Q. The soil of a riverbank is composed of 60% sand, 30% silt, and 10% clay. What is the percentage of silt in the soil? (2019)
A.
30%
B.
40%
C.
50%
D.
60%
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Solution
The percentage of silt in the soil is given as 30%.
Correct Answer:
A
— 30%
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Q. The song was sung by the choir. What is the active voice of this sentence? (2023)
A.
The choir sings the song.
B.
The choir is singing the song.
C.
The choir sang the song.
D.
The song is sung by the choir.
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Solution
The active voice focuses on the doer of the action. Here, 'the choir' is the doer, so it becomes 'The choir sang the song.'
Correct Answer:
C
— The choir sang the song.
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Q. The Speaker of the Lok Sabha is elected by?
A.
Members of the Lok Sabha
B.
Members of the Rajya Sabha
C.
President
D.
Prime Minister
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Solution
The Speaker of the Lok Sabha is elected by the members of the Lok Sabha.
Correct Answer:
A
— Members of the Lok Sabha
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Q. The speaker's eloquent delivery and profound insights captivated the audience, leaving them with a sense of _____ about the future of technology and its impact on society.
A.
dread
B.
optimism
C.
indifference
D.
confusion
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Solution
The word 'optimism' suggests a positive outlook, which aligns with the context of a captivating speech.
Correct Answer:
B
— optimism
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Q. The speaker's tone during the presentation was __________, which helped to engage the audience effectively.
A.
monotonous and dull.
B.
enthusiastic and dynamic.
C.
disinterested and aloof.
D.
confused and uncertain.
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Solution
An engaging presentation typically requires an enthusiastic and dynamic tone, making option 1 the best fit.
Correct Answer:
B
— enthusiastic and dynamic.
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Q. The speaker's tone was ______, as he recounted the events with a mix of humor and sadness, capturing the audience's attention.
A.
monotonous
B.
melancholic
C.
jubilant
D.
bittersweet
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Solution
The combination of humor and sadness suggests a 'bittersweet' tone.
Correct Answer:
D
— bittersweet
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Q. The speaker's tone was __________, suggesting a deep-seated frustration with the current political climate.
A.
optimistic
B.
sarcastic
C.
neutral
D.
enthusiastic
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Solution
Frustration typically aligns with sarcasm, making 'sarcastic' the most fitting option.
Correct Answer:
B
— sarcastic
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Q. The speaker's __________ tone captivated the audience, making them more receptive to the message being conveyed.
A.
monotonous
B.
enthusiastic
C.
dull
D.
dispassionate
Show solution
Solution
The word 'enthusiastic' describes a lively and engaging tone, which would indeed captivate an audience.
Correct Answer:
B
— enthusiastic
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Q. The specific heat capacity of a substance is defined as the amount of heat required to raise the temperature of: (2023)
A.
1 kg of the substance by 1°C
B.
1 g of the substance by 1°C
C.
1 L of the substance by 1°C
D.
1 mole of the substance by 1°C
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Solution
The specific heat capacity is defined as the amount of heat required to raise the temperature of 1 kg of the substance by 1°C.
Correct Answer:
A
— 1 kg of the substance by 1°C
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Q. The specific heat capacity of a substance is defined as: (2023)
A.
The amount of heat required to raise the temperature by 1 degree Celsius
B.
The amount of heat required to change the phase of a substance
C.
The heat required to raise the temperature of 1 kg of the substance by 1 degree Celsius
D.
The heat required to raise the temperature of 1 mole of the substance by 1 degree Celsius
Show solution
Solution
The specific heat capacity is defined as the amount of heat required to raise the temperature of 1 kg of the substance by 1 degree Celsius.
Correct Answer:
C
— The heat required to raise the temperature of 1 kg of the substance by 1 degree Celsius
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Q. The standard deviation of a data set is 5. If all values are increased by 2, what will be the new standard deviation? (2020)
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Solution
Standard deviation is unaffected by adding a constant. Therefore, new SD = 5.
Correct Answer:
B
— 5
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Q. The standard deviation of a data set is 5. What is the variance? (2023)
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Solution
Variance is the square of the standard deviation. Therefore, variance = 5² = 25.
Correct Answer:
B
— 25
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Q. The Stefan-Boltzmann Law relates to which mode of heat transfer?
A.
Conduction
B.
Convection
C.
Radiation
D.
Insulation
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Solution
The Stefan-Boltzmann Law relates to radiation, stating that the total energy radiated per unit surface area is proportional to the fourth power of the black body's temperature.
Correct Answer:
C
— Radiation
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Q. The study concluded that regular exercise not only improves physical health but also __________.
A.
increases the risk of injury.
B.
has a positive impact on mental well-being.
C.
requires a strict diet.
D.
is time-consuming and expensive.
