id int64 1 84 | question stringlengths 11 1.17k | response_choices stringlengths 0 901 | answer stringclasses 330 values | page_number int64 1 40 | image_available stringclasses 2 values | question_subject stringclasses 3 values |
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54 | Tangents are drawn to the hyperbola x^2/9 - y^2/4 = 1, parallel to the straight line 2x - y = 1. The points of contact of the tangents on the hyperbola are | (A) (9/√(2√2), 1/√2), (B) ( -9/√(2√2), -1/√2), (C) (3√3, -2√2), (D) (-3√3, 2√2) | AB | 23 | yes | mathematics |
55 | If y (x) satisfies the differential equation y' - y tan x = 2x sec x and y (0) = 0 , then | (A) y (π/4) = (π^2/(8√2)), (B) y' (π/4) = (π^2/18), (C) y (π/3) = (π^2/9), (D) y' (π/3) = (4π + 2π^2)/(3√3) | AD | 23 | no | mathematics |
56 | Let f : IR → IR be defined as f(x) = [x] + [x^2 - 1]. The total number of points at which f attains either a local maximum or a local minimum is | 5 | 24 | no | mathematics | |
57 | The value of 6 + log₂ ( (1/√2) / (4 - (1/√2)) / (4 - (1/√2)) / (4 - (1/√2)) ... ) is | 4 | 24 | no | mathematics | |
58 | Let p(x) be a real polynomial of least degree which has a local maximum at x = 1 and a local minimum at x = 3. If p(1) = 6 and p(3) = 2, then p'(0) is | 9 | 24 | no | mathematics | |
59 | If ā, b̄ and c̄ are unit vectors satisfying | ā - b̄ |^2 + | b̄ - c̄ |^2 + | c̄ - ā |^2 = 9, then | 2ā + 5b̄ + 5c̄ | is | 3 | 24 | no | mathematics | |
60 | Let S be the focus of the parabola y^2 = 8x and let PQ be the common chord of the circle x^2 +y^2 - 2x - 4y = 0 and the given parabola. The area of the triangle PQS is | 4 | 24 | no | mathematics | |
1 | 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 | (A) a^2Ik̂, (B) (π+1)/2a^2Ik̂, (C) -(π+1)/2a^2Ik̂, (D) (2π+1)a^2Ik̂ | B | 1 | yes | physics |
2 | 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 | (A), (B), (C), (D) [options represented by graphs] | D | 1 | yes | physics |
3 | 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 | (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. | A | 2 | no | physics |
4 | 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 | (A) +32 μC (B) +40 μC (C) +48 μC (D) +80 μC | C | 2 | yes | physics |
5 | 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) | (A) 62 J (B) 104 J (C) 124 J (D) 208 J | D | 2 | no | physics |
6 | 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 | (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. | C or D | 3 | yes | physics |
7 | 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 | (A) 14.0 cm (B) 15.2 cm (C) 16.4 cm (D) 17.6 cm | B | 3 | no | physics |
8 | 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 | A, B, C, D | A | 4 | yes | physics |
9 | For light incident from air on a meta-material, the appropriate ray diagram is | (A), (B), (C), (D) | C | 5 | yes | physics |
10 | 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. | N/A | N/A | 5 | no | physics |
10 | Choose the correct statement. | (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. | B | 6 | no | physics |
11 | What is the maximum energy of the anti-neutrino? | (A) Zero. (B) Much less than 0.8 × 10⁶ eV. (C) Nearly 0.8 × 10⁶ eV. (D) Much larger than 0.8 × 10⁶ eV. | C | 7 | no | physics |
12 | 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? | (A) 0 ≤ K ≤ 0.8 × 10⁶ eV (B) 3.0 eV ≤ K ≤ 0.8 × 10⁶ eV (C) 3.0 eV ≤ K < 0.8 × 10⁶ eV (D) 0 ≤ K < 0.8 × 10⁶ eV | D | 7 | no | physics |
13 | Which of the following statements about the instantaneous axis (passing through the centre of mass) is correct? | (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). | A | 8 | yes | physics |
