question: Using the expression 2d sin θ = λ, one calculates the values of d by measuring the corresponding angles θ in the range 0 to 90°. The wavelength λ is exactly known and the error in θ is constant for all values of θ. As θ increases from 0°,

response_choices: (A) the absolute error in d remains constant. (B) the absolute error in d increases. (C) the fractional error in d remains constant. (D) the fractional error in d decreases.

answer: D

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question_subject: physics


question: Two non-conducting spheres of radii R1 and R2 and carrying uniform volume charge densities +ρ and –ρ, respectively, are placed such that they partially overlap, as shown in the figure. At all points in the overlapping region,

response_choices: (A) the electrostatic field is zero. (B) the electrostatic potential is constant. (C) the electrostatic field is constant in magnitude. (D) the electrostatic field has same direction.

answer: CD

image_available: yes

question_subject: physics


question: The figure below shows the variation of specific heat capacity (C) of a solid as a function of temperature (T). The temperature is increased continuously from 0 to 500 K at a constant rate. Ignoring any volume change, the following statement(s) is (are) correct to a reasonable approximation.

response_choices: (A) the rate at which heat is absorbed in the range 0-100 K varies linearly with temperature T. (B) heat absorbed in increasing the temperature from 0-100 K is less than the heat required for increasing the temperature from 400-500 K. (C) there is no change in the rate of heat absorption in the range 400-500 K. (D) the rate of heat absorption increases in the range 200-300 K.

answer: ABCD or BCD

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question_subject: physics


question: The radius of the orbit of an electron in a Hydrogen-like atom is 4.5 a0, where a0 is the Bohr radius. Its orbital angular momentum is 3h/2π. It is given that h is Planck constant and R is Rydberg constant. The possible wavelength(s), when the atom de-excites, is (are)

answer: AC

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question_subject: physics


question: Two bodies, each of mass M, are kept fixed with a separation 2L. A particle of mass m is projected from the midpoint of the line joining their centres, perpendicular to the line. The gravitational constant is G. The correct statement(s) is (are)

response_choices: (A) The minimum initial velocity of the mass m to escape the gravitational field of the two bodies is 4√(GM/L). (B) The minimum initial velocity of the mass m to escape the gravitational field of the two bodies is 2√(GM/L). (C) The minimum initial velocity of the mass m to escape the gravitational field of the two bodies is √(2GM/L). (D) The energy of the mass m remains constant.

answer: BD

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question_subject: physics


question: A particle of mass m is attached to one end of a mass-less spring of force constant k, lying on a frictionless horizontal plane. The other end of the spring is fixed. The particle starts moving horizontally from its equilibrium position at time t = 0 with an initial velocity u0. When the speed of the particle is 0.5 u0, it collides elastically with a rigid wall. After this collision,

response_choices: (A) the speed of the particle when it returns to its equilibrium position is u0. (B) the time at which the particle passes through the equilibrium position for the first time is t = π√(m/k). (C) the time at which the maximum compression of the spring occurs is t = 4π/3√(m/k). (D) the time at which the particle passes through the equilibrium position for the second time is t = 5π/3√(m/k).

answer: AD

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question_subject: physics


question: A steady current I flows along an infinitely long hollow cylindrical conductor of radius R. This cylinder is placed coaxially inside an infinite solenoid of radius 2R. The solenoid has n turns per unit length and carries a steady current I. Consider a point P at a distance r from the common axis. The correct statement(s) is (are)

response_choices: (A) In the region 0 < r < R, the magnetic field is non-zero. (B) In the region R < r < 2R, the magnetic field is along the common axis. (C) In the region R < r < 2R, the magnetic field is tangential to the circle of radius r, centered on the axis. (D) In the region r > 2R, the magnetic field is non-zero.

answer: AD

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question_subject: physics


question: Two vehicles, each moving with speed u on the same horizontal straight road, are approaching each other. Wind blows along the road with velocity w. One of these vehicles blows a whistle of frequency f1. An observer in the other vehicle hears the frequency of the whistle to be f2. The speed of sound in still air is v. The correct statement(s) is (are)

response_choices: (A) If the wind blows from the observer to the source, f2>f1. (B) If the wind blows from the source to the observer, f2>f1. (C) If the wind blows from observer to the source, f2<f1. (D) If the wind blows from the source to the observer, f2<f1.

answer: AB

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question_subject: physics


question: The magnitude of the induced electric field in the orbit at any instant of time during the time interval of the magnetic field change is

answer: B

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question_subject: physics


question: The change in the magnetic dipole moment associated with the orbit, at the end of the time interval of the magnetic field change, is

answer: B

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question_subject: physics


question: The correct statement is

response_choices: (A) The nucleus 6Li can emit an alpha particle. (B) The nucleus 210Po can emit a proton. (C) Deuteron and alpha particle can undergo complete fusion. (D) The nuclei 70Zn and 34Se can undergo complete fusion.

