Question 1:

Let f : R → R be a function given by:
1 − cos(2x)/x², for x < 0
β√(1 − cos(x))/x, for x > 0.
If f is continuous at x = 0, then α² + β² is equal to:

1. 48
2. 12
3. 4
4. 6

Question 2:

Three urns A, B, and C contain 7 red, 5 black; 5 red, 7 black; and 6 red, 6 black balls, respectively. One of the urns is selected at random, and a ball is drawn. If the ball drawn is black, then the probability that it is drawn from urn A is:

1. 4/17
2. 5/18
3. 5/16
4. 6/17

Question 3:

The vertices of a triangle are A(−1, 3), B(−2, 2), and C(3,−1). A new triangle is formed by shifting the sides of the triangle one unit inwards. Then the equation of the side of the new triangle nearest to the origin is:

1. x − y − (2 + √2) = 0
2. −x + y − (2 − √2) = 0
3. x + y − (2 − √2) = 0
4. x + y + (2 − √2) = 0

Question 4:

If the solution y = y(x) of the differential equation (x⁴ + 2x³ + 3x² + 2x + 2) dy = (2x² + 2x + 3) dx satisfies y(−1) = −π/4, then y(0) is equal to:

1. −π/12
2. 0
3. π/4
4. π/2

Question 5:

Let the sum of the maximum and minimum values of the function f(x) = (2x² − 3x + 8)/(2x² + 3x + 8) be m/n, where gcd(m,n) = 1. Then m + n is equal to:

1. 182
2. 217
3. 195
4. 201

Question 6:

One of the points of intersection of the curves y = 1 + 3x − 2x² and y = 1/x is (1/2, 2). Let the area of the region enclosed by these curves be 1/24 (ℓ√5 + m) − n ln(1 + √5), where ℓ, m, n ∈ N. Then ℓ + m + n is equal to:

1. 32
2. 30
3. 29
4. 31

Question 7:

If the system of equations x + (√2 sinα) y + (√2 cosα) z = 0, x + (cosα) y + (sinα) z = 0, x + (sinα) y − (cosα) z = 0 has a non-trivial solution, then α ∈ (0, π/2) is equal to:

1. 3π/4
2. 7π/24
3. 5π/24
4. 11π/24

Question 8:

There are 5 points P₁, P₂, P₃, P₄, P₅ on the side AB, excluding A and B, of a triangle ABC. Similarly, there are 6 points P₆, P₇, ..., P₁₁ on the side BC and 7 points P₁₂, P₁₃, ..., P₁₈ on the side CA of the triangle. The number of triangles that can be formed using the points P₁, P₂, ..., P₁₈ as vertices is:

1. 776
2. 751
3. 796
4. 771

Question 9:

Let f(x) =

{
  x - 2, -2 < x < 0
  1 - 2x, 0 ≤ x ≤ 2
}

and h(x) = f(x) + f(x). Then ∫h(x) dx is equal to:

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

Question 10:

The sum of all rational terms in the expansion of (1/2⁵ + 1/5³)¹⁵ is equal to:

1. 3133
2. 633
3. 931
4. 6131

Question 11:

Let a unit vector which makes an angle of 60° with 2i + 2j − k and an angle of 45° with i − k be C. Then C + (−1/2 i + (1/3√2 j − √2/3 k)) is:

1. −√2/3 i + √2/3 j + (1/2 + 2√2/3) k
2. √2/3 i + 1/3√2 j − 1/2 k
3. (1/√3 + 1/2) i + (1/√3 − 1/3√2) j + (1/√3 + √2/3) k
4. √2/3 i − 1/2 k

Question 12:

Let the first three terms 2, p, and q, with q ≠ 2, of a G.P. be respectively the 7th, 8th, and 13th terms of an A.P. If the 5th term of the G.P. is the nth term of the A.P., then n is equal to:

1. 151
2. 169
3. 177
4. 163

Question 13:

Let a, b ∈ R. Let the mean and the variance of 6 observations −3, 4, 7, −6, a, b be 2 and 23, respectively. The mean deviation about the mean of these 6 observations is:

1. 13/3
2. 16/3
3. 11/3
4. 14/3

Question 14:

If 2 and 6 are the roots of the equation ax² + bx + 1 = 0, then the quadratic equation, whose roots are 1/(2a+b) and 1/(6a+b), is:

1. 2x² + 11x + 12 = 0
2. 4x² + 14x + 12 = 0
3. x² + 10x + 16 = 0
4. x² + 8x + 12 = 0

Question 15:

Let α and β be the sum and the product of all the non-zero solutions of the equation z² + |z| = 0, z ∈ C. Then 4(α² + β²) is equal to:

1. 6
2. 4
3. 8
4. 2

Question 16:

Let the point, on the line passing through the points P(1,−2, 3) and Q(5,−4, 7), farther from the origin and at a distance of 9 units from the point P, be (α, β, γ). Then α² + β² + γ² is equal to:

1. 155
2. 150
3. 160
4. 165

Question 17:

A square is inscribed in the circle x² + y² − 10x − 6y + 30 = 0. One side of this square is parallel to y = x + 3. If (xi, yi) are the vertices of the square, then Σ(x²i + y²i) is equal to:

1. 148
2. 156
3. 160
4. 152

Question 18:

If the domain of the function sin⁻¹((3x − 22)/(2x − 19)) + ln((3x² − 8x + 5)/(x² − 3x − 10)) is (α, β), then 3α + 10β is equal to:

1. 97
2. 100
3. 95
4. 98

Question 19:

Let f(x) = x⁵ + 2e^(x/4) for all x ∈ R. Consider a function g(x) such that (g ∘ f)(x) = x for all x ∈ R. Then the value of 8g′(2) is:

1. 16
2. 4
3. 8
4. 2

Question 20:

Let α ∈ (0,∞) and A =

[1 2 α]
[1 0 1]
[0 1 2]

If det(adj(2A − Aᵀ) ⋅ adj(A − 2Aᵀ)) = 28, then (det(A))² is equal to:

1. 1
2. 49
3. 16
4. 36

Question 21:

If lim_x→1 ((5x + 1)^(1/3) − (x + 5)^(1/3)) / ((2x + 3)^(1/2) − (x + 4)^(1/2)) = m√5 / n(2n)^(2/3), where gcd(m, n) = 1, then 8m + 12n is equal to:

1. 97
2. 64
3. 76
4. 100

Question 22:

In a survey of 220 students of a higher secondary school, it was found that at least 125 and at most 130 students studied Mathematics; at least 85 and at most 95 studied Physics; at least 75 and at most 90 studied Chemistry; 30 studied both Physics and Chemistry; 50 studied both Chemistry and Mathematics; 40 studied both Mathematics and Physics; and 10 studied none of these subjects. Let m and n respectively be the least and the most number of students who studied all three subjects. Then m + n is equal to:

1. 20
2. 25
3. 30
4. 35

Question 23:

Let the solution y = y(x) of the differential equation (dy/dx) − y = 1 + 4sin(x) satisfy y(π) = 1. Then y(π/2) + 10 is equal to:

1. 7
2. 8
3. 9
4. 10

Question 24:

The shortest distance between the lines (x+2)/2 = (y+3)/3 = (z−5)/4 and (x−3)/1 = (y−2)/−3 = (z+4)/2 is 38/√5 k and ∫₀^k [x²] dx = α−√α, where [x] denotes the greatest integer function, then 6α³ is equal to:

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

Question 25:

Let A be a 3×3 matrix of non-negative real elements such that A [1 1 1] = 3 [1 1 1]. Then the maximum value of det(A) is:

1. 4
2. 5
3. 6
4. 7

Question 26:

Let a = 1 + (2C2)/3! + (3C2)/4! + (4C2)/5! + ... and b = 1 + (1C0)/1! + (1C1)/1! + (2C0)/2! + (2C1)/2! + ... . Then 2b/a² is equal to:

1. 8
2. 9
3. 10
4. 11

Question 27:

Let A be a 3×3 matrix of non-negative real elements such that A [1 1 1] = 3 [1 1 1]. Then the maximum value of det(A) is:

1. 15
2. 20
3. 25
4. 30

Question 28:

Let the length of the focal chord PQ of the parabola y² = 12x be 15 units. If the distance of PQ from the origin is p, then 10p² is equal to:

1. 60
2. 72
3. 80
4. 90

Question 29:

Let ABC be a triangle of area 15√2 and the vectors AB = i + 2j − 7k, BC = ai + bj + ck, and AC = 6i + dj − 2k, d > 0. Then the square of the length of the largest side of the triangle ABC is:

1. 50
2. 52
3. 54
4. 56

Question 30:

If ∫₀^(π/4) (sin²x / (1 + sinx cosx)) dx = (1 / a) ln(a / 3) + (π / b√3), then a + b is equal to:

1. 6
2. 7
3. 8
4. 9

Question 31:

The electron will continue to move with uniform velocity along the axis of the solenoid when:

1. The electron will be accelerated along the axis.
2. The electron path will be circular about the axis.
3. The electron will experience a force at 45° to the axis and execute a helical path.
4. The electron will continue to move with uniform velocity along the axis of the solenoid.

Question 32:

The magnetic field induction of an electromagnetic wave is:

1. B = î 40 c cos(ω(t − z/c))
2. B = k̂ 40 c cos(ω(t − z/c))
3. B = ĵ 40 cos(ω(t − z/c))
4. B = ĵ 40 c cos(ω(t − z/c))

Question 33:

Which of the following nuclear fragments corresponding to nuclear fission between neutron (¹⁰n) and uranium isotope (²³⁵₉₂U) is correct?

1. ¹⁴⁴₅₆Ba + ⁸⁹₃₆Kr + 4 ¹⁰n
2. ¹⁴⁰₅₆Xe + ⁹⁴₃₈Sr + 3 ¹⁰n
3. ¹⁵³₅₁Sb + ⁹⁹₄₁Nb + 3 ¹⁰n
4. ¹⁴⁴₅₆Ba + ⁸⁹₃₆Kr + 3 ¹⁰n

Question 34:

In an experiment to measure focal length (f) of a convex lens, the least counts of the measuring scales for the position of object (u) and for the position of image (v) are ∆u and ∆v, respectively. The error in the measurement of the focal length of the convex lens will be:

1. ∆u/u + ∆v/v
2. f² [ ∆u/u² + ∆v/v² ]
3. f² [ ∆u/v² + ∆v/u² ]
4. f² [ ∆u/v + ∆v/u ]

Question 35:

Given below are two statements:
Statement I: When speed of liquid is zero everywhere, pressure difference at any two points depends on equation P₁ − P₂ = ρg(h₂ − h₁).
Statement II: In a venturi tube shown, 2gh = v₂² − v₁².
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 correct.
2. Statement I is incorrect but Statement II is correct.
3. Both Statement I and Statement II are incorrect.
4. Statement I is correct but Statement II is incorrect.

Question 36:

The resistances of the platinum wire of a platinum resistance thermometer at the ice point and steam point are 8Ω and 10Ω respectively. After inserting it in a hot bath of temperature 400°C, the resistance of platinum wire is:

1. 1Ω
2. 16Ω
3. 8Ω
4. 10Ω

Question 37:

A metal wire of uniform mass density having length L and mass M is bent to form a semicircular arc, and a particle of mass m is placed at the center of the arc. The gravitational force on the particle by the wire is:

1. GMmπ/2L²
2. 0
3. GmMπ²/L²
4. 2GMmπ/L²

Question 38:

On Celsius scale, the temperature of a body increases by 40°C. The increase in temperature on Fahrenheit scale is:

1. 70°F
2. 68°F
3. 72°F
4. 75°F

Question 39:

An effective power of a combination of 5 identical convex lenses which are kept in contact along the principal axis is 25 D. Focal length of each of the convex lenses is:

1. 20 cm
2. 50 cm
3. 500 cm
4. 25 cm

Question 40:

Which figure shows the correct variation of applied potential difference V with photoelectric current I at two different intensities of light (I₁ < I₂) of same wavelength:

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

Question 41:

A wooden block, initially at rest on the ground, is pushed by a force which increases linearly with time t. Which of the following curves best describes the acceleration of the block with time:

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

Question 42:

A rubber ball falls from a height h and rebounds up to the height of h/2, the percentage loss of total energy of the initial system as well as the velocity of the ball before it strikes the ground, respectively, are:

1. 50%, √gh/2
2. 50%, √gh
3. 40%, √2gh
4. 50%, √2gh

Question 43:

The equation of a stationary wave is: y = 2a sin(2πnt / λ) cos(2πx / λ). Which of the following is NOT correct?