14 | Which of the following statements regarding the angular speed about the instantaneous axis (passing through the centre of mass) is correct? | (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. | D | 9 | no | physics |
15 | 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) | (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. | C or AC | 10 | yes | physics |
16 | 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) | (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. | AC | 10 | no | physics |
17 | 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? | (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. | ABC | 11 | yes | physics |
18 | 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? | (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. | D | 11 | no | physics |
19 | 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 | (A) Vq > Vr > Vp (B) Vr > Vq > Vp (C) Vr/ Vp = 3 (D) Vp/ Vq = 1/2 | BD | 11 | no | physics |
20 | 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, | (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| | AB | 12 | yes | physics |
21 | 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 | (A) tetrahedral and tetrahedral, (B) square planar and square planar, (C) tetrahedral and square planar, (D) square planar and tetrahedral | C | 13 | no | chemistry |
22 | In the cyanide extraction process of silver from argentite ore, the oxidizing and reducing agents used are | (A) O2 and CO respectively., (B) O2 and Zn dust respectively., (C) HNO3 and Zn dust respectively., (D) HNO3 and CO respectively. | B | 13 | no | chemistry |
23 | 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 | (A) redox reaction; – 3 and – 5, (B) redox reaction; + 3 and + 5, (C) disproportionation reaction; – 3 and + 5, (D) disproportionation reaction; – 3 and + 3 | Zero Marks to all | 13 | no | chemistry |
24 | The shape of XeO3F2 molecule is | (A) trigonal bipyramidal, (B) square planar, (C) tetrahedral, (D) see-saw | D | 14 | no | chemistry |
25 | 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) | (A) 724, (B) 740, (C) 736, (D) 718 | A | 14 | no | chemistry |
26 | The compound that undergoes decarboxylation most readily under mild condition is | (A) Structure1, (B) Structure2, (C) Structure3, (D) Structure4 | B | 14 | yes | chemistry |
27 | 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.) | A) 1165, B) 837, C) 865, D) 815 | D | 15 | no | chemistry |
28 | The major product H of the given reaction sequence is CH₃ – CH₂ – CO – CH₃ → G → H | A) CH₃ – CH = C – COOH, B) CH₃ – CH = C – CN, C) CH₃ – CH₂ – C – COOH, D) CH₃ – CH = C – CO – NH₂ | A | 15 | yes | chemistry |
29 | Bleaching powder contains a salt of an oxoacid as one of its components. The anhydride of that oxoacid is | (A) Cl2O, (B) Cl2O7, (C) ClO2, (D) Cl2O6 | A | 16 | no | chemistry |
30 | 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 | (A) 0.48 M, (B) 0.96 M, (C) 0.24 M, (D) 0.024 M | C | 16 | no | chemistry |
31 | 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) | A) 1×10^-15, B) 4×10^-15, C) 1×10^-12, D) 4×10^-12 | B | 17 | no | chemistry |
32 | The value of Δ G (kJ mol^-1) for the given cell is (take 1F = 96500 C mol^-1) | A) −5.7, B) 5.7, C) 11.4, D) −11.4 | D | 17 | no | chemistry |
33 | The compound I is | (A) O-H (B) -OH (C) O-CH3 (D) H-H-H | A | 18 | yes | chemistry |
34 | The compound K is | (A) (B) O-O (C) O (D) O | C | 18 | yes | chemistry |
35 | 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? | (A) T1 = T2, (B) T3 > T1, (C) wisothermal > wadiabatic, (D) ΔUisothermal > ΔUadiabatic | ACD or AD | 19 | yes | chemistry |
36 | 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? | (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 | AC | 20 | yes | chemistry |
