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Q. What is the focal length of a concave lens with a power of -2 diopters?
A.
-0.5 m
B.
0.5 m
C.
-2 m
D.
2 m
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Solution
Power (P) = 1/focal length (f). Therefore, f = 1/P = 1/(-2) = -0.5 m.
Correct Answer: A — -0.5 m
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Q. What is the focal length of a concave mirror if an object is placed at a distance of 30 cm from the mirror and the image is formed at a distance of 15 cm from the mirror?
A.
10 cm
B.
15 cm
C.
20 cm
D.
25 cm
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Solution
Using the mirror formula, 1/f = 1/v + 1/u. Here, v = -15 cm (real image) and u = -30 cm (object distance). Thus, 1/f = 1/(-15) + 1/(-30) = -1/10, so f = -10 cm.
Correct Answer: A — 10 cm
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Q. What is the focal length of a concave mirror if an object placed 30 cm in front of it produces an image at 10 cm in front of the mirror?
A.
5 cm
B.
10 cm
C.
15 cm
D.
20 cm
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Solution
Using the mirror formula 1/f = 1/v + 1/u, where u = -30 cm and v = -10 cm, we find f = 15 cm.
Correct Answer: C — 15 cm
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Q. What is the focal length of a concave mirror if an object placed at a distance of 30 cm produces an image at a distance of 15 cm?
A.
10 cm
B.
15 cm
C.
20 cm
D.
25 cm
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Solution
Using the mirror formula, 1/f = 1/v + 1/u; here, v = -15 cm (real image) and u = -30 cm. Thus, 1/f = 1/(-15) + 1/(-30) = -1/10, so f = 10 cm.
Correct Answer: A — 10 cm
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Q. What is the focal length of a convex lens if it forms a real image at a distance of 30 cm when the object is placed at 15 cm from the lens?
A.
10 cm
B.
15 cm
C.
20 cm
D.
25 cm
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Solution
Using the lens formula 1/f = 1/v - 1/u, where v = 30 cm and u = -15 cm, we find f = 20 cm.
Correct Answer: C — 20 cm
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Q. What is the focal length of a lens if it forms a virtual image at a distance of 15 cm when the object is placed at 10 cm?
A.
-30 cm
B.
30 cm
C.
15 cm
D.
10 cm
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Solution
Using the lens formula 1/f = 1/v - 1/u, we have 1/f = 1/(-15) - 1/(-10) = -1/15 + 1/10 = -1/30, thus f = -30 cm.
Correct Answer: A — -30 cm
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Q. What is the focal length of a lens if it forms an image at infinity when the object is placed at 30 cm?
A.
30 cm
B.
15 cm
C.
60 cm
D.
20 cm
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Solution
For the image to be at infinity, the focal length must be equal to the object distance, hence f = 60 cm.
Correct Answer: C — 60 cm
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Q. What is the focal length of a plano-convex lens with a radius of curvature of 30 cm?
A.
15 cm
B.
30 cm
C.
45 cm
D.
60 cm
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Solution
Using the lens maker's formula for a plano-convex lens, f = R/2 = 30 cm / 2 = 30 cm.
Correct Answer: B — 30 cm
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Q. What is the force between two point charges of +2μC and -3μC separated by a distance of 0.5m in vacuum?
A.
-1.08 N
B.
-0.72 N
C.
1.08 N
D.
0.72 N
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Solution
Using Coulomb's law, F = k * |q1 * q2| / r^2 = (9 × 10^9) * |2 × 10^-6 * -3 × 10^-6| / (0.5)^2 = -1.08 N.
Correct Answer: A — -1.08 N
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Q. What is the force experienced by a charge q in an electric field E?
A.
F = qE
B.
F = E/q
C.
F = q/E
D.
F = q + E
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Solution
The force experienced by a charge q in an electric field E is given by F = qE.
Correct Answer: A — F = qE
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Q. What is the force experienced by a charge q moving with velocity v in a magnetic field B?
A.
qvB
B.
qvB sin(θ)
C.
qvB cos(θ)
D.
qvB tan(θ)
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Solution
The force experienced by a charge q moving with velocity v in a magnetic field B is given by the Lorentz force law: F = q(v × B), which can be expressed as F = qvB sin(θ), where θ is the angle between the velocity and the magnetic field.
Correct Answer: B — qvB sin(θ)
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Q. What is the force experienced by a charge q moving with velocity v in a magnetic field B at an angle θ?
A.
qvB
B.
qvB sin(θ)
C.
qvB cos(θ)
D.
qvB tan(θ)
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Solution
The magnetic force on a charge moving in a magnetic field is given by F = qvB sin(θ), where θ is the angle between the velocity and the magnetic field.
Correct Answer: B — qvB sin(θ)
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Q. What is the force required to keep a 15 kg object moving at a constant velocity?
A.
0 N
B.
15 N
C.
150 N
D.
None of the above
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Solution
According to Newton's first law, no net force is required to maintain constant velocity.
Correct Answer: A — 0 N
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Q. What is the formula for calculating boiling point elevation?
A.
ΔT_b = K_b * m
B.
ΔT_b = K_f * m
C.
ΔT_b = i * K_b * m
D.
ΔT_b = i * K_f * m
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Solution
The boiling point elevation is calculated using the formula ΔT_b = i * K_b * m, where i is the van 't Hoff factor.
Correct Answer: C — ΔT_b = i * K_b * m
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Q. What is the formula for calculating kinetic energy?
A.
KE = mv²
B.
KE = 1/2 mv²
C.
KE = mgh
D.
KE = 1/2 mgh
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Solution
The formula for calculating kinetic energy is KE = 1/2 mv², where m is mass and v is velocity.
