question: A loop carrying current I lies in the x-y plane as shown in the figure. The unit vector k̂ is coming out of the plane of the paper. The magnetic moment of the current loop is

answer: B

image_available: yes

question_subject: physics


question: An infinitely long hollow conducting cylinder with inner radius R/2 and outer radius R carries a uniform current density along its length. The magnitude of the magnetic field, |B| as a function of the radial distance r from the axis is best represented by

response_choices: (A), (B), (C), (D) [options represented by graphs]

answer: D

image_available: yes

question_subject: physics


question: A thin uniform cylindrical shell, closed at both ends, is partially filled with water. It is floating vertically in water in half-submerged state. If ρc is the relative density of the material of the shell with respect to water, then the correct statement is that the shell is

response_choices: (A) more than half-filled if ρc is less than 0.5. (B) more than half-filled if ρc is more than 1.0. (C) half-filled if ρc is more than 0.5. (D) less than half-filled if ρc is less than 0.5.

answer: A

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question_subject: physics


question: In the given circuit, a charge of +80 μC is given to the upper plate of the 4 μF capacitor. Then in the steady state, the charge on the upper plate of the 3 μF capacitor is

answer: C

image_available: yes

question_subject: physics


question: Two moles of ideal helium gas are in a rubber balloon at 30°C. The balloon is fully expandable and can be assumed to require no energy in its expansion. The temperature of the gas in the balloon is slowly changed to 35°C. The amount of heat required in raising the temperature is nearly (take R = 8.31 J/mol.K)

answer: D

image_available: no

question_subject: physics


question: Consider a disc rotating in the horizontal plane with a constant angular speed ω about its centre O. The disc has a shaded region on one side of the diameter and an unshaded region on the other side as shown in the figure. When the disc is in the orientation as shown, two pebbles P and Q are simultaneously projected at an angle towards R. The velocity of projection is in the y-z plane and is same for both pebbles with respect to the disc. Assume that (i) they land back on the disc before the disc has completed 1/8 rotation, (ii) their range is less than half the disc radius, and  (iii) ω remains constant throughout. Then

response_choices:
(A) P lands in the shaded region and Q in the unshaded region.
(B) P lands in the unshaded region and Q in the shaded region.
(C) Both P and Q land in the unshaded region.
(D) Both P and Q land in the shaded region.

answer: C or D

image_available: yes

question_subject: physics


question: A student is performing the experiment of Resonance Column. The diameter of the column tube is 4 cm. The frequency of the tuning fork is 512 Hz. The air temperature is 38°C in which the speed of sound is 336 m/s. The zero of the meter scale coincides with the top end of the Resonance Column tube. When the first resonance occurs, the reading of the water level in the column is

answer: B

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question_subject: physics


question: Two identical discs of same radius R are rotating about their axes in opposite directions with the same constant angular speed ω. The discs are in the same horizontal plane. At time t = 0, the points P and Q are facing each other as shown in the figure. The relative speed between the two points P and Q is vr. In one time period (T) of rotation of the discs, vr as a function of time is best represented by

response_choices: A, B, C, D

answer: A

image_available: yes

question_subject: physics


question: For light incident from air on a meta-material, the appropriate ray diagram is

answer: C

image_available: yes

question_subject: physics


question: Most materials have the refractive index, n > 1. So, when a light ray from air enters a naturally occurring material, then by Snell's law, (sin θ1) / (sin θ2) = n2 / n1, it is understood that the refracted ray bends towards the normal. But it never emerges on the same side of the normal as the incident ray. According to electromagnetism, the refractive index of the medium is given by the relation, n = (c / v) = ±√(εrμr), where c is the speed of electromagnetic waves in vacuum, v its speed in the medium, εr and μr are the relative permittivity and permeability of the medium respectively. In normal materials, both εr and μr are positive, implying positive n for the medium. When both εr and μr are negative, one must choose the negative root of n. Such negative refractive index materials can now be artificially prepared and are called meta-materials. They exhibit significantly different optical behavior, without violating any physical laws. Since n is negative, it results in a change in the direction of propagation of the refracted light. However, similar to normal materials, the frequency of light remains unchanged upon refraction even in meta-materials.