1. The dimensions of nt are [L].
2. The dimensions of n are [LT⁻¹].
3. The dimensions of n/λ are [T].
4. The dimensions of x are [L].

Question 44:

A body travels 102.5 m in the nth second and 115.0 m in the (n + 2)th second. The acceleration is:

1. 9 m/s²
2. 6.25 m/s²
3. 12.5 m/s²
4. 5 m/s²

Question 45:

To measure the internal resistance of a battery, a potentiometer is used. For R = 10Ω, the balance point is observed at ℓ = 500 cm and for R = 1Ω the balance point is observed at ℓ = 400 cm. The internal resistance of the battery is approximately:

1. 0.2Ω
2. 0.4Ω
3. 0.1Ω
4. 0.3Ω

Question 46:

An infinitely long positively charged straight thread has a linear charge density λ Cm⁻¹. An electron revolves along a circular path having its axis along the length of the wire. The graph that correctly represents the variation of the kinetic energy of the electron as a function of the radius of the circular path from the wire is:

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

Question 47:

The value of net resistance of the network as shown in the given figure is:

1. 5/2 Ω
2. 15/4 Ω
3. 6Ω
4. 30/11 Ω

Question 48:

P-T diagram of an ideal gas having three different densities ρ₁, ρ₂, ρ₃ (in three different cases) is shown in the figure. Which of the following is correct:

1. ρ₂ < ρ₃
2. ρ₁ > ρ₂
3. ρ₁ < ρ₂
4. ρ₁ = ρ₂ = ρ₃

Question 49:

The coordinates of a particle moving in the x-y plane are given by:
x = 2 + 4t, y = 3t + 8t².
The motion of the particle is:

1. Non-uniformly accelerated.
2. Uniformly accelerated having motion along a straight line.
3. Uniform motion along a straight line.
4. Uniformly accelerated having motion along a parabolic path.

Question 50:

In an AC circuit, the instantaneous current is zero, when the instantaneous voltage is maximum. In this case, the source may be connected to:

1. Pure inductor.
2. Pure capacitor.
3. Pure resistor.
4. Combination of an inductor and capacitor.

Question 51:

An infinite plane sheet of charge having uniform surface charge density +σ C/m² is placed on the x-y plane. Another infinitely long line charge having uniform linear charge density +λe C/m is placed at z = 4m plane and parallel to the y-axis. If the magnitude values |σ| = 2|λe| then at point (0, 0, 2), the ratio of magnitudes of electric field values due to sheet charge to that of line charge is π√n : 1. The value of n is:

1. 8
2. 12
3. 16
4. 20

Question 52:

A hydrogen atom changes its state from n = 3 to n = 2. Due to recoil, the percentage change in the wavelength of emitted light is approximately 1×10⁻ⁿ. The value of n is:

1. 5
2. 6
3. 7
4. 8

Question 53:

The magnetic field existing in a region is given by B = 0.2(1 + 2x)k̂ T. A square loop of edge 50 cm carrying 0.5A current is placed in the x-y plane with its edges parallel to the x- and y-axes. The magnitude of the net magnetic force experienced by the loop is:

1. 25 mN
2. 30 mN
3. 50 mN
4. 75 mN

Question 54:

An alternating current at any instant is given by i = (6 + √56 sin(100πt + π/3)) A. The rms value of the current is:

1. 6 A
2. 7 A
3. 8 A
4. 9 A

Question 55:

Twelve wires each having resistance 2Ω are joined to form a cube. A battery of 6V emf is joined across point a and c. The voltage difference between e and f is V:

1. 0.5V
2. 1V
3. 1.5V
4. 2V

Question 56:

A soap bubble is blown to a diameter of 7 cm. 36960 erg of work is done in blowing it further. If the surface tension of the soap solution is 40 dyne/cm, the new radius is:

1. 7 cm
2. 8 cm
3. 9 cm
4. 10 cm

Question 57:

Two wavelengths λ₁ and λ₂ are used in Young’s double slit experiment. λ₁ = 450 nm and λ₂ = 650 nm. The minimum order of fringe produced by λ₂ which overlaps with the fringe produced by λ₁ is n. The value of n is:

1. 5
2. 7
3. 9
4. 11

Question 58:

An elastic spring under tension of 3N has a length a. Its length under tension 2N is b. For its length (3a − 2b), the value of tension will be:

1. 4 N
2. 5 N
3. 6 N
4. 7 N

Question 59:

Two forces F₁ and F₂ are acting on a body. One force has magnitude thrice that of the other force, and the resultant of the two forces is equal to the force of larger magnitude. The angle between F₁ and F₂ is cos⁻¹(1/n). The value of |n| is:

1. 4
2. 5
3. 6
4. 7

Question 60:

A solid sphere and a hollow cylinder roll up without slipping on the same inclined plane with the same initial speed v. The sphere and the cylinder reach up to maximum heights h₁ and h₂, respectively, above the initial level. The ratio h₁ : h₂ is n/10. The value of n is:

1. 5
2. 6
3. 7
4. 8

Question 61:

What pressure (bar) of H₂ would be required to make the emf of the hydrogen electrode zero in pure water at 25°C?

1. 10⁻¹⁴
2. 10⁻⁷
3. 1
4. 0.5

Question 62:

The correct sequence of ligands in the order of decreasing field strength is:

1. CO > H₂O > F⁻ > S²⁻
2. OH⁻ > F⁻ > NH₃ > CN⁻
3. NCS⁻ > EDTA⁴⁻ > CN⁻ > CO
4. S²⁻ > OH⁻ > EDTA⁴⁻ > CO

Question 63:

Match List - I with List - II:

Choose the correct answer from the options given below:

1. (A) – (IV), (B) – (III), (C) – (I), (D) – (II)
2. (A) – (III), (B) – (I), (C) – (II), (D) – (IV)
3. (A) – (II), (B) – (IV), (C) – (III), (D) – (I)
4. (A) – (I), (B) – (II), (C) – (IV), (D) – (III)

Question 64:

What will be the decreasing order of basic strength of the following conjugate bases?

OH⁻, RO⁻, CH₃COO⁻, Cl⁻

1. Cl⁻ > OH⁻ > RO⁻ > CH₃COO⁻
2. RO⁻ > OH⁻ > CH₃COO⁻ > Cl⁻
3. OH⁻ > RO⁻ > CH₃COO⁻ > Cl⁻
4. Cl⁻ > RO⁻ > OH⁻ > CH₃COO⁻

Question 65:

In the precipitation of the iron group (III) in qualitative analysis, ammonium chloride is added before adding ammonium hydroxide to:

1. Prevent interference by phosphate ions
2. Decrease concentration of OH⁻ ions
3. Increase concentration of Cl⁻ ions
4. Increase concentration of NH₄⁺ ions

Question 66:

Identify the product in the following reaction:

1. Reaction: Hydrolysis of an ester with water
2. Reaction: Dehydration of an alcohol using concentrated H₂SO₄
3. Reaction: Oxidation of primary alcohol to aldehyde
4. Reaction: Reduction of an aldehyde with NaBH₄

Question 67:

One of the commonly used electrodes is the calomel electrode. Under which of the following categories does the calomel electrode come?

1. Metal – Insoluble Salt – Anion electrodes
2. Oxidation – Reduction electrodes
3. Gas – Ion electrodes
4. Metal ion – Metal electrodes

Question 68:

Number of complexes from the following with even number of unpaired d-electrons is:

[V(H₂O)₆]³⁺, [Cr(H₂O)₆]²⁺, [Fe(H₂O)₆]³⁺, [Ni(H₂O)₆]³⁺, [Cu(H₂O)₆]²⁺

[Given atomic numbers: V = 23, Cr = 24, Fe = 26, Ni = 28, Cu = 29]

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

Question 69:

Which one of the following molecules has the maximum dipole moment?

1. NF₃
2. CH₄
3. NH₃
4. PF₅

Question 70:

Number of molecules/ions from the following in which the central atom is involved in sp³ hybridization is:

NO₃⁻, BCl₃, ClO₂⁻, ClO₃⁻

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

Question 71:

Which among the following is an incorrect statement?

1. Electromeric effect dominates over inductive effect
2. The electromeric effect is a temporary effect
3. The organic compound shows electromeric effect in the presence of the reagent only
4. Hydrogen ion (H⁺) shows negative electromeric effect

Question 72:

Given below are two statements:

Statement I: Acidity of α-hydrogens of aldehydes and ketones is responsible for Aldol reaction.

Statement II: Reaction between benzaldehyde and ethanol will NOT give Cross-Aldol product.

