Measurement/Unit: notes and MCQs for State PSC prelims

Measurement/Unit is part of Physics. Below are notes on 12 sub-topics, followed by practice MCQs from State PSC and UPSC papers.

Derived Units and their Expression

Frequency: Hertz (Hz) = s⁻¹.
Power (Electric/Mechanical): Watt (W) = Joule/second (J/s) = Newton-meter/second (N·m/s).
Pressure: Pascal (Pa) = Newton/meter² (N/ m²) = kg/(m·s²). Other units include Bar, Atmosphere, and kg/cm². Note: N/m and J/m² are not units of pressure.
Force: Newton (N) = kg·m/s². In CGS, 1 dyne = 1 g·cm/s² = 10⁻⁵ N.
Spring Constant (k): Newton/meter (N/m).
Resistivity (ρ): Ohm-meter (Ω·m). Ohm-cm (Ω·cm) is a commonly used non-SI unit. Resistivity is an intrinsic property of a material, independent of its length or cross-section.
Energy: Joule (J) = Newton-meter (N·m) = kg·m²/s². Other units: Watt-hour (W·h). Note: kg·m/s² is a unit of force (Newton), not energy.
Gravitational Constant (G): N·m²/kg².
Impulse: Newton-second (N·s) = kg·m/s.
Electric Charge: Coulomb (C) = Amperesecond (A·s).
Electric Potential Difference (Voltage): Volt (V) = Joule/Coulomb (J/C).

17. Miscellaneous

112

Power of a Lens: Diopter (D) = 1/meter (m⁻¹).
Magnetic Field Strength (B): Tesla (T), Gauss (G).
Magnetic Field Intensity (H): Ampere/meter (A/m).
Magnetic Flux: Weber (Wb).
Inductance: Henry (H).
Acceleration: meter/second² (m/s² or m·s⁻²).
Weight: Newton (N).
Volume: Cubic meter (m³). 1 hectare-cm = 100 m³.
Stress: Pascal (Pa) = N/m² (same unit as pressure).
Thermal Conductivity: Watt per meter Kelvin (W/(m·K) or W·m⁻¹·K⁻¹).
Linear Momentum: kg·m/s = Newton-second (N·s).
Frequency (Sound): Hertz (Hz), s⁻¹, min⁻¹. Decibel (dB) is a unit for sound intensity level, not frequency.
Wavelength: Angstrom (Å), where 1 Å = 10⁻¹⁰ m.
High Speed: Mach (dimensionless quantity, defined as the ratio of an object's speed to the speed of sound).
1 kilowatt-hour (kWh) = 3.6 × 10⁶ Joule (J).

Dimensional

Analysis

(Dimensions,

Homogeneity, Applications)

Dimensions: Powers to which fundamental units (Mass M, Length L, Time T, Electric Current A, Temperature K, etc.) are raised to represent a physical quantity.
Principle of Homogeneity of Dimensions: An equation is dimensionally correct if the dimensions of all the terms on both sides of the equation are the same. Quantities with different dimensions cannot be added or subtracted.
Dimensionless Quantities:

Are expressed as M⁰L⁰T⁰.
Examples: Specific gravity, relative density, relative permittivity (dielectric constant), strain, angle, refractive index, Reynolds number, trigonometric ratios, Euler's number (e), other mathematical constants (π).
Any quantity that is a ratio of two similar physical quantities is dimensionless.

Common Dimensional Formulas:

Force (Thrust): [MLT⁻²]
Pressure (Stress, Young's Modulus): [ML⁻¹T⁻²] (Also same as Energy per unit Volume: [ML²T⁻²]/[L³] = [ML⁻¹T⁻²])
Energy (Work, Heat, Torque): [ML²T⁻²]

Equivalent to Power × Time (e.g., I²Rt, V²t/R, VIt).

Linear Momentum (Impulse): [MLT⁻¹] (Impulse = Force × Time)
Angular Momentum (Planck's Constant 'h', Angular Impulse): [ML²T⁻¹]

Planck's constant h = Energy/ Frequency.
Angular Impulse = Torque × Time.

Frequency: [T⁻¹]
Surface Tension: [MT⁻²] (Force/ Length)
Mass Density: [ML⁻³]
Specific Weight: [ML⁻²T⁻²] (Force/ Volume)
Specific Heat: [L²T⁻²K⁻¹] (Energy/ (Mass × Temperature))
Electric Field: [MLT⁻³A⁻¹] (Force/ Charge)
Electric Potential (Emf, Potential Difference): [ML²T⁻³A⁻¹] (Work/Charge)
Electric Dipole Moment: [LTA] (Charge × Distance)
Electric Flux: [ML³T⁻³A⁻¹] (Electric Field × Area)

Dimensional Equivalence:

The ratio of Inductance (L) to Resistance (R), i.e., L/R, has the dimension of Time [T] (time constant of an RL circuit).
Time is dimensionally equivalent to Distance/Velocity.
The unit of the ratio between Thrust (Force) and Impulse (Force × Time) is the same as that of Frequency ([T⁻¹]).

Distinguishing Dimensions:

Moment of Inertia ([ML²]) and Moment of a Force (Torque [ML²T⁻²]) have different dimensions.
Dipole moment, Electric flux, and Electric field have different dimensions.

Errors in Measurement (Types, Absolute, Relative, Percentage, Propagation)

Error in Measurement: Difference between the true value and the measured value of a quantity.
Types of Errors:

Systematic Errors: Errors that tend to be in one direction (either positive or negative). They arise due to identifiable causes and can be minimized or eliminated.

Instrumental Errors: Due to imperfect design or faulty calibration of the instrument (e.g., zero error, wear and tear, using a chain calibrated at one temperature in a different temperature – leads to a cumulative error).
Environmental Errors: Due to changes in external conditions like temperature, pressure, humidity (e.g., expansion/contraction of measuring tape with temperature – causes systematic cumulative error).
Observational/Personal Errors: Due to individual's bias, lack of proper setting of the apparatus, or carelessness in taking observations (e.g., parallax error).
Errors due to Imperfection in Experimental Technique/Procedure: (e.g., heat loss in calorimetry).
Cumulative Error: A systematic error that adds up over successive measurements, consistently affecting the result in the same direction (e.g., a short tape will consistently overestimate length, a long chain due to high temperature will consistently under-measure length).
Negative Error: Occurs when the measured value is less than the true value. (e.g., using an expanded chain at higher temperature; the chain is effectively longer, so it will cover a given distance in fewer applications, leading to an underestimation of the actual length – a negative error that is cumulative).

Random Errors: Errors that occur irregularly and are random in magnitude and direction. They arise due to unpredictable fluctuations in experimental conditions or personal judgment. They cannot be eliminated completely but can be minimized by taking multiple readings and averaging.

Compensating Error: Random errors often tend to cancel each other out over many observations, meaning the positive and negative errors balance out to some extent.

Gross Errors: Errors due to carelessness of the observer, like reading an instrument incorrectly, recording observations wrongly, or using wrong values in calculations. Can be avoided by being alert and careful.