37 | For the given aqueous reactions, which of the statement(s) is (are) true ? | (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. | ACD | 21 | yes | chemistry |
38 | With respect to graphite and diamond, which of the statement(s) given below is (are) correct? | (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. | BD | 22 | no | chemistry |
39 | With reference to the scheme given, which of the given statment(s) about T, U, V and W is (are) correct ? | (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 | ACD | 22 | yes | chemistry |
40 | Which of the given statement(s) about M, O, P and Q with respect to M is (are) correct? | (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 | ABC | 23 | yes | chemistry |
41 | 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 | (A) 5x - 11y + z = 17, (B) √(2x + y = 3√2 -1), (C) x + y + z = √3, (D) x - √2y = 1 - √2 | A | 24 | no | mathematics |
42 | 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 | (A) 3/4Λ, (B) 45/4Λ, (C) (3/4Λ)^2, (D) (45/4Λ)^2 | C | 24 | no | mathematics |
43 | 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 | (A) 0, (B) 3, (C) 4, (D) 8 | C | 24 | no | mathematics |
44 | 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 | (A) PX = [0 0 0]T, (B) PX = X, (C) PX = 2X, (D) PX = - X | D | 25 | yes | mathematics |
45 | 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 | (A) -5/2 and 1, (B) -1/2 and -1, (C) -7/2 and 2, (D) -9/2 and 3 | B | 25 | no | mathematics |
46 | 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 | (A) 91/216, (B) 108/216, (C) 125/216, (D) 127/216 | A | 25 | no | mathematics |
47 | The value of the integral ∫(π/2)(-π/2) (x^2 + ln(π+x/π-x))cosx dx is | (A) 0, (B) π^2/2 - 4, (C) π^2/2 + 4, (D) π^2/2 | B | 25 | no | mathematics |
48 | Let a1, a2, a3, ... be in harmonic progression with a1 = 5 and a20 = 25. The least positive integer n for which an < 0 is | (A) 22, (B) 23, (C) 24, (D) 25 | D | 25 | no | mathematics |
49 | The value of b_n is | (A) 7, (B) 8, (C) 9, (D) 11 | B | 26 | no | mathematics |
50 | Which of the following is correct? | (A) a_n = a_6 + a_5, (B) c_7 ≠ c_6 + c_5, (C) b_7 ≠ b_6 + c_6, (D) a_7 = c_7 + b_6 | A | 26 | no | mathematics |
51 | Which of the following is true? | (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, ∞) | B | 27 | yes | mathematics |
52 | 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 | (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 | C | 27 | yes | mathematics |
53 | A possible equation of L is | A) x - √3 y = 1 , B) x + √3 y = 1 , C) x - √3 y = -1 , D) x + √3 y = 5 | A | 28 | yes | mathematics |
54 | A common tangent of the two circles is | A) x = 4 , B) y = 2 , C) x + √3 y = 4 , D) x + 2√2 y = 6 | D | 28 | yes | mathematics |
55 | 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? | (A) an-1 - bn-1 = 0 (B) an - bn = 1 (C) an - bn+1 = 1 (D) an-1 - bn = -1 | BD | 29 | no | mathematics |
56 | If f (x) = ∫ x 0 e2 (t − 2)(t − 3) dt for all x ∈ (0,∞) , then | (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 | ABCD | 29 | no | mathematics |
57 | 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) | (A) y + 2z = -1, (B) y + z = -1, (C) y - z = -1, (D) y - 2z = -1 | BC | 30 | no | mathematics |
58 | 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? | (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 | AB | 30 | no | mathematics |
59 | 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) | (A) −2, (B) −1, (C) 1, (D) 2 | AD | 31 | no | mathematics |
60 | 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) | (A) 1 − √(3/2), (B) 1 + √(3/2), (C) 1 − √(2/3), (D) 1 + √(2/3) | Zero Marks to all | 31 | no | mathematics |
