cmeraki/elemento huggingface dataset:
Subject: chemistry
Question: The Henry's law constant for the solubility of N2 gas in water at 298 K is 1.0 x 10^4 atm. The mole fraction of N2 in air is 0.8. The number of moles of N2 from air dissolved in 10 moles of water at 298 K and 5 atm pressure is
Choices: (A) 4.0 x 10^4 (B) 4.0 x 10^5 (C) 5.0 x 10^4 (D) 4.0 x 10^6
Answer: A
Subject: chemistry
Question: The correct statement(s) regarding defects in solids is(are)
Choices: (A) Frenkel defect is usually favoured by a very small difference in the sizes of cation and anion (B) Frenkel defect is a dislocation defect (C) Trapping of an electron in the lattice leads to the formation of F-center (D) Schottky defects have no effect on the physical properties of solids
Answer: B C
Subject: chemistry
Question: The correct statement(s) about the compound H3C(HO)HC-CH-CH-CH(OH)CH3 (X) is(are)
Choices: (A) The total number of stereoisomers possible for X is 6 (B) The total number of diastereomers possible for X is 3 (C) If the stereochemistry about the double bond in X is trans, the number of enantiomers possible for X is 4 (D) If the stereochemistry about the double bond in X is cis, the number of enantiomers possible for X is 2
Answer: A D
Subject: chemistry
Question: Match each of the diatomic molecules in Column I with its property/properties in Column II.
Choices: Column I: (A) B₂ (B) N₂ (C) O₂⁻ (D) O₂ Column II: (p) Paramagnetic (q) Undergoes oxidation (r) Undergoes reduction (s) Bond order > 2 (t) Mixing of 's' and 'p' orbitals
Answer: p q r s t, p q r s t, p q r s t, p q r s t
Subject: chemistry
Question: Match each of the compounds in Column I with its characteristic reaction(s) in Column II.
Choices: A) CH₃CH₂CH₂CN, (B) CH₃CH₂OCOCH₃, (C) CH₃ – CH = CH – CH₂OH, (D) CH₃CH₂CH₂CH₂NH₂
Answer: A) p, q, r, s, t, B) p, q, r, s, t, C) p, q, r, s, t, D) p, q, r, s, t
Subject: mathematics
Question: Let P(3, 2, 6) be a point in space and Q be a point on the line r = (j - j + 2k) + μ(-3i + j + 5k). Then the value of μ for which the vector PQ is parallel to the plane x - 4y + 3z = 1 is
Choices: (A) 1/4, (B) -1/4, (C) 1/8, (D) -1/8
Answer: A
Subject: mathematics
Question: Tangents drawn from the point P(1, 8) to the circle x² + y² - 6x - 4y - 11 = 0 touch the circle at the points A and B. The equation of the circumcircle of the triangle PAB is
Choices: (A) x² + y² + 4x - 6y + 19 = 0, (B) x² + y² - 4x - 10y +19 = 0, (C) x² + y² - 2x + 6y - 29 = 0, (D) x² + y² - 6x - 4y +19 = 0
Answer: B
Subject: mathematics
Question: Let f be a non-negative function defined on the interval [0, 1]. If ∫[0, 1] (f(t))^2 dt = ∫[0, 1] f(t) dt,    0 ≤ x ≤ 1, and f(0) = 0, then
Choices: (A) f(1/2) < 1/2 and f(1/3) > 1/3, (B) f(1/2) > 1/2 and f(1/3) < 1/3, (C) f(1/2) < 1/2 and f(1/3) < 1/3, (D) f(1/2) > 1/2 and f(1/3) > 1/3
Answer: C
Subject: mathematics
Question: The line passing through the extremity A of the major axis and extremity B of the minor axis of the ellipse x^2 + 9y^2 = 9 meets its auxiliary circle at the point M. Then the area of the triangle with vertices at A, M and the origin O is
Choices: (A) 31/10, (B) 29/10, (C) 21/10, (D) 27/10
Answer: D
Subject: mathematics
Question: If a, b, c and d are unit vectors such that |a × b| |c × d| = 1 and a.c = 1/2, then
Choices: (A) a, b, c are non-coplanar, (B) b, c, d are non-coplanar, (C) b, d are non-parallel, (D) a, d are parallel and b, c are parallel
Answer: C
Subject: mathematics
Question: Let z = cos θ + i sin θ. Then the value of Σ[n=1 to 18] Im(z^2n+1) at θ = 2° is