Absolute Error (Δa): The magnitude of the difference between the true value (or mean value) and the individual measured value. Δa = |amean - ai|. Its unit is the same as the measured quantity.
Mean Absolute Error (Δamean): The arithmetic mean of all absolute errors. If amean is the true value, Δamean = ( Σ |Δai| ) / n.
Relative Error (δa): The ratio of the mean absolute error to the mean value of the quantity being measured. δa = Δamean / amean. It is a dimensionless quantity.
Percentage Error (% Error): The relative error expressed as a percentage. % Error = (Δamean / amean) × 100%. It is a dimensionless quantity.
Propagation of Errors: How errors combine in mathematical operations:

Error in a Sum or Difference (Z = A ± B): The maximum absolute error is the sum of the absolute errors: ΔZ = ΔA + ΔB.
Error in a Product or Quotient (Z = A × B or Z = A / B): The maximum relative error is the sum of the relative errors: ΔZ/Z = ΔA/A + ΔB/B.
Error in a Quantity Raised to a Power (Z = A^n): The maximum relative error is 'n' times the relative error of A: ΔZ/Z = n(ΔA/A).
Error in a General Combination (Z = A^p B^q / C^r): The maximum relative error is given by: ΔZ/Z = p(ΔA/A) + q(ΔB/B) + r(ΔC/C).

Least Count of Measuring Instruments

Least Count (LC): Smallest measurement an instrument can make accurately.
LC determines the precision of an instrument; a smaller LC means higher precision.
Measurements must be reported with their last significant digit corresponding to the instrument's LC.
Reporting a measurement with precision finer than the instrument's LC is incorrect (implies false precision).
Example: For a meter scale with LC = 1 mm (or 0.001 m):

A reading like 25.3 cm (or 253 mm) is appropriate (precision to 1 mm).

is over-precise (implies 0.1 mm LC).

A reading like 0.50 mm is over-precise (implies 0.01 mm LC).

Precision vs. Accuracy:

Precision: Consistency/reproducibility of measurements; fineness of measurement. Directly related to LC.
Accuracy: Closeness of a measurement to the true value.

Non-SI Units (e.g., Astronomical Unit, Light-Year, Electron-Volt)

Angstrom (Å): Unit of wavelength. 1 Å = 10⁻¹⁰ m. Typical atomic sizes are ~1 Å.
Nanometre (nm): Unit of length. 1 nm = 10⁻⁹ m. Nanotechnology deals with 1-100 nm sized particles.
Micron (µm): Unit of length (micrometre). 1 µm = 10⁻⁶ m = 10⁻⁴ cm.
Femtometre (fm) / Fermi: Unit for nuclear sizes. 1 fm = 10⁻¹⁵ m. Smallest unit of length among common options.
X-unit (XU): Unit for X-ray wavelengths. 1 XU ≈ 1.002 × 10⁻¹³ m.
Light-year (ly): Unit of very large distance, especially astronomical distances. It is the distance light travels in vacuum in one Julian year.

Reason for use: Constant speed of light in vacuum.

Astronomical Unit (AU): Unit of distance. Average distance between Earth and the Sun. 1 AU ≈ 1.496 × 10¹¹ m.
Parsec (pc): Unit of very large distance. 1 pc
Furlong: Unit of distance. 1 furlong ≈ 201.168 m.
Atmosphere (atm): Non-SI unit of pressure. 1 atm is the pressure exerted by a 760 mm column of mercury at 0 °C. 1 atm ≈ 1.01325 × 10⁵ Pa.
Bar: Non-SI unit of pressure. 1 bar = 10⁵ Pa. 1 atm ≈ 1.01325 bar.
Torr: Non-SI unit of pressure. 1 torr ≈ 133.322 Pa. (1 atm = 760 torr).
Curie (Ci): Non-SI unit of radioactivity. The SI unit is Becquerel (Bq). 1 Ci = 3.7 × 10¹⁰ Bq.
Carat: Unit of mass for gemstones (e.g., diamonds). 1 carat = 200 mg = 0.2 g.
Horsepower (HP): Non-SI unit of power. 1 HP ≈ 746 W.
Kilowatt-hour (kWh): Commercial unit of electrical energy. 1 kWh = 3.6 × 10⁶ J.
Jiffy: Unit of time (very short interval). Not a unit of distance.

Physical Quantities (Fundamental and Derived)

Physical Quantities are measurable properties of objects or systems.
Fundamental Quantities (Base Quantities): Independent quantities whose units are defined independently. Length (meter, m) 1. Mass (kilogram, kg) 2. Time (second, s) 3. Electric Current (ampere, A) 4. Thermodynamic Temperature (kelvin, 5. K) Amount of Substance (mole, mol) 6. Luminous Intensity (candela, cd) 7.
Derived Quantities: Quantities obtained by mathematically combining fundamental quantities.

Volume: Unit is m³ (e.g., Liter is a unit of volume, not fundamental).
Force: Unit is Newton (N) or kg·m/s².
Pressure: Unit is Pascal (Pa) or N/m².
Energy/Work/Heat: Unit is Joule (J) or Calorie (cal). (Joule and Calorie are units for the same physical quantity Energy).
Power: Unit is Watt (W) or J/s.
Stress: Unit is N/m² (same as pressure).

Scalar Quantities: Have magnitude only, no direction.

Examples: Energy, Power, Pressure, Temperature, Gravitational Potential, Mass, Length, Time, Distance, Speed.

Vector Quantities: Have both magnitude and direction.

Examples: Impulse, Force, Velocity, Acceleration, Displacement, Momentum.

Dimensionless (Unitless) Quantities: Quantities that are ratios of two similar physical quantities, hence having no units.

Example: Strain (change in dimension / original dimension).

Amplitude of Sound Waves: Can be measured in units of:

Distance (referring to particle displacement from equilibrium).
Pressure (referring to pressure variation from equilibrium pressure, called pressure amplitude).

Prefixes for SI Units

One nanometer (nm) = 10⁻⁹ metres (m).
One nanometer (nm) = 10⁻⁷ cm.
One metre (m) = 10⁹ nanometres (nm).
The word "Nano" is derived from the Greek word "nanos," meaning "dwarf."
Nanotechnology deals with particles typically of the size 10⁻⁹ m.
One Angstrom (Å) = 10⁻¹⁰ m.
The relation between Angstrom and nanometer is 1 nm = 10 Å.
One-millionth part of a gram (10⁻⁶ g) is known as a microgram (µg).
Prefix 'micro' (µ) denotes 10⁻⁶.
Prefix 'nano' (n) denotes 10⁻⁹.

SI Base Units and their Definitions

Kelvin (K): SI base unit for thermodynamic temperature. Cannot be negative; 0 K (absolute zero) is the lowest possible temperature.
Candela (cd): SI base unit for luminous intensity.
Ampere (A): SI base unit for electric current.
Kilogram (kg): SI base unit for mass.
Metre (m): SI base unit for length.
Second (s): SI base unit for time.
Newton (N): SI derived unit for force.
Pascal (Pa): SI derived unit for pressure.
Henry (H): SI derived unit for inductance.
Weber (Wb): SI derived unit for magnetic flux.
Coulomb (C): SI derived unit for electric charge.
Kilogram-metre per second (kg·m/s): SI derived unit for momentum.

Significant Figures

Definition: Significant figures (SF) are the 1. digits in a number that carry meaning contributing to its precision. Rules for Determining Significant Figures: 2.