1 | The diameter of a cylinder is measured using a Vernier callipers with no zero error. It is found that the zero of the Vernier scale lies between 5.10 cm and 5.15 cm of the main scale. The Vernier scale has 50 divisions equivalent to 2.45 cm. The 24th division of the Vernier scale exactly coincides with one of the main scale divisions. The diameter of the cylinder is | A) 5.112 cm, B) 5.124 cm, C) 5.136 cm, D) 5.148 cm | B | 1 | no | physics |
2 | A ray of light travelling in the direction 1/2(i+√3j) is incident on a plane mirror. After reflection, it travels along the direction 1/2(i-√3j). The angle of incidence is | A) 30°, B) 45°, C) 60°, D) 75° | A | 1 | no | physics |
3 | In the Young's double slit experiment using a monochromatic light of wavelength λ, the path difference (in terms of an integer n) corresponding to any point having half the peak intensity is | (A) (2n+1)λ/2 (B) (2n+1)λ/4 (C) (2n+1)λ/8 (D) (2n+1)λ/16 | B | 2 | no | physics |
4 | Two non-reactive monoatomic ideal gases have their atomic masses in the ratio 2 : 3. The ratio of their partial pressures, when enclosed in a vessel kept at a constant temperature, is 4 : 3. The ratio of their densities is | (A) 1 : 4 (B) 1 : 2 (C) 6 : 9 (D) 8 : 9 | D | 2 | no | physics |
5 | Two rectangular blocks, having identical dimensions, can be arranged either in configuration I or in configuration II as shown in the figure. One of the blocks has thermal conductivity k and the other 2k. The temperature difference between the ends along the x-axis is the same in both the configurations. It takes 9 s to transport a certain amount of heat from the hot end to the cold end in the configuration I. The time to transport the same amount of heat in the configuration II is | A) 2.0 s, B) 3.0 s, C) 4.5 s, D) 6.0 s | A | 3 | yes | physics |
6 | A pulse of light of duration 100 ns is absorbed completely by a small object initially at rest. Power of the pulse is 30 mW and the speed of light is 3 × 10^8 ms^-1. The final momentum of the object is | (A) 0.3 × 10^-17 kg ms^-1, (B) 1.0 × 10^-17 kg ms^-1, (C) 3.0 × 10^-17 kg ms^-1, (D) 9.0 × 10^-17 kg ms^-1 | B | 4 | no | physics |
7 | A particle of mass m is projected from the ground with an initial speed u0 at an angle α with the horizontal. At the highest point of its trajectory, it makes a completely inelastic collision with another identical particle, which was thrown vertically upward from the ground with the same initial speed u0. The angle that the composite system makes with the horizontal immediately after the collision is | (A) π/4, (B) π/4+α, (C) π/2-α, (D) π/2 | A | 4 | no | physics |
8 | The work done on a particle of mass m by a force, K [ (x^2 + y^2)^(1/2) i + (x^2 + y^2)^(1/2) j] (K being a constant of appropriate dimensions), when the particle is taken from the point (a, 0) to the point (0, a) along a circular path of radius a about the origin in the x-y plane is | A) 2Kπ/a, B) Kπ/a, C) Kπ/2a, D) 0 | D | 5 | yes | physics |
9 | One end of a horizontal thick copper wire of length 2L and radius 2R is welded to an end of another horizontal thin copper wire of length L and radius R. When the arrangement is stretched by applying forces at two ends, the ratio of the elongation in the thin wire to that in the thick wire is | (A) 0.25 (B) 0.50 (C) 2.00 (D) 4.00 | C | 6 | no | physics |
10 | The image of an object, formed by a plano-convex lens at a distance of 8 m behind the lens, is real and is one-third the size of the object. The wavelength of light inside the lens is 2/3 times the wavelength in free space. The radius of the curved surface of the lens is | (A) 1 m (B) 2 m (C) 3 m (D) 6 m | C | 6 | no | physics |
