Major Competitive Exams

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Q. If the simple interest on a sum of money is $300 after 4 years at a rate of 5% per annum, what is the principal?

A. $1500
B. $1200
C. $1000
D. $900

Solution

Simple Interest = Principal × Rate × Time, so Principal = SI / (Rate × Time) = 300 / (0.05 × 4) = $1500.

Correct Answer: A — $1500

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Q. If the simple interest on a sum of money is $300 in 3 years at a rate of 4% per annum, what is the principal amount?

A. $2000
B. $2500
C. $3000
D. $3500

Solution

Simple Interest = P * r * t => 300 = P * 0.04 * 3 => P = 300 / (0.12) = 2500.

Correct Answer: A — $2000

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Q. If the slit width is equal to the wavelength of light used, what is the expected diffraction pattern?

A. No diffraction
B. Single maximum
C. Wide central maximum
D. Narrow central maximum

Solution

When the slit width is equal to the wavelength, a wide central maximum is observed due to significant diffraction.

Correct Answer: C — Wide central maximum

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Q. If the slit width is halved in a single-slit diffraction experiment, what happens to the width of the central maximum?

A. It doubles
B. It halves
C. It remains the same
D. It quadruples

Solution

If the slit width is halved, the width of the central maximum doubles, as it is inversely proportional to the slit width.

Correct Answer: A — It doubles

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Q. If the slit width is halved in a single-slit diffraction experiment, what happens to the angular width of the central maximum?

A. It doubles
B. It halves
C. It remains the same
D. It quadruples

Solution

Halving the slit width increases the angular width of the central maximum, making it double.

Correct Answer: A — It doubles

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Q. If the slope of a riverbed is 1:1000, what is the vertical drop over a distance of 2 km? (2000)

A. 2 m
B. 1 m
C. 3 m
D. 4 m

Solution

Vertical drop = Distance × Slope = 2000 m × (1/1000) = 2 m.

Correct Answer: A — 2 m

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Q. If the soil erosion rate in a river basin is 2 tons per hectare per year, how much soil will be eroded from a 50-hectare area in 5 years? (2023)

A. 500 tons
B. 1000 tons
C. 2000 tons
D. 2500 tons

Solution

Soil eroded = 2 tons/hectare/year × 50 hectares × 5 years = 500 tons.

Correct Answer: C — 2000 tons

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Q. If the soil erosion rate is 2 tons per hectare per year, how much soil will be eroded from 50 hectares in 5 years?

A. 500 tons
B. 1000 tons
C. 200 tons
D. 100 tons

Solution

Soil eroded = Erosion rate × Area × Time = 2 tons/hectare/year × 50 hectares × 5 years = 500 tons.

Correct Answer: B — 1000 tons

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Q. If the soil in a river delta is primarily clay, what is the expected drainage capacity compared to sandy soil? (2023)

A. Higher
B. Lower
C. Same
D. Depends on water content

Solution

Clay has lower drainage capacity compared to sandy soil.

Correct Answer: B — Lower

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Q. If the soil in a riverbank has a porosity of 30% and the volume of soil is 100 m³, what is the volume of water it can hold?

A. 30 m³
B. 20 m³
C. 10 m³
D. 40 m³

Solution

Volume of water = Porosity × Volume of soil = 0.3 × 100 m³ = 30 m³.

Correct Answer: A — 30 m³

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Q. If the soil moisture content is 25% and the dry weight of the soil is 200 kg, what is the weight of the water in the soil? (2020)

A. 50 kg
B. 25 kg
C. 75 kg
D. 100 kg

Solution

Weight of water = Moisture content × Dry weight = 0.25 × 200 kg = 50 kg.

Correct Answer: A — 50 kg

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Q. If the soil moisture content is 25% and the weight of the dry soil is 200 kg, what is the weight of the water in the soil? (2022)

A. 50 kg
B. 25 kg
C. 75 kg
D. 100 kg

Solution

Weight of water = Moisture content x Weight of dry soil = 0.25 x 200 kg = 50 kg.

Correct Answer: A — 50 kg

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Q. If the soil moisture content is 30% and the bulk density of the soil is 1.5 g/cm³, what is the water holding capacity of 1 m³ of soil?

A. 300 liters
B. 450 liters
C. 600 liters
D. 750 liters

Solution

Water holding capacity = Soil moisture content × Volume of soil = 0.30 × 1000 liters = 300 liters.

Correct Answer: A — 300 liters

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Q. If the solubility product (Ksp) of AgCl is 1.77 x 10^-10, what is the molar solubility of AgCl?

A. 1.77 x 10^-5 M
B. 1.77 x 10^-10 M
C. 1.77 x 10^-7 M
D. 1.77 x 10^-3 M

Solution

Ksp = [Ag+][Cl-] = s^2, thus s = sqrt(1.77 x 10^-10) = 1.77 x 10^-5 M.

Correct Answer: C — 1.77 x 10^-7 M

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Q. If the solution to the linear equation 4x + 5y = 20 is (2, 0), what is the value of y when x = 2?

A. 0
B. 4
C. 5
D. 2

Solution

Substituting x = 2 into the equation gives 4(2) + 5y = 20, leading to y = 0.

Correct Answer: A — 0

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Q. If the Speaker of the Lok Sabha is elected by a majority of 300 votes and there are 500 total votes, what is the minimum number of votes required to win?

A. 150
B. 200
C. 250
D. 300

Solution

Minimum votes required = (500/2) + 1 = 251.

Correct Answer: C — 250

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Q. If the Speaker of the Lok Sabha is elected by a majority of the members, and there are 545 members, how many votes are needed for a simple majority?