All non-zero digits are significant. (e.g., 123.45 has 5 SF).
Zeros between two non-zero digits are significant. (e.g., 101.05 has 5 SF).
Leading zeros (zeros before the first non-zero digit) are NOT significant. They only indicate the position of the decimal point. (e.g., 0.00051 has 2 SF).
Trailing zeros (zeros at the end of a number) are significant if the number contains a decimal point. (e.g., 12.00 has 4 SF, 120. has 3 SF).
Trailing zeros are NOT significant if the number does not contain a decimal point, unless specified by scientific notation. (e.g., 1200 has 2 SF, but 1.200 x 10^3 has 4 SF).
Exact numbers (e.g., counts, defined constants like the '6' in surface area = 6s²) have infinite significant figures and do not limit the SF in a calculation. Rules for Arithmetic Operations with 3. Significant Figures:
Multiplication and Division: The result should retain the same number of significant figures as the quantity with the least number of significant figures involved in the calculation.
Addition and Subtraction: The result should retain the same number of decimal places as the quantity with the least number of decimal places. Rounding Rules: 4.
If the digit to be dropped is less than 5, the preceding digit is left unchanged. (e.g., 7.24 rounded to 2 SF becomes 7.2).
If the digit to be dropped is greater than 5, the preceding digit is increased by one. (e.g., 7.26 rounded to 2 SF becomes 7.3).
If the digit to be dropped is exactly 5:

If the preceding digit is even, it is left unchanged. (e.g., 7.25 rounded to 2 SF becomes 7.2).
If the preceding digit is odd, it is increased by one. (e.g., 7.35 rounded to 2 SF becomes 7.4). Application Example (Cube Calculation): 5.

Given side (s) = 7.203 m (4 SF).
Surface Area (SA) = 6 s² = 6 (7.203 m)² = 6 51.883209 m² = 311.299254 m².
Rounding SA to 4 SF (as 7.203 has 4 SF): 311.3 m².
Volume (V) = s³ = (7.203 m)³ = 373.714754427 m³.
Rounding V to 4 SF: 373.7 m³.

Systems of Units (SI, CGS, MKS)

Systems of Units: Standardized sets of units for fundamental quantities (length, mass, time, etc.) for scientific and technical measurements.
CGS System (Centimetre-Gram-Second):

Length: Centimetre (cm)
Mass: Gram (gm)
Time: Second (s)
Derived Unit Example (Density): Density = Mass/Volume = gm/cm³.

MKS System (Metre-Kilogram-Second):

Length: Metre (m)
Mass: Kilogram (kg)
Time: Second (s)

SI System (Système International d'Unités):

The modern form of the metric system, developed from the MKS system, adopted globally.
Seven Base Units: Length: Metre (m) 1. Mass: Kilogram (kg) 2. Time: Second (s) 3. Electric Current: Ampere (A) 4. Thermodynamic Temperature: 5. Kelvin (K) Amount of Substance: Mole 6. (mol) Luminous Intensity: Candela 7. (cd)
Derived Units: Units for all other physical quantities, formed by multiplying and/or dividing base units (e.g., Newton for Force, Joule for Energy).
Coherence: Derived units are formed without numerical factors (e.g., 1N = 1 kg·m/s²).
Universality: Globally accepted for scientific, technical, and commercial applications.

Unit Conversion Techniques

Length Unit Conversion:
1 nanometer (nm) = 10⁻⁹ meter (m).
To determine the number of hydrogen atoms (radius 10⁻¹⁰ m) required to form a length of one nanometre: (1 nm / 10⁻¹⁰ m) = (10⁻⁹ m / 10⁻¹⁰ m) = 10 atoms.
Energy Unit Conversion (Electrical):
1 kilowatt-hour (kWh) = 3.6 × 10⁶ Joules (J).
Derivation: 1 kWh = 1 kW × 1 hour = 1000 Watts × 3600 seconds = 3,600,000 Wattseconds = 3.6 × 10⁶ J.
Temperature Unit Conversion (Celsius and Fahrenheit):
Conversion formula from Celsius to Fahrenheit: °F = (1.8 × °C) + 32.
Alternatively: °F = (⁹⁄₅ × °C) + 32.
Conversion formula from Fahrenheit to Celsius: °C = (°F - 32) / 1.8 or °C = ⁵⁄₉ × (°F - 32).
Example: 10°C converts to Fahrenheit as (1.8 × 10) + 32 = 18 + 32 = 50°F.
The temperature at which Celsius and Fahrenheit scales show the same reading is -40 degrees (i.e., -40°C = -40°F).

Units of Measurement (Definition and Characteristics)

Frequency: Hertz (Hz).
Power of a lens: Dioptre.
Standard atmospheric pressure at sea level:

millibars (mb).

Distance (astronomical): Light-year.
Amount of substance: Mole.
Electric charge: Coulomb (C).
Energy: Watt-hour (Wh).
Natural units of time: Day, Lunar month, Tropical year.
Non-natural/Standardized unit of time: Standard Time.
Powndal: Unit of weight/force (FPS system).
Radioactivity: Curie (Ci), Becquerel (Bq).
Units of pressure: Pascal (Pa), Bar, Torr, Atmosphere (atm).

2. Measuring Instruments and Scales

Practice MCQs: Measurement/Unit

Derived Units and their Expression

Frequency is measured in
Asked in: BPSC Prelims Exam 64th
1. hertz
2. meter/second
3. radian
4. watt
Show answer
Answer: A. hertz
- Frequency measures the rate of repetition of an event. - The standard SI unit for frequency is the Hertz (Hz). - 1 Hz = 1 cycle/second = $1 \text{ s} ^{-1}$. - Other options represent units for speed, angle, and power respectively.
The unit of electric power is
Asked in: BPSC Prelims Exam 64th
1. ampere
2. volt
3. coulomb
4. watt
Show answer
Answer: D. watt
BPSC Prelims Exam-65th Electric power is defined as the rate at which electrical energy is transferred or used. Its standard unit in the International System of Units (SI) is the watt (W).
What is the unit of pressure?
Asked in: BPSC Prelims Exam 64th
1. Newton/sq. meter
2. Newton-meter
3. Newton
4. Newton/meter
Show answer
Answer: A. Newton/sq. meter
Pressure is defined as force per unit area. The standard unit of force is the Newton (N), and the standard unit of area is the square meter (m²). Therefore, the unit of pressure is Newton/sq. meter (N/m²).
The unit of pressure is
Asked in: BPSC Prelims Exam 65th
1. kg/cm²
2. kg/cm
3. kg/mm
4. kg/cm³
Show answer
Answer: A. kg/cm²
Pressure is force per unit area. Kg/cm² (interpreting kg as kg-force) is a unit of pressure.
The SI unit of mechanical power is :
Asked in: UPSC CDS 1 2016
1. Joule
2. Watt
3. Newton-second
4. Joule-second
Show answer
Answer: B. Watt
Power is defined as the rate at which work is done or energy is transferred. In the International System of Units (SI), the unit of work or energy is the Joule (J), and the unit of time is the second (s). Therefore, the unit of power is Joule per second (J/s), which is defined as the Watt (W).
The unit of the force constant $k$ of a spring is
Asked in: UPSC CDS 1 2020
1. N-m
2. N/m
3. N-m$^2$
4. N/m$^2$
Show answer
Answer: B. N/m
- Hooke's Law: $F = kx$. - F is force (unit: N). - x is displacement (unit: m). - k is the force constant.
The resistivity $\rho$ of a material may be expressed in units of
Asked in: UPSC CDS 1 2020
1. ohm
2. ohm/cm
3. ohm-cm
4. ohm-cm$^2$
Show answer
Answer: C. ohm-cm
The unit of resistance ($R$) is Ohm ($\Omega$). The unit of area ($A$) is typically square meters (m²) or square centimeters (cm²). The unit of length ($L$) is typically meters (m) or centimeters (cm). Substituting these units into the formula for $\rho$: $\text{Units of } \rho = \Omega \times \frac{\text{cm}^2}{\text{cm}} = \Omega \cdot \text{cm}$. Alternatively, using meters: $ \text{Units of } \rho = \Omega \times \frac{\text{m}^2}{\text{m}} = \Omega \cdot \text{m}$. Therefore, the resistivity is commonly expressed in ohm-centimeters ($\Omega \cdot \text{cm}$) or ohm-meters ($\Omega \cdot \text{m}$).
'Joule' is related to energy in the same way as 'Pascal' is related to
Asked in: CGPSC Prelims Exam 2015
1. Mass
2. Pressure
3. Density
4. Purity
Show answer
Answer: B. Pressure
- This question tests the knowledge of standard units for physical quantities. - Energy is the capacity to do work, measured in Joules. - Pressure is force per unit area, measured in Pascals.