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Solution
The context suggests a holistic benefit of exercise, making option 1 the most logical completion.
Correct Answer:
B
— has a positive impact on mental well-being.
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Q. The study concluded that students who engage in regular physical activity tend to perform better academically, indicating that __________.
A.
exercise has no impact on cognitive function.
B.
there is a correlation between physical health and academic success.
C.
academic performance is solely determined by intelligence.
D.
only elite athletes excel in academics.
Show solution
Solution
The conclusion drawn from the study suggests a positive relationship between physical activity and academic performance, supporting option 1.
Correct Answer:
B
— there is a correlation between physical health and academic success.
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Q. The sudden change in policy was met with ______ from the employees, who felt blindsided by the decision.
A.
apathy
B.
enthusiasm
C.
resistance
D.
acceptance
Show solution
Solution
The word 'resistance' indicates that the employees opposed the change, which fits the context of feeling blindsided.
Correct Answer:
C
— resistance
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Q. The sudden increase in prices was attributed to ______ factors that had not been anticipated by economists.
A.
predictable
B.
unforeseen
C.
stable
D.
consistent
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Solution
The word 'unforeseen' suggests that the factors were unexpected, which aligns with the context of the price increase.
Correct Answer:
B
— unforeseen
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Q. The sudden increase in technology use during the pandemic has led to a __________ in the way we perceive work-life balance. (2023)
A.
regression
B.
transformation
C.
stagnation
D.
disruption
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Solution
An increase in technology use typically transforms perceptions rather than regresses or stagnates them.
Correct Answer:
B
— transformation
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Q. The sum of the angles in a triangle is equal to how many degrees? (2021)
A.
90
B.
180
C.
270
D.
360
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Solution
The sum of the angles in any triangle is always 180 degrees.
Correct Answer:
B
— 180
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Q. The sum of the first n natural numbers is given by which formula?
A.
n(n+1)/2
B.
n^2
C.
n(n-1)/2
D.
n(n+1)/3
Show solution
Solution
The sum of the first n natural numbers is given by the formula n(n+1)/2.
Correct Answer:
A
— n(n+1)/2
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Q. The sum of the first n terms of a harmonic progression is given by which of the following formulas?
A.
n/(a+b)
B.
2n/(a+b)
C.
n/(ab)
D.
2n/(ab)
Show solution
Solution
The sum of the first n terms of a harmonic progression can be expressed as 2n/(a+b) where a and b are the first two terms.
Correct Answer:
B
— 2n/(a+b)
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Q. The sum of the first n terms of an arithmetic series is given by S_n = 3n^2 + 2n. What is the 10th term?
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Solution
The nth term a_n = S_n - S_(n-1) = (3n^2 + 2n) - (3(n-1)^2 + 2(n-1)). For n=10, a_10 = 32.
Correct Answer:
C
— 36
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Q. The sum of the roots of the equation 2x^2 - 3x + 1 = 0 is equal to what?
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Solution
Using Vieta's formulas, the sum of the roots is -(-3)/2 = 3/2.
Correct Answer:
B
— 3/2
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Q. The sum of the roots of the equation 2x^2 - 4x + k = 0 is 3. What is the value of k?
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Solution
The sum of the roots is given by -b/a = 4/2 = 2. Setting this equal to 3 gives k = 1.
Correct Answer:
A
— 1
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Q. The sum of the roots of the equation 3x^2 - 12x + 9 = 0 is:
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Solution
The sum of the roots is given by -b/a = 12/3 = 4.
Correct Answer:
C
— 4
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Q. The sum of the roots of the equation x^2 - 7x + 10 = 0 is?
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Solution
The sum of the roots is given by -b/a = 7/1 = 7.
Correct Answer:
C
— 7
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Q. The sum of the roots of the equation x^2 - 7x + k = 0 is 7. What is the value of k if the product of the roots is 10? (2023)
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Solution
Using Vieta's formulas, the sum of the roots is 7 and the product is k = 10.
Correct Answer:
A
— 10
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Q. The sum of the roots of the quadratic equation 2x^2 - 4x + k = 0 is 3. What is the value of k?
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Solution
Using the sum of roots formula -b/a, we have 4/2 = 2, thus 2 + 1 = 3, so k = 1.
Correct Answer:
B
— 2
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Q. The sum of the roots of the quadratic equation 2x^2 - 8x + 6 = 0 is equal to what? (2020)
Show solution
Solution
The sum of the roots is given by -b/a = 8/2 = 4.
Correct Answer:
B
— 4
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Q. The sum of the roots of the quadratic equation 3x^2 + 12x + 12 = 0 is equal to what? (2022)
Show solution
Solution
Using Vieta's formulas, the sum of the roots is -b/a = -12/3 = -4.
Correct Answer:
A
— -4
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