11 | A horizontal stretched string, fixed at two ends, is vibrating in its fifth harmonic according to the equation, y(x, t) = (0.01 m) sin [(62.8 m^-1) x] cos [(628 s^-1)t]. Assuming π = 3.14, the correct statement(s) is (are) | (A) The number of nodes is 5. (B) The length of the string is 0.25 m. (C) The maximum displacement of the midpoint of the string, from its equilibrium position is 0.01 m. (D) The fundamental frequency is 100 Hz. | BC | 7 | no | physics |
12 | A solid sphere of radius R and density ρ is attached to one end of a mass-less spring of force constant k. The other end of the spring is connected to another solid sphere of radius R and density 3ρ. The complete arrangement is placed in a liquid of density 2ρ and is allowed to reach equilibrium. The correct statement(s) is (are) | (A) the net elongation of the spring is 4πR^3ρg/3k. (B) the net elongation of the spring is 8πR^3ρg/3k. (C) the light sphere is partially submerged. (D) the light sphere is completely submerged. | AD | 8 | no | physics |
13 | A particle of mass M and positive charge Q, moving with a constant velocity v₁ = 4i ms⁻¹, enters a region of uniform static magnetic field normal to the x-y plane. The region of the magnetic field extends from x = 0 to x = L for all values of y. After passing through this region, the particle emerges on the other side after 10 milliseconds with a velocity v₂ = 2(√3i + j) ms⁻¹. The correct statement(s) is (are) | A) The direction of the magnetic field is -z direction.
B) The direction of the magnetic field is +z direction.
C) The magnitude of the magnetic field 50πM/3Q units.
D) The magnitude of the magnetic field is 100πM/3Q units. | AC | 9 | no | physics |
14 | Two non-conducting solid spheres of radii R and 2R, having uniform volume charge densities ρ1 and ρ2 respectively, touch each other. The net electric field at a distance 2R from the centre of the smaller sphere, along the line joining the centres of the spheres, is zero. The ratio ρ1/ρ2 can be | (A) -4, (B) -32/25, (C) 32/25, (D) 4 | B | 10 | no | physics |
15 | In the circuit shown in the figure, there are two parallel plate capacitors each of capacitance C. The switch S1 is pressed first to fully charge the capacitor C1 and then released. The switch S2 is then pressed to charge the capacitor C2. After some time, S2 is released and then S3 is pressed. After some time, | (A) the charge on the upper plate of C1 is 2CV0; (B) the charge on the upper plate of C1 is CV0; (C) the charge on the upper plate of C2 is 0; (D) the charge on the upper plate of C2 is -CV0 | BD | 11 | yes | physics |
16 | The work functions of Silver and Sodium are 4.6 and 2.3 eV, respectively. The ratio of the slope of the stopping potential versus frequency plot for Silver to that of Sodium is | 1 | 12 | no | physics | |
17 | A freshly prepared sample of a radioisotope of half-life 1386 s has activity 103 disintegrations per second. Given that ln 2 = 0.693, the fraction of the initial number of nuclei (expressed in nearest integer percentage) that will decay in the first 80 s after preparation of the sample is | 4 | 12 | no | physics | |
18 | A particle of mass 0.2 kg is moving in one dimension under a force that delivers a constant power 0.5 W to the particle. If the initial speed (in ms^-1) of the particle is zero, the speed (in ms^-1) after 5 s is | No response choices provided | 5 | 13 | no | physics |