Dimensional Analysis (Dimensions, Homogeneity, Applications)

Which one of the following physical quantities has the same dimensions as that of Planck's constant h?
Asked in: UPSC CDS 2 2016
1. Linear momentum
2. Angular momentum
3. Force
4. Potential energy
Show answer
Answer: B. Angular momentum
- Planck's constant (h) relates the energy (E) of a photon to its frequency (ν) by the equation E = hν. The dimensions of E are [ML²T⁻²] and the dimensions of ν are [T⁻¹]. Therefore, the dimensions of h are [E/ν] = [ML²T⁻²] / [T⁻¹] = [ML²T⁻¹]. - Let's check the dimensions of the given options: - Linear momentum (p = mv): [M] [LT⁻¹] = [MLT⁻¹]. - Angular momentum (L = Iω or L = rp): [Moment of inertia Angular velocity] or [Radius Linear momentum]. Dimensions are [ML²] [T⁻¹] or [L] [MLT⁻¹] = [ML²T⁻¹]. - Force (F = ma): [M] [LT⁻²] = [MLT⁻²]. - Potential energy (e.g., mgh): [M] [LT⁻²] [L] = [ML²T⁻²]. - Comparing the dimensions, angular momentum [ML²T⁻¹] has the same dimensions as Planck's constant [ML²T⁻¹].
The dimension of dielectric constant i
Asked in: CGPSC Prelims Exam 2024
1. M⁰L⁰T⁰
2. ML⁰T⁰
3. MLT⁰
4. M⁰L⁰T
Show answer
Answer: A. M⁰L⁰T⁰
Dielectric constant (relative permittivity, εr) is defined as the ratio of the permittivity of a material (ε) to the permittivity of free space (ε₀). Since both ε and ε₀ have the same physical dimensions, their ratio is a dimensionless quantity.
Which one of the following quantities is dimensionless?
Asked in: UPSC Geoscientist 2023
1. Specific weight
2. Specific heat
3. Specific density
4. Specific gravity
Show answer
Answer: D. Specific gravity
Specific gravity is defined as the ratio of the density of a substance to the density of a standard substance, making it a dimensionless quantity.
Which one of the following expressions has dimensions of energy (here V is the voltage across a resistor of resistance R and I is the current through the resistor, and t is the time)?
Asked in: UPSC Geoscientist 2023
1. V2 / I t
2. V2 / R t
3. I2 / R t
4. I2 / V t
Show answer
Answer: C. I2 / R t
- Energy = Power × Time. - Power in a resistor = V²/R = I²R = VI. - Dimensions of Energy = [Force × Distance] = [MLT⁻² × L] = [ML²T⁻²].
The unit of the ratio between thrust and impulse is same as that of
Asked in: UPSC NDA 2 2021
1. frequency
2. speed
3. wavelength
4. acceleration
Show answer
Answer: A. frequency
Thrust is a force. The SI unit of force is Newton (N), which is equivalent to $\text{kg} \cdot \text{m/s}^2$. Impulse is the change in momentum, or force multiplied by time. The SI unit of impulse is N·s, which is equivalent to $(\text{kg} \cdot \text{m/s}^2) \cdot \text{s} = \text{kg} \cdot \text{m/s}$. The ratio $\frac{\text{Thrust}} {\text{Impulse}}$ has units $\frac{\text{N}} {\text{N} \cdot \text{s}} = \frac{1}{\text{s}}$. The unit $1/\text{s}$ is the unit of frequency. Frequency is the number of cycles or events per unit time, measured in Hertz (Hz), where 1 Hz = $1/\text{s}$. Let's check the units of the options: A) Frequency: $1/\text{s}$ or Hz. B) Speed: m/s. C) Wavelength: m. D) Acceleration: m/s². The unit of the ratio is the same as the unit of frequency.
Which of the following sets have different dimensions?
Asked in: TNPSC CS Prelims 2015
1. Pressure, Young's modulus, Stress
2. Emf, potential difference, Electric potential
3. Heat, Work done, Energy
4. Dipole moment, Electric flux, Electric field
Show answer
Answer: D. Dipole moment, Electric flux, Electric field
Let's analyze the dimensions of each quantity: A) Pressure, Young's modulus, Stress: All have dimensions of Force/Area, which is [ML⁻¹T⁻²]. B) Emf, potential difference, Electric potential: All are potential energy per unit charge, with dimensions [ML²T⁻³I⁻¹]. C) Heat, Work done, Energy: All are forms of energy, with dimensions [ML²T⁻²]. D) Dipole moment: Charge x distance, dimensions [IT] [L] = [LIT]. Electric flux: Electric field x Area, dimensions [Force/Charge] x Area = ([MLT⁻²]/[IT]) x [L²] = [ML³T⁻³I⁻¹]. Electric field: Force/Charge, dimensions [MLT⁻²]/[IT] = [MLT⁻³I⁻¹]. The dimensions in set D ([LIT], [ML³T⁻³I⁻¹], [MLT⁻³I⁻¹]) are all different.
Which one of the following pairs of quantities has no length in their dimension?
Asked in: UPSC CISF AC EXE 2019
1. Surface tension and angular momentum
2. Surface tension and strain
3. Angular momentum and mass density
4. Pressure gradient and angle
Show answer
Answer: B. Surface tension and strain
We need to find the pair of quantities whose dimensions do not include length ([L]). Let's analyze the dimensions of each quantity: - Surface tension Defined as force per unit length. Dimension is [Force]/[Length] = [MLT⁻²]/[L] = [MT⁻²]. It has no length dimension. - Angular momentum Defined as the product of moment of inertia and angular velocity (Iω) or cross product of position and linear momentum (r x p). Dimension is [ML²] [T⁻¹] = [ML²T⁻¹]. It has a length dimension. - Strain Defined as the ratio of change in dimension to the original dimension (e.g., change in length / original length). Dimension is [L]/[L] = [Dimensionless]. It has no length dimension. - Mass density Defined as mass per unit volume. Dimension is [M]/[L³] = [ML⁻³]. It has a length dimension. - Pressure gradient Defined as change in pressure per unit distance. Dimension is [Pressure]/[Length]. Pressure is [Force]/[Area] = [MLT⁻²]/[L²] = [ML⁻²T⁻²]. So, pressure gradient is [ML⁻²T⁻²]/[L] = [ML⁻³T⁻²]. It has a length dimension. - Angle Defined as the ratio of arc length to radius. Dimension is [L]/[L] = [Dimensionless]. It has no length dimension.Now let's check the pairs: A) Surface tension ([MT⁻²]) and angular momentum ([ML²T⁻¹]). Angular momentum has length. B) Surface tension ([MT⁻²]) and strain ([Dimensionless]). Neither has length. C) Angular momentum ([ML²T⁻¹]) and mass density ([ML⁻³]). Both have length. D) Pressure gradient ([ML⁻³T⁻²]) and angle ([Dimensionless]). Pressure gradient has length.The pair with no length dimension is Surface tension and Strain.
In terms of basic units of mass (M), length (L) and time (T), dimension of energy is
Asked in: WBCS Main Paper 4 2021
1. ML²T⁻¹
2. MLT
3. MLT⁻¹
4. ML²T⁻²
Show answer
Answer: D. ML²T⁻²
Dimension of Work = Dimension of Energy. Work = Force × distance. Force = mass × acceleration. Dimension of mass = [M], length = [L], time = [T]. Dimension of acceleration = [LT⁻²]. Dimension of force = [MLT⁻²]. Dimension of energy = [ML²T⁻²].