Choices: (A) 1/sin 2°, (B) 1/3 sin 2°, (C) 1/2 sin 2°, (D) 1/4 sin 2°
Answer: D
Subject: mathematics
Question: Area of the region bounded by the curve y = e^x and lines x = 0 and y = e is
Choices: (A) e - 1 (B) \int_{1}^{e} (e + 1 - y) dy (C) e - \int_{e}^{1} e^x dx (D) \int_{1}^{e} \ln y dy
Answer: B C D
Subject: mathematics
Question: Let L = \lim_{x \to 0} \frac{a - \sqrt{a^2 - x^2} - \frac{x^2}{4}}{x^4}, a > 0. If L is finite, then
Choices: (A) a = 2 (B) a = 1 (C) L = \frac{1}{64} (D) L = \frac{1}{32}
Answer: A C
Subject: mathematics
Question: In a triangle ABC with fixed base BC, the vertex A moves such that cos B + cos C = 4 sin^2 \frac{A}{2}. If a, b and c denote the lengths of the sides of the triangle opposite to the angles A, B and C, respectively, then
Choices: (A) b + c = 4a (B) b + c = 2a (C) locus of point A is an ellipse (D) locus of point A is a pair of straight lines
Answer: B C
Subject: mathematics
Question: If (sin^4 x)/2 + (cos^4 x)/3 = 1/5, then
Choices: (A) tan^2 x = 2/3, (B) (sin^8 x)/(8) + (cos^8 x)/(27) = 1/125, (C) tan^2 x = 1/3, (D) (sin^8 x)/(8) + (cos^8 x)/(27) = 2/125
Answer: A, B
Subject: physics
Question: Three concentric metallic spherical shells of radii R, 2R, 3R, are given charges Q1, Q2, Q3, respectively. It is found that the surface charge densities on the outer surfaces of the shells are equal. Then, the ratio of the charges given to the shells, Q1 : Q2 : Q3, is
Choices: A) 1 : 2 : 3 , (B) 1 : 3 : 5 , (C) 1 : 4 : 9 , (D) 1 : 8 : 18
Answer: B
Subject: physics
Question: A block of base 10 cm × 10 cm and height 15 cm is kept on an inclined plane. The coefficient of friction between them is √3. The inclination θ of this inclined plane from the horizontal plane is gradually increased from 0°. Then
Choices: (A) at θ = 30°, the block will start sliding down the plane (B) the block will remain at rest on the plane up to certain θ and then it will topple (C) at θ = 60°, the block will start sliding down the plane and continue to do so at higher angles (D) at θ = 60°, the block will start sliding down the plane and on further increasing θ, it will topple at certain θ
Answer: B
Subject: physics
Question: A ball is dropped from a height of 20 m above the surface of water in a lake. The refractive index of water is 4/3. A fish inside the lake, in the line of fall of the ball, is looking at the ball. At an instant, when the ball is 12.8 m above the water surface, the fish sees the speed of ball as
Choices: (A) 9 m/s , (B) 12 m/s , (C) 16 m/s , (D) 21.33 m/s
Answer: C
Subject: physics
Question: Look at the drawing given in the figure which has been drawn with ink of uniform line-thickness. The mass of ink used to draw each of the two inner circles, and each of the two line segments is m. The mass of the ink used to draw the outer circle is 5m. The coordinates of the centres of the different parts are: outer circle (0, 0), left inner circle (-a, a), right inner circle (a, a), vertical line (0, 0) and horizontal line (0, -a). The y-coordinate of the centre of mass of the ink in this drawing is
Choices: (A) a/10 , (B) a/8 , (C) a/12 , (D) a/3
Answer: A
Subject: physics
Question: Two small particles of equal masses start moving in opposite directions from a point A in a horizontal circular orbit. Their tangential velocities are v and 2v, respectively, as shown in the figure. Between collisions, the particles move with constant speeds. After making how many elastic collisions, other than that at A, these two particles will again reach the point A?