Correct Answer: B — KE = 1/2 mv²
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Q. What is the formula for calculating the magnetic force on a charged particle moving in a magnetic field?
A.
F = qE
B.
F = qvBsinθ
C.
F = mv^2/r
D.
F = qvE
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Solution
The magnetic force on a charged particle is given by F = qvBsinθ, where q is the charge, v is the velocity, B is the magnetic field, and θ is the angle between v and B.
Correct Answer: B — F = qvBsinθ
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Q. What is the formula for calculating the number of moles?
A.
Moles = Mass / Volume
B.
Moles = Mass x Volume
C.
Moles = Mass / Molar Mass
D.
Moles = Molar Mass / Mass
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Solution
The number of moles is calculated using the formula: Moles = Mass / Molar Mass.
Correct Answer: C — Moles = Mass / Molar Mass
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Q. What is the formula for calculating the work done by a force?
A.
W = Fd
B.
W = F/v
C.
W = F/t
D.
W = mv
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Solution
The work done by a force is calculated using the formula W = Fd, where F is the force and d is the distance moved in the direction of the force.
Correct Answer: A — W = Fd
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Q. What is the formula for gravitational potential energy?
A.
PE = mgh
B.
PE = 1/2 mv²
C.
PE = mv
D.
PE = mgh²
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Solution
Gravitational potential energy is calculated using the formula PE = mgh, where m is mass, g is acceleration due to gravity, and h is height.
Correct Answer: A — PE = mgh
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Q. What is the formula for the angular position of the m-th order maximum in a double-slit experiment?
A.
d sin θ = mλ
B.
d cos θ = mλ
C.
d tan θ = mλ
D.
d = mλ/sin θ
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Solution
The correct formula for the angular position of the m-th order maximum is d sin θ = mλ.
Correct Answer: A — d sin θ = mλ
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Q. What is the formula for the complex formed when silver ion reacts with ammonia?
A.
Ag(NH3)2+
B.
Ag(NH3)2Cl
C.
Ag(NH3)3+
D.
Ag(NH3)4+
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Solution
The complex formed is Ag(NH3)2+, which is known as the diamminesilver(I) ion.
Correct Answer: A — Ag(NH3)2+
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Q. What is the formula for the equivalent resistance of two resistors R1 and R2 in series?
A.
R_eq = R1 + R2
B.
R_eq = R1 * R2 / (R1 + R2)
C.
R_eq = R1 - R2
D.
R_eq = R1 / R2
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Solution
The equivalent resistance of two resistors in series is simply the sum of their resistances: R_eq = R1 + R2.
Correct Answer: A — R_eq = R1 + R2
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Q. What is the formula for the fringe separation in a double-slit experiment?
A.
λD/d
B.
d/λD
C.
D/λd
D.
λd/D
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Solution
The fringe separation (β) is given by the formula β = λD/d, where λ is the wavelength, D is the distance to the screen, and d is the distance between the slits.
Correct Answer: A — λD/d
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Q. What is the formula for the fringe width in a double-slit experiment?
A.
λD/d
B.
d/λD
C.
D/λd
D.
λd/D
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Solution
The fringe width (β) is given by the formula β = λD/d, where D is the distance from the slits to the screen and d is the distance between the slits.
Correct Answer: A — λD/d
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Q. What is the formula for the magnetic field (B) inside a solenoid?
A.
B = μ₀(nI)
B.
B = μ₀I
C.
B = μ₀(nI)/L
D.
B = μ₀I²
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Solution
The magnetic field inside a solenoid is given by B = μ₀(nI), where n is the number of turns per unit length.
Correct Answer: A — B = μ₀(nI)
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Q. What is the formula for the magnetic force experienced by a charged particle moving in a magnetic field?
A.
F = qE
B.
F = qvBsin(θ)
C.
F = mv^2/r
D.
F = BIL
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Solution
The magnetic force on a charged particle is given by F = qvBsin(θ), where q is the charge, v is the velocity, B is the magnetic field strength, and θ is the angle between the velocity and the magnetic field.
Correct Answer: B — F = qvBsin(θ)
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Q. What is the formula for the magnetic force on a charge q moving with velocity v in a magnetic field B?
A.
F = qvB
B.
F = qvBsinθ
C.
F = qB
D.
F = qvBcosθ
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Solution
The magnetic force on a charge moving in a magnetic field is given by F = qvBsinθ, where θ is the angle between v and B.
Correct Answer: B — F = qvBsinθ
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Q. What is the formula for the magnetic force on a charged particle moving in a magnetic field?
A.
F = qE
B.
F = qvBsinθ
C.
F = mv^2/r
D.
F = qvE
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Solution
The magnetic force on a charged particle is given by F = qvBsinθ, where q is the charge, v is the velocity, B is the magnetic field strength, and θ is the angle between v and B.
Correct Answer: B — F = qvBsinθ
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Q. What is the formula for the modulus of resilience?
A.
U = 1/2 * σ * ε
B.
U = σ * ε
C.
U = 1/2 * ε^2
D.
U = σ^2 / 2
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Solution
The modulus of resilience is given by U = 1/2 * σ * ε, where σ is the yield stress and ε is the yield strain.
Correct Answer: A — U = 1/2 * σ * ε
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Q. What is the formula for the total power in a series RLC circuit?
A.
P = VI
B.
P = I^2R
C.
P = V^2/R
D.
P = VI cos(φ)
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Solution
The total power in a series RLC circuit is given by P = VI cos(φ), where φ is the phase angle.
Correct Answer: D — P = VI cos(φ)
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