Errors in Measurement (Types, Absolute, Relative, Percentage, Propagation)

The least number of six digits, which when divided by 4, 6, 10 and 15, leave same remainder 2 in each case. Then what is the sum of the digits of that number?
Asked in: GPSC Prelims CSP 1 2023
1. 3
2. 5
3. 4
4. 6
Show answer
Answer: B. 5
The problem asks for the least six-digit number which, when divided by 4, 6, 10, and 15, leaves the same remainder 2 in each case. This means the number N is 2 more than a common multiple of 4, 6, 10, and 15. The common multiples of these numbers are the multiples of their Least Common Multiple (LCM). LCM(4, 6, 10, 15): 4 = 2² 6 = 2 3 10 = 2 5 15 = 3 5 LCM(4, 6, 10, 15) = 2² 3 5 = 4 3 5 = 60. So, the number N must be of the form N = 60k + 2, where k is a non-negative integer. We are looking for the least six-digit number of this form. The smallest six-digit number is 100000. We need to find the smallest integer k such that 60k + 2 >= 100000. 60k >= 100000 - 2 = 99998. k >= 99998 /
k >= 1666.633... Since k must be an integer, the smallest integer value for k is 1667. The least six- digit number is N = 60 1667 + 2. 60 1667 = 100020. N = 100020 + 2 = 100022. The number is 100022. The sum of the digits of this number is 1 + 0 + 0 + 0 + 2 + 2 = 5. 54. If a clock takes 5 minutes to strike five times at 5 o'clock, then how much time will it take to strike nine times at 9 o'clock at the same speed?
Asked in: JPSC CS Prelims 2011
1. 5 minutes
2. 9 minutes
3. 10 minutes
4. 8 minutes
Show answer
Answer: C. 10 minutes
When a clock strikes 'n' times, there are 'n-1' intervals between the strikes. The time taken to strike five times means there are 5 - 1 = 4 intervals. If 4 intervals take 5 minutes, then the time taken for one interval is 5 minutes / 4 = 1.25 minutes. To strike nine times, there are 9 - 1 = 8 intervals. At the same speed, the time taken for 8 intervals will be 8 1.25 minutes = 10 minutes.
When a chain is used at a temperature more than the temperature it was calibrated, the error in measured length will be
Asked in: Civil Engg GA 24 2023 CO 1505 2024
1. cumulative
2. compensating
3. negative
4. observational
Show answer
Answer: A. cumulative
Temperature correction for chains: When the temperature is higher than the calibration temperature, the chain expands, making it longer than its standard length. This leads to a negative error in measurement (measured length is less than true length), and this error is cumulative.

Least Count of Measuring Instruments

A student measures certain lengths using a meter scale having least count equal to 1 mm. Which one of the following measurements is more precise ?
Asked in: UPSC NDA 2 2019
1. 0$\cdot$50 mm
2. 29$\cdot$07 cm
3. 0$\cdot$925 m
4. 910 mm
Show answer
Answer: A. 0$\cdot$50 mm
- The precision of a measurement is indicated by the number of significant figures and the position of the last significant digit relative to the least count of the instrument. - With a scale of 1 mm least count, readings are usually taken to the nearest 1 mm or estimated to the nearest 0.1 mm. - The number of decimal places in the unit of the least count often suggests the level of precision in the recorded value.

Non-SI Units (e.g., Astronomical Unit, Light-Year, Electron-Volt)

Angstrom is a unit of
Asked in: BPSC Prelims Exam 64th
1. wavelength
2. energy
3. frequency
4. velocity
Show answer
Answer: A. wavelength
- Angstrom is a unit of length. - 1 Å = $10^{-10}$ meters. - It is commonly used for atomic scale measurements and wavelengths of light.
'Light-year' is a unit of
Asked in: BPSC Prelims Exam 66th HPPSC HPAS Prelims 2016
1. time
2. speed
3. distance
4. intensity of light
Show answer
Answer: C. distance
While it involves 'light' and 'year', it is a unit of distance, not time or speed.
The size of particles being studied in 'nano- technology' is about
Asked in: UPSC CDS 1 2021
1. 1 Å – 10 nm
2. 1 – 100 nm
3. 1 – 50 µ
4. 1 mm – 10 mm
Show answer
Answer: B. 1 – 100 nm
A nanometer (nm) is one billionth of a meter (10⁻⁹ m). The 1 to 100 nm range is considered the nanoscale because materials within this size range often exhibit unique physical, chemical, and biological properties that differ significantly from their bulk counterparts. This is due to quantum mechanical effects and a large surface area-to-volume ratio.
The pressure exerted by a 760 mm column of mercury at 0 °C is known as
Asked in: UPSC CDS 2 2016
1. 1 pascal
2. 1 atmosphere
3. 1 bar
4. 1 poise
Show answer
Answer: B. 1 atmosphere
- Standard atmospheric pressure is defined as the pressure that supports a column of mercury exactly 760 millimeters (or 76 cm or 29.92 inches) high at 0 °C at sea level and standard gravitational acceleration. - This pressure is internationally defined as 1 standard atmosphere (atm). - 1 atm is equivalent to 101,325 Pascals (Pa), which is the SI unit of pressure. - 1 bar is another unit of pressure, equal to 100,000 Pa, which is slightly less than 1 atm. - Pascal is the SI unit of pressure (N/m²). - Poise is a unit of dynamic viscosity.
One astronomical unit is the average distance between
Asked in: JPSC CS Prelims 2011
1. the Earth and the Sun
2. the Earth and the Moon
3. the Jupiter and the Sun
4. the Pluto and the Sun
Show answer
Answer: A. the Earth and the Sun
- The average distance is used because the Earth's orbit around the Sun is elliptical, so the distance varies slightly throughout the year. - The official value of 1 AU is defined as exactly 149,597,870,700 meters.
Light year is a unit of
Asked in: JPSC CS Prelims 2024 · RPSC RAS Prelims 1998
1. distance
2. time
3. energy
4. intensity of light
Show answer
Answer: A. distance
Light travels at a speed of approximately 299,792,458 meters per second in a vacuum. One light-year is a very large unit of distance, used primarily in astronomy to measure the vast distances between celestial objects like stars and galaxies.
Light year is a unit for measurement of
Asked in: UPSC NDA 1 2018
1. age of universe
2. very small time intervals
3. very high temperature
4. very large distance
Show answer
Answer: D. very large distance
A light-year is defined as the distance that light travels in vacuum in one Julian year (365.25 days). Since the speed of light is constant and very high, a light-year represents a very large distance. It is commonly used in astronomy to measure the distances between celestial objects, such as stars and galaxies. It is not a unit of time, temperature, or a measure related to the age of the universe (although the size of the observable universe is often expressed in light-years, its age is in years).
Light year is a unit of measurement of
Asked in: UPSC NDA 1 2019
1. very large distances
2. time interval in years
3. amount of light received on earth in a year
4. mass of atoms
Show answer
Answer: A. very large distances
APPSC Draughtman-2008 A light-year is defined as the distance that light travels in vacuum in one Julian year (365.25 days). It is a unit of length used to express astronomical distances.