answer: N/A

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question_subject: physics


question: Choose the correct statement.

response_choices: (A) The speed of light in the meta-material is v = c|r|, (B) The speed of light in the meta-material is v = c/|r|, (C) The speed of light in the meta-material is v = c, (D) The wavelength of the light in the meta-material (λm) is given by λm = λair|r|, where λair is the wavelength of the light in air.

answer: B

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question_subject: physics


question: What is the maximum energy of the anti-neutrino?

response_choices: (A) Zero. (B) Much less than 0.8 × 10⁶ eV. (C) Nearly 0.8 × 10⁶ eV. (D) Much larger than 0.8 × 10⁶ eV.

answer: C

image_available: no

question_subject: physics


question: If the anti-neutrino had a mass of 3 eV/c² (where c is the speed of light) instead of zero mass, what should be the range of the kinetic energy, K, of the electron?

answer: D

image_available: no

question_subject: physics


question: Which of the following statements about the instantaneous axis (passing through the centre of mass) is correct?

response_choices: (A) It is vertical for both the cases (a) and (b). (B) It is vertical for case (a); and is at 45° to the x-z plane and lies in the plane of the disc for case (b). (C) It is horizontal for case (a); and is at 45° to the x-z plane and is normal to the plane of the disc for case (b). (D) It is vertical for case (a); and is at 45° to the x-z plane and is normal to the plane of the disc for case (b).

answer: A

image_available: yes

question_subject: physics


question: Which of the following statements regarding the angular speed about the instantaneous axis (passing through the centre of mass) is correct?

response_choices: (A) It is √2ω for both the cases. (B) It is ω for case (a); and ω/√2 for case (b). (C) It is ω for case (a); and √2ω for case (b). (D) It is ω for both the cases.

answer: D

image_available: no

question_subject: physics


question: In the given circuit, the AC source has ω = 100 rad/s. Considering the inductor and capacitor to be ideal, the correct choice(s) is(are)

response_choices:
(A) The current through the circuit, I is 0.3 A.
(B) The current through the circuit, I is 0.3√2 A.
(C) The voltage across 100 Ω resistor = 10 √2 V.
(D) The voltage across 50 Ω resistor = 10 V.

answer: C or AC

image_available: yes

question_subject: physics


question: A current carrying infinitely long wire is kept along the diameter of a circular wire loop, without touching it. The correct statement(s) is(are)

response_choices:
(A) The emf induced in the loop is zero if the current is constant.
(B) The emf induced in the loop is finite if the current is constant.
(C) The emf induced in the loop is zero if the current decreases at a steady rate.
(D) The emf induced in the loop is finite if the current decreases at a steady rate.

answer: AC

image_available: no

question_subject: physics


question: Six point charges are kept at the vertices of a regular hexagon of side L and centre O, as shown in the figure. Given that K = 1/(4πε0 × L), which of the following statement(s) is(are) correct?

response_choices:
(A) The electric field at O is 6K along OD.
(B) The potential at O is zero.
(C) The potential at all points on the line PR is same.
(D) The potential at all points on the line ST is same.

answer: ABC

image_available: yes

question_subject: physics


question: Two solid cylinders P and Q of same mass and same radius start rolling down a fixed inclined plane from the same height at the same time. Cylinder P has most of its mass concentrated near its surface, while Q has most of its mass concentrated near the axis. Which statement(s) is(are) correct?

response_choices:
(A) Both cylinders P and Q reach the ground at the same time.
(B) Cylinder P has larger linear acceleration than cylinder Q.
(C) Both cylinders reach the ground with same translational kinetic energy.
(D) Cylinder Q reaches the ground with larger angular speed.