answer: C

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question_subject: physics


question: The kinetic energy (in keV) of the alpha particle, when the nucleus 210Po at rest undergoes alpha decay, is

answer: A

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question_subject: physics


question: The speed of the block when it reaches the point Q is

answer: B

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question_subject: physics


question: The magnitude of the normal reaction that acts on the block at the point Q is

answer: A

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question_subject: physics


question: If the direct transmission method with a cable of resistance 0.4 Ω km⁻¹ is used, the power dissipation (in %) during transmission is

answer: B

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question_subject: physics


question: In the method using the transformers, assume that the ratio of the number of turns in the primary to that in the secondary in the step-up transformer is 1 : 10. If the power to the consumers has to be supplied at 200 V, the ratio of the number of turns in the primary to that in the secondary in the step-down transformer is

answer: A

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question_subject: physics


question: Match List I with List II and select the correct answer using the codes given below the lists:

response_choices:
List I: P. Boltzmann constant, Q. Coefficient of viscosity, R. Planck constant, S. Thermal conductivity
List II: 1. [ML^2T^-1], 2. [ML^-1T^-1], 3. [MLT^-3K^-1], 4. [ML^2T^-2K^-1]
Codes: (A) P-3, Q-1, R-2, S-4
(B) P-3, Q-2, R-1, S-4
(C) P-4, Q-2, R-1, S-3
(D) P-4, Q-1, R-2, S-3

answer: C

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question_subject: physics


question: A right angled prism of refractive index μ1 is placed in a rectangular block of refractive index μ2, which is surrounded by a medium of refractive index μ3, as shown in the figure. A ray of light 'e' enters the rectangular block at normal incidence. Depending upon the relationships between μ1, μ2 and μ3, it takes one of the four possible paths 'ef', 'eg', 'eh' or 'ei'.

response_choices:
List I / सूची I: P. e→f, Q. e→g, R. e→h, S. e→i

List II / सूची II:
1. μ1 > √2 μ2
2. μ2 > μ1 and/√√√ μ2 > μ3
3. μ1 = μ2
4. μ2 < μ1 < √2 μ2 and/√√√ μ2 > μ3

answer: D

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question_subject: physics


question: Match List I of the nuclear processes with List II containing parent nucleus and one of the end products of each process and then select the correct answer using the codes given below the lists:

answer: C

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question_subject: physics


question: One mole of a monatomic ideal gas is taken along two cyclic processes E→F→G→E and E→F→H→E as shown in the PV diagram. The processes involved are purely isochoric, isobaric, isothermal or adiabatic.

response_choices: Match the paths in List I with the magnitudes of the work done in List II and select the correct answer using the codes given below the lists.

answer: A

image_available: yes

question_subject: physics


question: The correct statement(s) about O3 is(are)

response_choices: (A) O-O bond lengths are equal. (B) Thermal decomposition of O3 is endothermic. (C) O3 is diamagnetic in nature. (D) O3 has a bent structure.

answer: ACD

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question_subject: chemistry


question:
In the nuclear transmutation
 ₚ⁹Be + X → ⁸₄Be + Y
(X, Y) is(are)
(A) (ℓ, n) (B) (p, D) (C) (n, D) (D) (ℓ, p)
 ₚ⁹Be + X → ⁸₄Be + Y
m̄ (X, Y) ई/है
(A) (ℓ, n) (B) (p, D) (C) (n, D) (D) (ℓ, p)

answer: AB

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question_subject: chemistry


question: The carbon-based reduction method is NOT used for the extraction of (A) tin from SnO₂ (B) iron from Fe₂O₃ (C) aluminium from Al₂O₃ (D) magnesium from MgCO₃ · CaCO₃

response_choices: (A) SnO₂ से टिन (B) Fe₂O₃ से आयरन (C) Al₂O₃ से एल्युमिनियम (D) MgCO₃·CaCO₃ से मैग्नीशियम

answer: CD

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question_subject: chemistry


question: The thermal dissociation equilibrium of CaCO₃(s) is studied under different conditions. CaCO₃(s) ⇌ CaO(s) + CO₂(g) For this equilibrium, the correct statement(s) is(are) (A) ΔH is dependent on T (B) K is independent of the initial amount of CaCO₃ (C) K is dependent on the pressure of CO₂ at a given T (D) ΔH is independent of the catalyst, if any

response_choices: (A) ΔH तापमान पर निर्भर करता है । (B) सामयावस्था स्थिरांक (K) CaCO₃ के प्रारंभिक परिमाण पर निर्भर नहीं करता है । (C) K निर्दिष्ट तापमान पर CO₂ के दाब पर निर्भर करता है । (D) ΔH उत्प्रेरक (अगर हो) के प्रभाव पर निर्भर नहीं करता है ।