Physical Quantities (Fundamental and Derived)

If (5)ˣ²+2x+7 = (125)²x+1 then the value of x is
Asked in: BPSC Prelims Exam 65th
1. 5
2. 4
3. 3
4. 2
Show answer
Answer: D. 2
We know that $125 = 5^3$. Substitute this into the equation: $(5)^{x^2+2x+7} = (5^3)^{2x+1}$. Using the power of a power rule $(a^m)^n = a^{mn}$, we get $(5)^{x^2+2x+7} = 5^{3(2x+1)} = 5^{6x+3}$.
If the radii of circles A and B are in the ratio 1.5 : 1, then the areas of the circles A and B will be in the ratio
Asked in: BPSC Prelims Exam 65th
1. 1.5 : 1
2. 2 : 1
3. 2.25 : 1
4. 2.5 : 1
Show answer
Answer: C. 2.25 : 1
- The formula for the area of a circle is A = πr², where A is the area and r is the radius. - If the ratio of radii is r₁ : r₂, the ratio of areas is (πr₁²) : (πr₂²) = r₁² : r₂².
Which one of the following quantities does not have unit?
Asked in: BPSC Prelims Exam 65th
1. Stress
2. Force
3. Strain
4. Pressure
Show answer
Answer: C. Strain
Strain is a dimensionless quantity calculated as a ratio of change in dimension to original dimension.
The missing number in the sequence 4, 18, 48, 100, ?, 294, 448 is
Asked in: BPSC Prelims Exam 66th
1. 94
2. 164
3. 180
4. 192
Show answer
Answer: C. 180
- Identifying the pattern in the sequence is key. - The pattern relates the term value to its position in the sequence.
Which one of the following cannot be the square of a natural number.
Asked in: BPSC Prelims Exam 66th
1. 26569
2. 143642
3. 30976
4. 28561
Show answer
Answer: B. 143642
The unit digit of a perfect square can only be 0, 1, 4, 5, 6, or 9. A number ending in 2, 3, 7, or 8 cannot be a perfect square.
The value of the continued fraction $2- \frac{1}{2-\frac{1}{2-\cdots}}$ is
Asked in: BPSC Prelims Exam 67th Cancelled
1. 1
2. -1
3. 2
4. 0
Show answer
Answer: A. 1
Since the expression repeats, we can write: $x = 2 - \frac{1}{x}$ Multiply by x: $x^2 = 2x - 1$ Rearrange the equation: $x^2 - 2x + 1 = 0$ This is a perfect square trinomial: $(x - 1)^2 = 0$ Solving for x: $x - 1 = 0$ $x = 1$
If n is any positive integer, then $(3^{4n}-4^{3n})$ is always divisible by
Asked in: BPSC Prelims Exam 67th Cancelled
1. 7
2. 17
3. 112
4. 145
Show answer
Answer: B. 17
The given expression is $3^{4n} - 4^{3n}$. This can be rewritten using exponent rules as $(3^4)^n - (4^3)^n$. Calculate the bases: $3^4 = 3 \times 3 \times 3 \times 3 = 81$. Calculate the bases: $4^3 = 4 \times 4 \times 4 = 64$. So, the expression becomes $81^n - 64^n$. A property of exponents states that for any positive integer $n$, $a^n - b^n$ is always divisible by $(a-b)$. In this case, $a = 81$ and $b = 64$. The difference $a-b = 81 - 64 = 17$. Therefore, $81^n - 64^n$ is always divisible by 17.
The value of log$_{\sqrt{2}}$ (32) is
Asked in: BPSC Prelims Exam 67th Cancelled
1. $\frac{5}{2}$
2. 5
3. 10
4. $\frac{1}{10}$
Show answer
Answer: C. 10
The expression is $\log_{\sqrt{2}}(32)$. Let this value be $y$. By the definition of logarithms, $ \log_b(a) = y$ is equivalent to $b^y = a$. So, we have $(\sqrt{2})^y = 32$. To solve for $y$, we should express both sides of the equation with the same base. The most convenient base here is 2. We know that $\sqrt{2} = 2^{1/2}$. We also know that $32 = 2 \times 2 \times 2 \times 2 \times 2 = 2^5$. Substitute these into the equation: $(2^{1/2})^y = 2^5$. Using the exponent rule $(a^m)^n = a^{mn} $, we get $2^{(1/2) \times y} = 2^5$, which is $2^{y/2} = 2^5$. Since the bases are equal, the exponents must be equal: $\frac{y}{2} = 5$. Multiply both sides by 2: $y = 5 \times 2 = 10$. Thus, $ \log_{\sqrt{2}}(32) = 10$.