answer: D

image_available: no

question_subject: physics


question: Two spherical planets P and Q have the same uniform density ρ, masses Mp and Mq, and surface areas A and 4A, respectively. A spherical planet R also has uniform density ρ and its mass is (Mp + Mq). The escape velocities from the planets P, Q and R, are Vp, Vq and Vr, respectively. Then

response_choices: (A) Vq > Vr > Vp 	(B) Vr > Vq > Vp 	(C) Vr/ Vp = 3 	(D) Vp/ Vq = 1/2

answer: BD

image_available: no

question_subject: physics


question: The figure shows a system consisting of (i) a ring of outer radius 3R rolling clockwise without slipping on a horizontal surface with angular speed ω and (ii) an inner disc of radius 2R rotating anti-clockwise with angular speed ω/2. The ring and disc are separated by frictionless ball bearings. The system is in the x-z plane. The point P on the inner disc is at a distance R from the origin, where OP makes an angle of 30° with the horizontal. Then with respect to the horizontal surface,

response_choices:
(A) the point O has a linear velocity 3Rωι̂
(B) the point P has a linear velocity (1/4)Rωι̂ + (√3/4)Rωκ̂
(C) the point P has a linear velocity (3/4)Rωι̂ - (√3/4)Rωκ̂
(D) the point P has a linear velocity |(3 - √3/4)Rωι̂ + (1/4)Rωκ̂|

answer: AB

image_available: yes

question_subject: physics


question: NiCl2(P(C2H5)3)2(C7H8))2 exhibits temperature dependent magnetic behaviour (paramagnetic / diamagnetic). The coordination geometries of Ni2+ in the paramagnetic and diamagnetic states are respectively

response_choices: (A) tetrahedral and tetrahedral, (B) square planar and square planar, (C) tetrahedral and square planar, (D) square planar and tetrahedral

answer: C

image_available: no

question_subject: chemistry


question: In the cyanide extraction process of silver from argentite ore, the oxidizing and reducing agents used are

response_choices: (A) O2 and CO respectively., (B) O2 and Zn dust respectively., (C) HNO3 and Zn dust respectively., (D) HNO3 and CO respectively.

answer: B

image_available: no

question_subject: chemistry


question: The reaction of white phosphorus with aqueous NaOH gives phosphine along with another phosphorus containing compound. The reaction type; the oxidation states of phosphorus in phosphine and the other product are respectively

response_choices: (A) redox reaction; – 3 and – 5, (B) redox reaction; + 3 and + 5, (C) disproportionation reaction; – 3 and + 5, (D) disproportionation reaction; – 3 and + 3

answer: Zero Marks to all

image_available: no

question_subject: chemistry


question: The shape of XeO3F2 molecule is

response_choices: (A) trigonal bipyramidal, (B) square planar, (C) tetrahedral, (D) see-saw

answer: D

image_available: no

question_subject: chemistry


question: For a dilute solution containing 2.5 g of a non-volatile non-electrolyte solute in 100 g of water, the elevation in boiling point at 1 atm pressure is 2°C. Assuming concentration of solute is much lower than the concentration of solvent, the vapour pressure (mm of Hg) of the solution is (take Kb = 0.76 K kg mol^-1)

answer: A

image_available: no

question_subject: chemistry


question: The compound that undergoes decarboxylation most readily under mild condition is

response_choices: (A) Structure1, (B) Structure2, (C) Structure3, (D) Structure4

answer: B

image_available: yes

question_subject: chemistry


question: Using the data provided, calculate the multiple bond energy (kJ mol^-1) of a C≡C bond in C₂H₂. That energy is (take the bond energy of a C-H bond as 350 kJ mol^-1.)