Choices: (A) 4, (B) 3, (C) 2, (D) 1
Answer: C
Subject: physics
Question: The figure shows certain wire segments joined together to form a coplanar loop. The loop is placed in a perpendicular magnetic field in the direction going into the plane of the figure. The magnitude of the field increases with time. If and Ia are the currents in the segments ab and cd. Then,
Choices: (A) I1 > I2, (B) I1 < I2, (C) Ia is in the direction ba and Ic is in the direction cd, (D) I1 is in the direction ab and I2 is in the direction dc
Answer: D
Subject: physics
Question: A disk of radius a/4 having a uniformly distributed charge 6 C is placed in the x-y plane with its centre at (-a/2, 0, 0). A rod of length a carrying a uniformly distributed charge 8 C is placed on the x-axis from x = a/4 to x = 5a/4. Two point charges –7 C and 3 C are placed at (a/4, -a/4, 0) and (-5a/4, 3a/4, 0), respectively. Consider a cubical surface formed by six surfaces x = +a/2, y = +a/2, z = +a/2. The electric flux through this cubical surface is
Choices: (A) -2 C/ε0, (B) 2 C/ε0, (C) 10 C/ε0, (D) 12 C/ε0
Answer: A
Subject: physics
Question: The x-t graph of a particle undergoing simple harmonic motion is shown below. The acceleration of the particle at t = 4/3 s is
Choices: (A) √3 π2 cm/s2 / 32, (B) – π2 cm/s2 / 32, (C) π2 cm/s2 / 32, (D) √5 π2 cm/s2 / 32
Answer: D
Subject: physics
Question: If the resultant of all the external forces acting on a system of particles is zero, then from an inertial frame, one can surely say that
Choices: (A) linear momentum of the system does not change in time, (B) kinetic energy of the system does not change in time, (C) angular momentum of the system does not change in time, (D) potential energy of the system does not change in time
Answer: A
Subject: physics
Question: A student performed the experiment of determination of focal length of a concave mirror by u-v method using an optical bench of length 1.5 meter. The focal length of the mirror used is 24 cm. The maximum error in the location of the image can be 0.2 cm. The 5 sets of (u, v) values recorded by the student (in cm) are: (42, 56), (48, 48), (60, 40), (66, 33), (73, 39). The data set(s) that cannot come from experiment and is (are) incorrectly recorded, is (are)
Choices: (A) (42, 56), (B) (48, 48), (C) (66, 33), (D) (73, 39)
Answer: CD
Subject: physics
Question: For the circuit shown in the figure
Choices: (A) the current I through the battery is 7.5 mA, (B) the potential difference across R1 is 18 V, (C) ratio of powers dissipated in R1 and R2 is 3, (D) if R1 and R2 are interchanged, magnitude of the power dissipated in R2 will decrease by a factor of 9
Answer: D
Subject: chemistry
Question: Cv and Cp denote the molar specific heat capacities of a gas at constant volume and constant pressure, respectively. Then
Choices: (A) Cp - Cv is larger for a diatomic ideal gas than for a monatomic ideal gas, (B) Cp + Cv is larger for a diatomic ideal gas than for a monatomic ideal gas, (C) Cp/Cv is larger for a diatomic ideal gas than for a monatomic ideal gas, (D) Cp · Cv is larger for a diatomic ideal gas than for a monatomic ideal gas
Answer: B
Subject: physics
Question: Assume that two deuteron nuclei in the core of fusion reactor at temperature T are moving towards each other, each with kinetic energy 1.5 eT, when the separation between them is large enough to neglect Coulomb potential energy. Also neglect any interaction from other particles in the core. The minimum temperature T required for them to reach a separation of 4 × 10^(-14) m is in the range
Choices: (A) 1.0×10^9 K ≤ T < 2.0×10^9 K (B) 2.0×10^9 K ≤ T < 3.0×10^9 K (C) 3.0×10^9 K ≤ T < 4.0×10^9 K (D) 4.0×10^9 K ≤ T < 5.0×10^9 K
Answer: A
Subject: physics
Question: Results of calculations for four different designs of a fusion reactor using D-D reaction are given below. Which of these is most promising based on Lawson criterion?
Choices: (A) deuteron density = 2.0×10^(14) cm^(-3), confinement time = 5.0×10^(-8) s (B) deuteron density = 8.0×10^(14) cm^(-3), confinement time = 9.0×10^(-8) s (C) deuteron density = 4.0×10^(13) cm^(-3), confinement time = 1.0×10^(-11) s (D) deuteron density = 1.0×10^(21) cm^(-3), confinement time = 4.0×10^(-12) s
Answer: B
Subject: physics
Question: Six point charges, each of the same magnitude q, are arranged in different manners as shown in Column II. In each case, a point M and a line PQ passing through M are shown. Let E be the electric field and V be the electric potential at M (potential at infinity is zero) due to the given charge distribution when it is at rest. Now, the whole system is set into rotation with a constant angular velocity about the line PQ. Let B be the magnetic field at M and μ be the magnetic moment of the system in this condition. Assume each rotating charge to be equivalent to a steady current.
Choices: Column I: (A) E = 0, (B) V ≠ 0, (C) B = 0, (D) μ ≠ 0
Answer: p q r s t
Subject: physics
Question: Column II shows five systems in which two objects are labelled as X and Y. Also in each case a point P is shown. Column I gives some statements about X and/or Y. Match these statements to the appropriate system(s) from Column II.
Choices: A) The force exerted by X on Y has a magnitude Mg.
B) The gravitational potential energy of X is continuously increasing.
C) Mechanical energy of the system X + Y is continuously decreasing.
D) The torque of the weight of Y about point P is zero.
Answer: p
q
r
s
t