A. 273
B. 274
C. 275
D. 276

Solution

Simple majority = (545/2) + 1 = 273.

Correct Answer: A — 273

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Q. If the Speaker of the Lok Sabha is elected by the members of the Lok Sabha, and there are 545 members, how many votes are needed to secure a simple majority?

A. 273
B. 274
C. 275
D. 276

Solution

A simple majority requires more than half, so (545/2) + 1 = 274 votes are needed.

Correct Answer: B — 274

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Q. If the speed of a wave in a medium is 300 m/s and its wavelength is 3 m, what is the frequency of the wave?

A. 100 Hz
B. 150 Hz
C. 200 Hz
D. 300 Hz

Solution

Frequency f = v/λ = 300 m/s / 3 m = 100 Hz.

Correct Answer: B — 150 Hz

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Q. If the speed of an object in circular motion is doubled, what happens to the centripetal acceleration?

A. It remains the same
B. It doubles
C. It quadruples
D. It halves

Solution

Centripetal acceleration a_c = v²/r. If v is doubled, a_c increases by a factor of 4.

Correct Answer: C — It quadruples

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Q. If the speed of light in a vacuum is 3 x 10^8 m/s, what is its speed in water (n = 1.33)?

A. 2.26 x 10^8 m/s
B. 2.25 x 10^8 m/s
C. 2.27 x 10^8 m/s
D. 2.28 x 10^8 m/s

Solution

The speed of light in a medium is given by v = c/n. Thus, v = (3 x 10^8 m/s) / 1.33 ≈ 2.26 x 10^8 m/s.

Correct Answer: A — 2.26 x 10^8 m/s

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Q. If the speed of light in a vacuum is approximately 3 x 10^8 m/s, what is its value in km/s?

A. 300 km/s
B. 3000 km/s
C. 30000 km/s
D. 300000 km/s

Solution

To convert m/s to km/s, divide by 1000. Therefore, 3 x 10^8 m/s = 300000 km/s.

Correct Answer: D — 300000 km/s

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Q. If the speed of light in a vacuum is approximately 3 x 10^8 m/s, what is the wavelength of light with a frequency of 6 x 10^14 Hz?

A. 500 nm
B. 600 nm
C. 700 nm
D. 800 nm

Solution

Using the formula c = fλ, where c = 3 x 10^8 m/s and f = 6 x 10^14 Hz. Thus, λ = c/f = (3 x 10^8)/(6 x 10^14) = 500 nm.

Correct Answer: A — 500 nm

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Q. If the speed of light in vacuum is 3 x 10^8 m/s, what is its speed in a medium with refractive index 1.5?

A. 2 x 10^8 m/s
B. 2.5 x 10^8 m/s
C. 3 x 10^8 m/s
D. 1.5 x 10^8 m/s

Solution

The speed of light in a medium is given by v = c/n, where c is the speed of light in vacuum and n is the refractive index. Thus, v = 3 x 10^8 m/s / 1.5 = 2 x 10^8 m/s.

Correct Answer: A — 2 x 10^8 m/s

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Q. If the speed of light in vacuum is 3 x 10^8 m/s, what is its speed in a medium with a refractive index of 1.5?

A. 2 x 10^8 m/s
B. 2.5 x 10^8 m/s
C. 3 x 10^8 m/s
D. 1.5 x 10^8 m/s

Solution

Speed of light in a medium = speed of light in vacuum / refractive index = (3 x 10^8 m/s) / 1.5 = 2 x 10^8 m/s.

Correct Answer: A — 2 x 10^8 m/s

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Q. If the speed of light in vacuum is 3 x 10^8 m/s, what is its speed in glass (n = 1.5)?

A. 2 x 10^8 m/s
B. 2.5 x 10^8 m/s
C. 3 x 10^8 m/s
D. 1.5 x 10^8 m/s

Solution

The speed of light in a medium is given by v = c/n. Therefore, v = (3 x 10^8 m/s) / 1.5 = 2 x 10^8 m/s.

Correct Answer: A — 2 x 10^8 m/s

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Q. If the speed of light in vacuum is 3 x 10^8 m/s, what is the speed of light in a medium with a refractive index of 1.5?

A. 2 x 10^8 m/s
B. 2.5 x 10^8 m/s
C. 3 x 10^8 m/s
D. 1.5 x 10^8 m/s

Solution

Speed of light in medium = c/n = (3 x 10^8 m/s) / 1.5 = 2 x 10^8 m/s.

Correct Answer: A — 2 x 10^8 m/s

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Q. If the speed of light is 3 x 10^8 m/s, what is its value in km/s? (2021)

A. 3 x 10^5 km/s
B. 3 x 10^6 km/s
C. 3 x 10^7 km/s
D. 3 x 10^8 km/s

Solution

To convert m/s to km/s, divide by 1000. Therefore, 3 x 10^8 m/s = 3 x 10^5 km/s.

Correct Answer: A — 3 x 10^5 km/s

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Q. If the speed of sound in air is 340 m/s, how long does it take for sound to travel 1 km?

A. 2.94 s
B. 3.5 s
C. 4.5 s
D. 5.5 s

Solution

Time = distance/speed = 1000 m / 340 m/s ≈ 2.94 s.

Correct Answer: A — 2.94 s

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Q. If the standard deviation of a data set is 0, what can be said about the data?

A. All values are different
B. All values are the same
C. Values are in a range
D. Data is not valid

Solution

A standard deviation of 0 indicates that all values in the data set are the same.

Correct Answer: B — All values are the same

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Major Competitive Exams

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