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

Question 73:

Which of the following nitrogen-containing compounds does not give Lassaigne’s test?

1. Phenyl hydrazine
2. Glycine
3. Urea
4. Hydrazine

Question 74:

Which of the following is the correct structure of L-Glucose?

1. Chemical formula or structure provided in the figure (shown below)
2. Chemical structure of D-Glucose
3. Chemical formula of L-Glucose
4. Chemical structure of D-Fructose

Question 75:

The element which shows only one oxidation state other than its elemental form is:

1. Cobalt
2. Scandium
3. Titanium
4. Nickel

Question 76:

Identify the product in the following reaction:

Reduction of an aldehyde with NaBH₄

1. Primary alcohol
2. Hydrolysis of an ester with water
3. Dehydration of an alcohol using concentrated H₂SO₄
4. Oxidation of primary alcohol to aldehyde

Question 77:

Number of elements from the following that CANNOT form compounds with valencies which match their respective group valencies:

B, C, N, S, O, F, P, Al, Si

1. 7
2. 5
3. 6
4. 3

Question 78:

The Molarity (M) of an aqueous solution containing 5.85 g of NaCl in 500 mL water is:

1. 20
2. 0.2
3. 2
4. 4

Question 79:

Identify the correct set of reagents or reaction conditions ‘X’ and ‘Y’ in the following set of transformation:

1. X = conc. alc. NaOH, 80°C, Y = Br₂/CHCl₃
2. X = dil. aq. NaOH, 20°C, Y = HBr/acetic acid
3. X = conc. alc. NaOH, 80°C, Y = HBr/acetic acid
4. X = dil. aq. NaOH, 20°C, Y = Br₂/CHCl₃

Question 80:

The correct order of first ionization enthalpy values of the following elements is:

(A) O, (B) N, (C) Be, (D) F, (E) B

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

Question 81:

The enthalpy of formation of ethane (C₂H₆) from ethylene by addition of hydrogen where the bond energies of C–H, C–C, H–H are 414 kJ, 347 kJ, 615 kJ, and 435 kJ respectively is:

1. 125 kJ
2. 150 kJ
3. 175 kJ
4. 200 kJ

Question 82:

The number of correct reactions among the following is:

1. Friedel-Crafts acylation using anhydrous AlCl₃ and a carboxylic acid chloride
2. Pd/BaSO₄ (Rosenmund reduction conditions) is used to reduce an acyl chloride to an aldehyde
3. Carboxylic acid reacting with CO and HCl under anhydrous conditions with AlCl₃ or CuCl
4. Benzene derivative with CONH₂ and HCl

Question 83:

X g of ethylamine is subjected to reaction with NaNO₂/HCl followed by water; evolved dinitrogen gas occupied 2.24 L volume at STP. X is × 10⁻¹ g.

1. 35 × 10⁻¹ g
2. 40 × 10⁻¹ g
3. 45 × 10⁻¹ g
4. 50 × 10⁻¹ g

Question 84:

The de-Broglie wavelength of an electron in the 4th orbit is πa₀. (a₀ = Bohr’s radius)

1. 4
2. 8
3. 16
4. 32

Question 85:

Only 2 mL of KMnO₄ solution of unknown molarity is required to reach the endpoint of a titration of 20 mL of oxalic acid (2 M) in acidic medium. The molarity of KMnO₄ solution should be:

1. 0.5 M
2. 2 M
3. 4 M
4. 8 M

Question 86:

Consider the following reaction: MnO₂ + KOH + O₂ → A + H₂O. Product ‘A’ in neutral or acidic medium disproportionates to give products ‘B’ and ‘C’ along with water. The sum of spin-only magnetic moment values of B and C is BM (nearest integer). (Given atomic number of Mn is 25)

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

Question 87:

The number of different chain isomers for C₇H₁₆ is:

1. 7
2. 8
3. 9
4. 10

Question 88:

Number of molecules/species from the following having one unpaired electron is:

O₂, O₂⁻, NO, CN⁻, O₂²⁻

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

Question 89:

The number of different chain isomers for C₇H₁₆ is:

1. 7
2. 8
3. 9
4. 10

Question 90:

Number of molecules/species from the following having one unpaired electron is:

O₂, O₂⁻, NO, CN⁻, O₂²⁻

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