Prefixes for SI Units

Which one of the following is the value of one nanometer?
Asked in: UPSC CDS 1 2018
1. 10-7 cm
2. 10-6 cm
3. 10-4 cm
4. 10-3 cm
Show answer
Answer: A. 10-7 cm
- The prefix 'nano' (n) represents a factor of 10⁻⁹. - The base unit of length in SI is the meter (m). - 1 meter = 100 centimeters = 10² cm. - To convert from meters to centimeters, multiply by 10².
The word Nano came from __________.
Asked in: GPSC Prelims CSP 2 2024
1. Greek word
2. Italian word
3. Latin word
4. French word
Show answer
Answer: A. Greek word
The prefix "nano" originates from the Greek word for dwarf.
Nanotechnology is where particles of the following size are used :
Asked in: HPPSC HPAS Prelims 2010
1. 10⁹ cm
2. 10⁻⁹ m
3. 10⁻⁹ cm
4. 10⁹ m
Show answer
Answer: B. 10⁻⁹ m
Nanotechnology involves the manipulation of matter on an atomic, molecular, and supramolecular scale. The relevant length scale for nanotechnology is generally considered to be from 1 to 100 nanometers (nm). One nanometer is defined as 10⁻⁹ meters (m).
Which one of the following is the correct relation between Å and nm?
Asked in: UPSC NDA 2 2018
1. 1 nm = 10⁻¹ Å
2. 1 nm = 10 Å
3. 1 nm = 1 Å
4. 1 nm = 10⁻² Å
Show answer
Answer: B. 1 nm = 10 Å
This question tests the knowledge of common units of length used in physics and chemistry, particularly at the atomic and molecular scales, and the ability to convert between them based on their definitions in terms of meters.
One Nanometer is equal to
Asked in: UKPSC CS Prelims 2016 · Protection Officer 2018
1. $10^{-9}$ m
2. $10^{-6}$ m
3. $10^{-10}$ m
4. $10^{-3}$ m
Show answer
Answer: A. $10^{-9}$ m
- "nano-" is an SI prefix. - The value of "nano-" is $10^{-9}$. - 1 nanometer (nm) = $10^{-9}$ meters (m).
1 nm is equivalent to
Asked in: WBPSC CS Prelims 2017
1. 10Å
2. 100Å
3. 10µm
4. .01mm
Show answer
Answer: A. 10Å
This question requires conversion between different units of length. - 1 nanometer (nm) = 10⁻⁹ meters (m). - 1 Ångström (Å) = 10⁻¹⁰ meters (m). - 1 micrometer (µm) = 10⁻⁶ meters (m). - 1 millimeter (mm) = 10⁻³ meters (m).To find the equivalent of 1 nm in Ångströms: 1 nm = 10⁻⁹ m 1 Å = 10⁻⁰ m Divide 1 nm by 1 Å: (10⁻⁹ m) / (10⁻⁰ m) = 10⁻⁹ / 10⁻⁰ = 10⁻⁹⁺⁰ = 10¹ = 10. So, 1 nm = 10 Å.Comparing this to the options: A) 10Å = 1 nm (Correct) B) 100Å = 100 × 10⁻⁰ m = 10⁻⁸ m = 10 nm (Incorrect) C) 10µm = 10 × 10⁻⁶ m = 10⁻⁵ m = 10,000 nm (Incorrect) D) 0.01mm = 0.01 × 10⁻³ m = 10⁻² × 10⁻³ m = 10⁻⁵ m = 10,000 nm (Incorrect)
One-millionth part of a gram is known as
Asked in: Field Investigator 2020
1. microgram
2. infigram
3. minigram
4. atomic gram
Show answer
Answer: A. microgram
A microgram is a unit of mass in the metric system equal to one-millionth (10⁻⁶) of a gram. The prefix "micro-" signifies one-millionth.
Which of the following is correct ?
Asked in: RO ARO pre 2023
1. 1 metre = $10^{19}$ nanometre
2. 1 metre = $10^{90}$ nanometre
3. 1 metre = $10^9$ nanometre
4. None of the above
Show answer
Answer: C. 1 metre = $10^9$ nanometre
Understanding scientific prefixes and unit conversions is fundamental in physics and general science.

SI Base Units and their Definitions

Which of the following statements regarding temperature of an object in Kelvin scale is/ are correct ? 1. It can be a negative, zero or positive quantity. 2. It can either be a negative or a positive quantity. 3. It can never be negative. 4. It can be a positive definite quantity. Select the correct answer using the code given below :
Asked in: UPSC CISF AC EXE 2018
1. 1 and 2 only
2. 2 and 4 only
3. 3 and 4 only
4. 4 only
Show answer
Answer: C. 3 and 4 only
Temperature on the Kelvin scale is always non- negative ($\ge 0$).
What is the SI unit of inductance?
Asked in: APPSC Group II Prelims 2018
1. Farad
2. Ohm
3. Henry
4. Candela
Show answer
Answer: C. Henry
APPSC Miscellaneous-2023 Inductance is the property of an electrical conductor or circuit that opposes a change in current. Its SI unit is named after Joseph Henry.
Q93: What is the unit of pressure?
Asked in: Asstt. Jailor 2013
1. Angstrom
2. Kelvin
3. Newton
4. Pascal
Show answer
Answer: D. Pascal
Pressure is defined as force applied perpendicular to the surface of an object per unit area over which that force is distributed. The SI unit of force is Newton (N), and the SI unit of area is square meter (m²). Therefore, the SI unit of pressure is Newton per square meter (N/m²), which is defined as Pascal (Pa).
The S.I. unit of magnetic flux is :
Asked in: Clerk GR II Comb. Comp. Exam 2013
1. Tesla
2. Weber
3. Gauss
4. Ampere
Show answer
Answer: B. Weber
The Weber (Wb) is the SI unit used to measure magnetic flux.
SI unit of force is :
Asked in: Protection Officer 2018
1. joule
2. newton
3. pound
4. pascal
Show answer
Answer: B. newton
Force is a push or pull that can cause an object to accelerate. Its SI unit is the Newton.
SI unit of momentum is - - kilogram – metre per second - newton – metre per second - gram – centimeter per second - Joule – metre per second
Asked in: School Lecturer (School Edu.) 2018 3 2018
1. (1) kilogram – metre per second
2. (2) gram – centimeter per second
3. (3) newton – metre per second
4. (4) Joule – metre per second
Show answer
Answer: A. (1) kilogram – metre per second
SI units are a standardized system of measurement. Understanding the definitions of physical quantities and their constituent units is crucial for determining the SI unit of derived quantities like momentum.
75 The SI Unit of Charge is-
Asked in: Sub Inspector Comb. Comp. Exam 2016
1. Ampere
2. Volt
3. Coulomb
4. Ohm
Show answer
Answer: C. Coulomb
This question tests fundamental knowledge of SI units in physics, specifically those related to electricity.
Candela is a S.I. unit of -
Asked in: Staff Nurse Examination 2023
1. Luminous intensity
2. Electric current
3. Circular motion
4. Electromagnetic current
Show answer
Answer: A. Luminous intensity
Candela (cd) is the base unit of luminous intensity in the International System of Units (SI).

Significant Figures

The significant figures in 0.00051 are
Asked in: ae 2024
1. 26
2. 2
3. 5
4. 3
Show answer
Answer: B. 2
Rules for significant figures: - Non-zero digits are always significant. - Leading zeros are never significant. - Zeros between non-zero digits are always significant. - Trailing zeros are significant only if the number contains a decimal point.

Systems of Units (SI, CGS, MKS)

The unit of density in CGS system is
Asked in: WBCS Main Paper 4 2021
1. gm/cm⁴
2. gm/cm³
3. gm/cm²
4. gm/cm
Show answer
Answer: B. gm/cm³
Density is defined as mass per unit volume. In the CGS system, mass is measured in grams (gm), and volume is measured in cubic centimetres (cm³). Therefore, the unit of density in the CGS system is grams per cubic centimetre.