19 | A uniform circular disc of mass 50 kg and radius 0.4 m is rotating with an angular velocity of 10 rad s^-1 about its own axis, which is vertical. Two uniform circular rings, each of mass 6.25 kg and radius 0.2 m, are gently placed symmetrically on the disc in such a manner that they are touching each other along the axis of the disc and are horizontal. Assume that the friction is large enough such that the rings are at rest relative to the disc and the system rotates about the original axis. The new angular velocity (in rad s^-1) of the system is | No response choices provided | 8 | 13 | no | physics |
20 | A bob of mass m, suspended by a string of length l1, is given a minimum velocity required to complete a full circle in the vertical plane. At the highest point, it collides elastically with another bob of mass m suspended by a string of length l2, which is initially at rest. Both the strings are mass-less and inextensible. If the second bob, after collision acquires the minimum speed required to complete a full circle in the vertical plane, the ratio l1/l2 is | 5 | 14 | no | physics | |
21 | The compound that does NOT liberate CO2, on treatment with aqueous sodium bicarbonate solution, is | (A) Benzoic acid, (B) Benzenesulphonic acid, (C) Salicylic acid, (D) Carbolic acid (Phenol) | D | 15 | no | chemistry |
22 | Concentrated nitric acid, upon long standing, turns yellow-brown due to the formation of | (A) NO, (B) NO2, (C) N2O, (D) N2O4 | B | 15 | no | chemistry |
23 | Methylene blue, from its aqueous solution, is adsorbed on activated charcoal at 25 °C. For this process, the correct statement is | (A) The adsorption requires activation at 25 °C. (B) The adsorption is accompanied by a decrease in enthalpy. (C) The adsorption increases with increase of temperature. (D) The adsorption is irreversible. | B | 16 | no | chemistry |
24 | Sulfide ores are common for the metals | (A) Ag, Cu and Pb (B) Ag, Cu and Sn (C) Ag, Mg and Pb (D) Al, Cu and Pb | A | 17 | no | chemistry |
25 | The arrangement of X¯ ions around A+ ion in solid AX is given in the figure (not drawn to scale). If the radius of X¯ is 250 pm, the radius of A+ is | (A) 104 pm (B) 125 pm (C) 183 pm (D) 57 pm | A | 17 | yes | chemistry |
26 | Upon treatment with ammoniacal H₂S, the metal ion that precipitates as a sulfide is | A) Fe(III), B) Al(III), C) Mg(II), D) Zn(II) | D | 18 | no | chemistry |
27 | The standard enthalpies of formation of CO₂(g), H₂O(l) and glucose(s) at 25 °C are –400 kJ/mol, –300 kJ/mol and –1300 kJ/mol, respectively. The standard enthalpy of combustion per gram of glucose at 25 °C is | A) +2900 kJ, B) –2900 kJ, C) –16.11 kJ, D) +16.11 kJ | C | 18 | no | chemistry |
28 | Consider the following complex ions, P, Q and R. P = [FeF6]3-, Q = [V(H2O)6]2+ and R = [Fe(H2O)6]2+. The correct order of the complex ions, according to their spin-only magnetic moment values (in B.M.) is | (A) R < Q < P, (B) Q < R < P, (C) R < P < Q, (D) Q < P < R | B | 19 | no | chemistry |
29 | In the reaction, P + Q → R + S the time taken for 75% reaction of P is twice the time taken for 50% reaction of P. The concentration of Q varies with reaction time as shown in the figure. The overall order of the reaction is | (A) 2, (B) 3, (C) 0, (D) 1 | D | 20 | yes | chemistry |
30 | KI in acetone, undergoes SN2 reaction with each of P, Q, R and S. The rates of the reaction vary as | A) P > Q > R > S, B) S > P > R > Q, C) P > R > Q > S, D) R > P > S > Q | B | 21 | yes | chemistry |
31 | The pair(s) of coordination complexes/ions exhibiting the same kind of isomerism is(are) | (A) [Cr(NH3)5Cl]Cl2 and [Cr(NH3)4Cl2]Cl
(B) [Co(NH3)4Cl2]+ and [Pt(NH3)2(H2O)Cl]+
(C) [CoBr2Cl2]2- and [PtBr2Cl2]2-
(D) [Pt(NH3)3(NO2)]Cl and [Pt(NH3)3Cl]Br | BD | 22 | no | chemistry |
32 | Among P, Q, R and S, the aromatic compound(s) is/are | A) P, B) Q, C) R, D) S | ABCD | 23 | yes | chemistry |
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