answer: D

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question_subject: chemistry


question: The major product H of the given reaction sequence is CH₃ – CH₂ – CO – CH₃ → G → H

response_choices: A) CH₃ – CH = C – COOH, B) CH₃ – CH = C – CN, C) CH₃ – CH₂ – C – COOH, D) CH₃ – CH = C – CO – NH₂

answer: A

image_available: yes

question_subject: chemistry


question: Bleaching powder contains a salt of an oxoacid as one of its components. The anhydride of that oxoacid is

answer: A

image_available: no

question_subject: chemistry


question: 25 mL of household bleach solution was mixed with 30 mL of 0.50 M KI and 10 mL of 4 N acetic acid. In the titration of the liberated iodine, 48 mL of 0.25 N Na2S2O3 was used to reach the end point. The molarity of the household bleach solution is

answer: C

image_available: no

question_subject: chemistry


question: The solubility product (Ksp: mol3 dm-9) of MX3 at 298 K based on the information available for the given concentration cell is (take 2.303 × R × 298/F = 0.059 V)

answer: B

image_available: no

question_subject: chemistry


question: The value of Δ G (kJ mol^-1) for the given cell is (take 1F = 96500 C mol^-1)

answer: D

image_available: no

question_subject: chemistry


question: The compound I is

response_choices: (A) O-H    (B) -OH    (C) O-CH3    (D) H-H-H

answer: A

image_available: yes

question_subject: chemistry


question: The compound K is

answer: C

image_available: yes

question_subject: chemistry


question: The reversible expansion of an ideal gas under adiabatic and isothermal conditions is shown in the figure. Which of the following statement(s) is (are) correct?

response_choices: (A) T1 = T2, (B) T3 > T1, (C) wisothermal > wadiabatic, (D) ΔUisothermal > ΔUadiabatic

answer: ACD or AD

image_available: yes

question_subject: chemistry


question: The given graphs / data I, II, III and IV represent general trends observed for different physisorption and chemisorption processes under mild conditions of temperature and pressure. Which of the following choice(s) about I, II, III and IV is (are) correct?

response_choices: (A) I is physisorption and II is chemisorption (B) I is physisorption and III is chemisorption (C) IV is chemisorption and II is chemisorption (D) IV is chemisorption and III is chemisorption

answer: AC

image_available: yes

question_subject: chemistry


question: For the given aqueous reactions, which of the statement(s) is (are) true ?

response_choices:
(A) The first reaction is a redox reaction.
(B) White precipitate is Zn₃[Fe(CN)₆]₂.
(C) Addition of filtrate to starch solution gives blue colour.
(D) White precipitate is soluble in NaOH solution.

answer: ACD

image_available: yes

question_subject: chemistry


question: With respect to graphite and diamond, which of the statement(s) given below is (are) correct?

response_choices: (A) Graphite is harder than diamond. (B) Graphite has higher electrical conductivity than diamond. (C) Graphite has higher thermal conductivity than diamond. (D) Graphite has higher C-C bond order than diamond.

answer: BD

image_available: no

question_subject: chemistry


question: With reference to the scheme given, which of the given statment(s) about T, U, V and W is (are) correct ?

response_choices: (A) T is soluble in hot aqueous NaOH (B) U is optically active (C) Molecular formula of W is C10H18O4 (D) V gives effervescence on treatment with aqueous NaHCO3

answer: ACD

image_available: yes

question_subject: chemistry


question: Which of the given statement(s) about M, O, P and Q with respect to M is (are) correct?

response_choices: (A) M and N are non-mirror image stereoisomers, (B) M and O are identical, (C) M and P are enantiomers, (D) M and Q are identical

answer: ABC

image_available: yes

question_subject: chemistry


question: The equation of a plane passing through the line of intersection of the planes x + 2y + 3z = 2 and x - y + z = 3 and at a distance 2/√3 from the point (3, 1, - 1) is

answer: A

image_available: no

question_subject: mathematics


question: Let PQR be a triangle of area Δ with a = 2, b = 7/2 and c = 5/2, where a, b and c are the lengths of the sides of the triangle opposite to the angles at P, Q and R respectively. Then 2 sin P - sin 2 P / 2 sin P + sin 2 P equals

answer: C

image_available: no

question_subject: mathematics


question: If a and b are vectors such that |a + b| = √29 and a × (2i + 3j + 4k) = (2i + 3j + 4k) × b, then a possible value of (a + b)·(–7i + 2j + 3k) is