answer: ABD

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question_subject: chemistry


question: The Ksp of Ag2CrO4 is 1.1 × 10⁻¹² at 298 K. The solubility (in mol/L) of Ag2CrO4 in a 0.1 M AgNO3 solution is

answer: B

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question_subject: chemistry


question: In the following reaction, the product(s) formed is(are)

response_choices: (A) P (major) (B) Q (minor) (C) R (minor) (D) S (major)

answer: BD

image_available: yes

question_subject: chemistry


question: The major product(s) of the following reaction is(are)

response_choices: A) P, B) Q, C) R, D) S

answer: Q

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question_subject: chemistry


question: After completion of the reactions (I and II), the organic compound(s) in the reaction mixtures is(are)

response_choices: (A) Reaction I : P and Reaction II : P, (B) Reaction I : U, acetone and Reaction II : Q, acetone, (C) Reaction I : T, U, acetone and Reaction II : P, (D) Reaction I : R, acetone and Reaction II : S, acetone

answer: C

image_available: yes

question_subject: chemistry


question: The succeeding operations that enable this transformation of states are

response_choices:
(A) Heating, cooling, heating, cooling
(B) Cooling, heating, cooling, heating
(C) Heating, cooling, cooling, heating
(D) Cooling, heating, heating, cooling

answer: C

image_available: yes

question_subject: chemistry


question: The pair of isochoric processes among the transformation of states is

response_choices:
(A) K to L and L to M
(B) L to M and N to K
(C) L to M and M to N
(D) M to N and N to K

answer: B

image_available: yes

question_subject: chemistry


question: P and Q, respectively, are the sodium salts of

response_choices: (A) hypochlorus and chloric acids (B) hypochlorus and perchloric acids (C) chloric and perchloric acids (D) chloric and hypochlorus acids

answer: A

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question_subject: chemistry


question: R, S and T, respectively, are

response_choices: (A) SO₂Cl₂, PCl₃ and H₃PO₄ (B) SO₂Cl₂, PCl₃ and H₃PO₃ (C) SOCl₂, PCl₃ and H₃PO₂ (D) SOCl₂, PCl₃ and H₃PO₄

answer: A

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question_subject: chemistry


question: The precipitate P contains

answer: A

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question_subject: chemistry


question: The coloured solution S contains

response_choices: (A) Fe2(SO4)3  (B) CuSO4  (C) ZnSO4  (D) Na2CrO4

answer: D

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question_subject: chemistry


question: Compounds formed from P and Q are, respectively

response_choices:
(A) Optically active S and optically active pair (T, U)
(B) Optically inactive S and optically inactive pair (T, U)
(C) Optically active pair (T, U) and optically active S
(D) Optically inactive pair (T, U) and optically inactive S

answer: B

image_available: yes

question_subject: chemistry


question: In the following reaction sequences V and W are, respectively

answer: A

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question_subject: chemistry


question: Match the chemical conversions in List I with the appropriate reagents in List II and select the correct answer using the code given below the lists:

answer: A

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question_subject: chemistry


question: The unbalanced chemical reactions given in List I show missing reagent or condition (?) which are provided in List II. Match List I with List II and select the correct answer using the code given below the lists:

answer: D

image_available: no

question_subject: chemistry


question:
The standard reduction potential data at 25 °C is given below.

E°(Fe3+, Fe2+) = + 0.77 V;
E°(Fe2+, Fe) = - 0.44 V
E°(Cu2+, Cu) = + 0.34 V;
E°(Cu+, Cu) = + 0.52 V
E°[O2(g) + 4H+ + 4e- → 2H2O] = +1.23 V;
E°[O2(g)+2H2O+ 4e- → 4OH-] = + 0.40 V
E°(Cr3+, Cr) = - 0.74 V;
E°(Cr2+, Cr) = - 0.91 V

Match E° of the redox pair in List I with the values given in List II and select the correct answer using the code given below the lists :

answer: D

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question_subject: chemistry


question: An aqueous solution of X is added slowly to an aqueous solution of Y as shown in List I. The variation in conductivity of these reactions is given in List II. Match List I with List II and select the correct answer using the code given below the lists:

response_choices: P. (C2H5)3N + CH3COOH, Q. KI (0.1M) + AgNO3 (0.01M), R. CH3COOH + KOH, S. NaOH + HI

answer: A

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question_subject: chemistry


question: Let w = √(3 + i)/2 and P = {wⁿ : n = 1, 2, 3, ...}. Further H₁ = {z ∈ C : Re z > 1/2} and H₂ = {z ∈ C : Re z < -1/2}, where C is the set of all complex numbers. If z₁ ∈ P ∩ H₁, z₂ ∈ P ∩ H₂ and O represents the origin, then ∠ z₁ O z₂ =