Unit Conversion Techniques

If sign + represents multiplication, × addition, – division, + difference, > equal and = represents greater than, then which of the following relation is true ?
Asked in: BPSC Prelims Exam 60 62rd
1. 12-2+3+8×1>12
2. 11×2+4-2+1=11
3. 7+2×5-5+2=7
4. 5×6-3+3+1>4
Show answer
Answer: C. 7+2×5-5+2=7
The symbol substitutions are: + represents × × represents + – represents / > represents = = represents > (The second rule "+ represents difference" is ignored as conflicting with the first rule for '+')Let's evaluate each relation: A) 12-2+3+8×1>12 Substitute: 12/2 × 3 × 8 + 1 = 12 Calculate: (12/2) × 3 × 8 + 1 = 6 × 3 × 8 + 1 = 18 × 8 + 1 = 144 + 1 = 145. So, 145 = 12. False.B) 11×2+4-2+1=11 Substitute: 11+2 × 4 / 2 × 1 > 11 Calculate: (11+2) × (4/2) × 1 > 11 = 13 × 2 × 1 > 11 = 26 × 1 > 11 = 26 > 11. True.C) 7+2×5-5+2=7 Substitute: 7×2 + 5 / 5 × 2 > 7 Calculate: (7×2) + (5/5) × 2 > 7 = 14 + 1 × 2 > 7 = 14 + 2 > 7 = 16 > 7. True.D) 5×6-3+3+1>4 Substitute: 5+6 / 3 × 3 × 1 = 4 Calculate: 5 + (6/3) × 3 × 1 = 5 + 2 × 3 × 1 = 5 + 6 × 1 = 5 + 6 = 11. So, 11 =
False.Since both relations B and C are true, the correct option is E (More than one of the above). 128. A number when divided by 342 gives a remainder 47. When the same number is divided by 19, what would be the remainder?
Asked in: BPSC Prelims Exam 63rd
1. 0
2. 9
3. 18
4. 8
Show answer
Answer: B. 9
Let the number be N. N = 342q + 47, where q is the quotient and 47 is the remainder. To find the remainder when N is divided by 19, we can express 342 and 47 in terms of 19.
How many prime numbers are there between 1 and 50?
Asked in: BPSC Prelims Exam 64th
1. 17
2. 15
3. 14
4. 16
Show answer
Answer: B. 15
- A prime number is a whole number greater than 1 with exactly two divisors: 1 and itself. - 1 is not a prime number. - 2 is the only even prime number. - Systematically listing and checking numbers within the given range is required.
If x = -2⁄3, then 9x2 – 3x – 11 is equal to
Asked in: BPSC Prelims Exam 64th
1. -13
2. 13
3. -5
4. -17
Show answer
Answer: C. -5
- Substitute the given value of the variable into the expression. - Follow the order of operations (PEMDAS/BODMAS): Parentheses/Brackets, Exponents/Orders, Multiplication and Division (from left to right), Addition and Subtraction (from left to right). - Pay careful attention to signs (positive and negative).
If $3^{x+8} = 27^{2x+1}$, then the value of $x$ is
Asked in: BPSC Prelims Exam 64th
1. 9
2. 1
3. -1
4. 10
Show answer
Answer: B. 1
- To solve exponential equations, express both sides with the same base if possible. - Use the property $ (a^m)^n = a^{mn}$. - If $a^m = a^n$ and $a \neq 0, 1, -1$, then $m=n$. - Solve the resulting linear equation.
If x³ - y³ = 117/8 and x - y = 3/2, then the value of x² + xy + y² will be
Asked in: BPSC Prelims Exam 65th
1. 1
2. 5/8
3. 39/4
4. 39/8
Show answer
Answer: C. 39/4
We use the algebraic identity for the difference of cubes: $a^3 - b^3 = (a - b)(a^2 + ab + b^2)$. Applying this to the given expression: $x^3 - y^3 = (x - y)(x^2 + xy + y^2)$.
The smallest fraction, which is exactly divisible by each of 6/7, 5/14, 10/21 is ______.
Asked in: GPSC Prelims CSP 1 2024
1. 30/7
2. 60/147
3. 50/293
4. None of the above
Show answer
Answer: A. 30/7
The smallest fraction divisible by a set of fractions is their Least Common Multiple (LCM). The LCM of fractions is calculated as the LCM of the numerators divided by the HCF of the denominators.
A 15 cm coloured cube is cut into 3 cm smaller cubes, then how many cubes are formed which have only one face painted?
Asked in: GPSC Prelims CSP 1 2024
1. 54
2. 48
3. 36
4. None of the above
Show answer
Answer: A. 54
Cubes with only one face painted are those that are on the faces of the large cube but are not on its edges or corners. These form the interior of each face.

Units of Measurement (Definition and Characteristics)

What is measured in hertz?
Asked in: BPSC Prelims Exam 65th
1. Frequency
2. Energy
3. Heat
4. Quality
Show answer
Answer: A. Frequency
Hertz (Hz) is the SI unit of frequency. Frequency measures the number of cycles per second of a periodic phenomenon.
The power of a lens is measured in
Asked in: MPPSC CS Prelims 2017
1. dioptre
2. aeon
3. lumen
4. candela
Show answer
Answer: A. dioptre
The power of a lens is a measure of its ability to converge or diverge light, and it is measured in dioptres (D). One dioptre is defined as the reciprocal of the focal length in meters (Power = 1 / focal length in meters). Aeon is a unit of geological time. Lumen is the SI unit of luminous flux, measuring the total amount of visible light emitted by a source. Candela is the SI unit of luminous intensity, measuring the light output in a particular direction.
What is the atmospheric pressure at sea level ?
Asked in: MPSC CS Prelims 2012
1. 76 cm
2. 29.9 inch
3. 1013.2 millibar
4. all the above
Show answer
Answer: D. all the above
Standard atmospheric pressure at sea level is approximately equivalent to: A) 76 cm of mercury (Hg). B) 29.9 inches of mercury (Hg). (Standard is approximation). C) 1013.2 millibars (Standard is imation). Since options A, B, and C are all valid ways to represent the standard atmospheric pressure at sea level, option D, "all the above," is the correct answer.
Match List I with List II and select the correct answer using the code given below the Lists : List I (Physical quantity) List II (Unit)
Asked in: UPSC NDA 1 2015
1. Distance 1. Mole
2. Amount of material 2. Coulomb
3. Amount of electrical charge 3. Light year
4. Energy 4. Watt hour A. 3 1 2 4 B. 3 2 1 4 C. 4 2 1 3 D. 4 1 2 3
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Answer: A. Distance 1. Mole
Matching common physical quantities with their standard or relevant units.
Which one of the following is not a natural unit of time ?
Asked in: UKPSC CS Prelims 2016
1. Tropical year
2. Lunar month
3. Standard time
4. Day
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Answer: C. Standard time
Natural units of time are based on naturally occurring astronomical cycles. Examples include the tropical year (Earth's orbit around the Sun, determining seasons), the lunar month (Moon's orbit around the Earth), and the day (Earth's rotation on its axis).
Powndal is a unit of
Asked in: WBCS Main Paper 4 2023
1. mass
2. weight
3. momentum
4. energy
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Answer: B. weight
A powndal is defined as the force required to accelerate a mass of one pound by one foot per second squared (1 pdl = 1 lb · ft/s²). Weight is a force exerted on a mass due to gravity (W = mass × acceleration due to gravity). Therefore, the powndal is a unit used to measure force, including weight.

Derived Units and their Expression

17. Miscellaneous

112

Dimensional

Analysis

(Dimensions,

Homogeneity, Applications)

Errors in Measurement (Types, Absolute, Relative, Percentage, Propagation)

Least Count of Measuring Instruments

Non-SI Units (e.g., Astronomical Unit, Light-Year, Electron-Volt)

Physical Quantities (Fundamental and Derived)

Prefixes for SI Units

SI Base Units and their Definitions

Significant Figures

Systems of Units (SI, CGS, MKS)

Unit Conversion Techniques

Units of Measurement (Definition and Characteristics)

2. Measuring Instruments and Scales

Practice MCQs: Measurement/Unit

Derived Units and their Expression

Dimensional Analysis (Dimensions, Homogeneity, Applications)

Errors in Measurement (Types, Absolute, Relative, Percentage, Propagation)

Least Count of Measuring Instruments

Non-SI Units (e.g., Astronomical Unit, Light-Year, Electron-Volt)

Physical Quantities (Fundamental and Derived)

Prefixes for SI Units

SI Base Units and their Definitions

Significant Figures

Systems of Units (SI, CGS, MKS)

Unit Conversion Techniques

Units of Measurement (Definition and Characteristics)

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