answer: C

image_available: no

question_subject: mathematics


question: If P is a 3 x 3 matrix such that PT = 2P + I, where PT is the transpose of P and I is the 3 x 3 identity matrix, then there exists a column matrix X = [x y z]T such that

answer: D

image_available: yes

question_subject: mathematics


question: Let α(a) and β(a) be the roots of the equation √(1+a-1)x^2 + (√(1+a-1)x + (√(1+a-1) = 0 where a > -1. Then lim a→0+ α(a) and lim a→0+ β(a) are

answer: B

image_available: no

question_subject: mathematics


question: Four fair dice D1, D2, D3 and D4, each having six faces numbered 1, 2, 3, 4, 5 and 6, are rolled simultaneously. The probability that D4 shows a number appearing on one of D1, D2 and D3 is

answer: A

image_available: no

question_subject: mathematics


question: The value of the integral ∫(π/2)(-π/2) (x^2 + ln(π+x/π-x))cosx dx is

answer: B

image_available: no

question_subject: mathematics


question: Let a1, a2, a3, ... be in harmonic progression with a1 = 5 and a20 = 25. The least positive integer n for which an < 0 is

answer: D

image_available: no

question_subject: mathematics


question: The value of b_n is

answer: B

image_available: no

question_subject: mathematics


question: Which of the following is correct?

answer: A

image_available: no

question_subject: mathematics


question: Which of the following is true?

response_choices:
(A) g is increasing on (1, ∞)
(B) g is decreasing on (1, ∞)
(C) g is increasing on (1, 2) and decreasing on (2, ∞)
(D) g is decreasing on (1, 2) and increasing on (2, ∞)

answer: B

image_available: yes

question_subject: mathematics


question:
Consider the statements :

P : There exists some x ∈ ℝ such that f (x) + 2x = 2(1 + x²)

Q : There exists some x ∈ ℝ such that 2f (x) + 1= 2x(1 + x)

Then

response_choices:
(A) both P and Q are true
(B) P is true and Q is false
(C) P is false and Q is true
(D) both P and Q are false

answer: C

image_available: yes

question_subject: mathematics


question: A possible equation of L is

answer: A

image_available: yes

question_subject: mathematics


question: A common tangent of the two circles is

answer: D

image_available: yes

question_subject: mathematics


question: For every integer n, let an and bn be real numbers. Let function f : R → R be given by f(x) = { an + sin π x, for x ∈ [2n, 2n + 1] for all integers n. bn + cos π x, for x ∈ (2n − 1, 2n) If f is continuous, then which of the following hold(s) for all n?

answer: BD

image_available: no

question_subject: mathematics


question: If f (x) = ∫ x 0 e2 (t − 2)(t − 3) dt for all x ∈ (0,∞) , then

response_choices: (A) f has a local maximum at x = 2 (B) f is decreasing on (2, 3) (C) there exists some c ∈ (0, ∞) such that f ″(c) = 0 (D) f has a local minimum at x = 3

answer: ABCD

image_available: no

question_subject: mathematics


question: If the straight lines x-1 = y+1-z/k and x+1 = y+1-z/5 are coplanar, then the plane(s) containing these two lines is(are)

answer: BC

image_available: no

question_subject: mathematics


question: Let X and Y be two events such that P(X | Y) = 1/2, P(Y | X) = 1/3 and P(X ∩ Y) = 1/6. Which of the following is (are) correct?

response_choices: (A) P(X U Y) = 2/3, (B) X and Y are independent, (C) X and Y are not independent, (D) P(X^c ∩ Y) = 1/3

answer: AB

image_available: no

question_subject: mathematics


question: If the adjoint of a 3x3 matrix P is [1 4 4, 2 1 7, 1 1 3], then the possible value(s) of the determinant of P is (are)

answer: AD

image_available: no

question_subject: mathematics


question: Let f : (-1, 1) → IR be such that f (cos 4θ) = (2 − sec² θ) for θ ∈ (0, π/4) ∪ (π/4, π/2). Then the value(s) of f (1/3) is (are)

answer: Zero Marks to all

image_available: no

question_subject: mathematics