Cr₂O₇²⁻ + 4NaOH → Na₂Cr₂O₄ + 2NaCl + 2H₂O
A + 2Cl₂ + 2H₂O → B + 3H₂O

• (1) A = Na₂Cr₂O₄, B = CrO₃
• (2) A = Na₂Cr₂O₄, B = Cr₂O₇
• (3) A = Na₂Cr₂O₄, B = NaCrO₄
• (4) A = Na₂Cr₂O₄, B = Cr₃O₈

Choose the correct statements about the hydrides of group 15 elements:
1. A: The stability of the hydrides decreases in the order NH₃ > PH₃ > AsH₃ > SbH₃ > BiH₃.
2. B: The reducing ability of the hydrides increases in the order NH₃ < PH₃ < AsH₃ < SbH₃ < BiH₃.
3. C: Among the hydrides, NH₃ is a strong reducing agent while BiH₃ is a mild reducing agent.
4. D: The basicity of the hydrides increases in the order NH₃ < PH₃ < AsH₃ < SbH₃ < BiH₃.
Choose the most appropriate from the options given below:

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

Reduction potential of ions are given below:
ClO₃⁻: E° = 1.19 V
IO₃⁻: E° = 1.65 V
BrO₃⁻: E° = 1.74 V
The correct order of their oxidising power is:

• (1) ClO₃⁻ > IO₃⁻ > BrO₃⁻
• (2) BrO₃⁻ > IO₃⁻ > ClO₃⁻
• (3) IO₃⁻ > ClO₃⁻ > BrO₃⁻
• (4) IO₃⁻ > BrO₃⁻ > ClO₃⁻

Number of complexes which show optical isomerism is:
(1) cis-[Cr(ox)₂Cl₂]³⁻
(2) [Co(en)₃]³⁺
(3) cis-[Pt(en)₂Cl₂]²⁺
(4) trans-[Cr(ox)₂Cl₂]³⁻

• (1) [Co(en)₃]³⁺

NO₂, required for a reaction, is produced by decomposition of N₂O₄ in CCl₄, as per the equation:
2N₂O₄ ⇌ 4NO₂ + O₂
The initial concentration of N₂O₄ is 3 mol L⁻¹ and it is 2.75 mol L⁻¹ after 30 minutes. The rate of formation of NO₂ is x × 10⁻³ mol L⁻¹ min⁻¹. The value of x is:

• (1) 16
• (2) 17
• (3) 18
• (4) 19

Two reactions are given below:
2Fe³⁺ + 3O₂(g) → Fe₂O₃(s), ∆Hf = −822 kJ/mol
C(g) + ½O₂(g) → CO(g), ∆Hf = −110 kJ/mol
Enthalpy change for the reaction:
3C(g) + Fe₂O₃(s) → 2Fe(g) + 3CO(g), ∆H = ?

• (1) 492
• (2) 494
• (3) 496
• (4) 498

The total number of correct statements regarding the nucleic acids is:
A. RNA is regarded as the reserve of genetic information.
B. DNA molecule self-duplicates during cell division.
C. DNA synthesizes proteins in the cell.
D. The message for the synthesis of particular proteins is present in DNA.
E. Identical DNA strands are transferred to daughter cells.

• (1) 3
• (2) 4
• (3) 2
• (4) 1

The pH of an aqueous solution containing 1M benzoic acid (pKa = 4.20) and 1M sodium benzoate is 4.5. The volume of benzoic acid solution in 300 mL of this buffer solution is mL.

• (1) 90
• (2) 100
• (3) 110
• (4) 120

Number of geometrical isomers possible for the given structure is/are:

• (1) 2
• (2) 3
• (3) 4
• (4) 5

Total number of species from the following which can undergo disproportionation reaction:
H₂O₂, ClO₃⁻, P₄, Cl₂, Ag⁺, F₂, NO₂, K

• (1) 6
• (2) 7
• (3) 8
• (4) 9

Number of metal ions characterized by flame test among the following:
Sr²⁺, Ba²⁺, Ca²⁺, Cu²⁺, Zn²⁺, Co²⁺, Fe²⁺

• (1) 3
• (2) 4
• (3) 5
• (4) 6

2-chlorobutane + Cl₂ → C₄H₇Cl₃ (isomers)
Total number of optically active isomers shown by C₄H₇Cl₃, obtained in the above reaction is:

• (1) 4
• (2) 5
• (3) 6
• (4) 7

Number of spectral lines obtained in He⁺ spectra, when an electron makes a transition from the fifth excited state to the first excited state is:

• (1) 8
• (2) 9
• (3) 10
• (4) 11