answer: CD

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question_subject: mathematics


question: If 3ˣ = 4ˣ⁻¹, then x =

answer: ABC

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question_subject: mathematics


question: Let ω be a complex cube root of unity with ω ≠ 1 and P = [pij] be a n × n matrix with pij = ω^{ij}. Then P^2 ≠ 0, when n =

answer: BCD

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question_subject: mathematics


question: The function f(x) = 2 | x | + | x + 2 | - | | x + 2 | - 2 | x || has a local minimum or a local maximum at x =

answer: AB

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question_subject: mathematics


question: For a ∈ ℝ (the set of all real numbers), a ≠ -1, lim n→∞ ((1ª + 2^n + ... + n^n) / (n + 1)^n-1 [(na + 1) + (na + 2) + ... + (na + n)]) = 1/60 Then a =

answer: B

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question_subject: mathematics


question: Circle(s) touching x -- axis at a distance 3 from the origin and having an intercept of length 2√7 on y -- axis is (are)

answer: AC

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question_subject: mathematics


question: Two lines L1 : x = 5, y/(3 - α) = z/-2 and L2 : x = α, y/(-1 - 2 - α) = z/2 - α are coplanar. Then α can take value(s)

answer: AD

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question_subject: mathematics


question: In a triangle PQR, P is the largest angle and cos P = 1/3. Further the incircle of the triangle touches the sides PQ, QR and RP at N, L and M respectively, such that the lengths of PN, QL and RM are consecutive even integers. Then possible length(s) of the side(s) of the triangle is (are)

answer: BD

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question_subject: mathematics


question: Area of S = S₁ ∩ S₂ ∩ S₃, where S₁ = {z ∈ C : |z| < 4}, S₂ = {z ∈ C : Im[(z - 1 + √3i) / (1 - √3i)] > 0} and S₃ = {z ∈ C : Re z > 0}.

answer: B

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question_subject: mathematics


question: min |1 - 3t - z| =

answer: C

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question_subject: mathematics


question: If 1 ball is drawn from each of the boxes B1, B2 and B3, the probability that all 3 drawn balls are of the same colour is

answer: A

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question_subject: mathematics


question: If 2 balls are drawn (without replacement) from a randomly selected box and one of the balls is white and the other ball is red, the probability that these 2 balls are drawn from box B2 is

answer: D

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question_subject: mathematics


question: Which of the following is true for 0 < x < 1 ?

answer: D

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question_subject: mathematics


question: If the function e^x f(x) assumes its minimum in the interval [0, 1] at x = 1/4, which of the following is true ?

answer: C

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question_subject: mathematics


question: Length of chord PQ is

answer: B

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question_subject: mathematics


question: If chord PQ subtends an angle θ at the vertex of y^2 = 4ax, then tan θ =

answer: D

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question_subject: mathematics


question: A line L : y = mx + 3 meets y - axis at E(0, 3) and the arc of the parabola y² = 16x, 0 ≤ y ≤ 6 at the point F(x0, y0). The tangent to the parabola at F(x0, y0) intersects the y-axis at G(0, y1). The slope m of the line L is chosen such that the area of the triangle EFG has a local maximum. Match List I with List II and select the correct answer using the code given below the lists :

answer: A

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question_subject: mathematics


question: Match List I with List II and select the correct answer using the code given below the lists:

answer: B

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question_subject: mathematics


question: P. (1/(y^2*(cot(sin^-1y)+tan(sin^-1y)))+(y sin(tan^-1y)+y cos(tan^-1y))^2)^(1/2) takes value

answer: 1

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question_subject: mathematics


question: Q. If cos x + cos y + cos z = 0 = sin x + sin y + sin z then possible value of cos (x-y)/2 is

answer: 2

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question_subject: mathematics


question: R. If cos((π/4)-x) cos 2x + sin x sin 2x sec x = cos x sin 2x sec x +

answer: 3

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question_subject: mathematics


question: S. If cot (sin^-1√(1-x^2)) = sin (tan^-1(x√6)) , x ≠ 0, then possible value of x is

answer: 4

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question_subject: mathematics


question: Consider the lines L1 : x - 1/2 = y/-1 = z + 3/1 , L2 : x - 4/1 = y + 3/1 = z + 3/2 and the planes P1 : 7x + y + 2z = 3, P2 : 3x + 5y - 6z = 4. Let ax + by + cz = d be the equation of the plane passing through the point of intersection of lines L1 and L2, and perpendicular to planes P1 and P2. Match List - I with List - II and select the correct answer using the code given below the lists.

answer: A

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question_subject: mathematics


question: Match List–I with List–II and select the correct answer using the code given below the lists:

answer: C

image_available: no

question_subject: mathematics