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Question 1 of 5
1. Question
With reference to the above passage, the following assumptions have been made:
I. The quest for convenience in digital life often undermines individual autonomy and freedom.
II. People tend to undervalue privacy when it is traded for comfort or speed.
III. Technological advancement automatically ensures the protection of user data and autonomy.Which of the above assumptions is/are valid?
Correct
Answer: (b)
Explanation:
Assumption I is valid: The passage argues that convenience leads individuals to “trade privacy for efficiency,” resulting in a loss of autonomy and potential manipulation — a clear undermining of freedom.
Assumption II is valid: The author emphasizes that individuals make this trade-off “without realizing the cost,” suggesting they undervalue privacy in pursuit of comfort.
Assumption III is invalid: The passage portrays technology as capable of both innovation and surveillance, implying that advancement alone cannot safeguard privacy.
Hence, only I and II are valid, making (b) the correct answer.Incorrect
Answer: (b)
Explanation:
Assumption I is valid: The passage argues that convenience leads individuals to “trade privacy for efficiency,” resulting in a loss of autonomy and potential manipulation — a clear undermining of freedom.
Assumption II is valid: The author emphasizes that individuals make this trade-off “without realizing the cost,” suggesting they undervalue privacy in pursuit of comfort.
Assumption III is invalid: The passage portrays technology as capable of both innovation and surveillance, implying that advancement alone cannot safeguard privacy.
Hence, only I and II are valid, making (b) the correct answer. -
Question 2 of 5
2. Question
Two runners, P and Q, are running on a circular track in the same direction with uniform speeds. At the start, Q is ahead of P and their positions subtend an angle of 45° at the centre of the circle. When P reaches the point diametrically opposite to his starting point, he meets Q. What is the ratio of the speeds of P and Q?
Correct
Answer: B
Solution:
Given that P and Q are on a circular track and Q is ahead of P by 45°.
When P reaches the diametrically opposite point, P has covered half the circumference = πr.
In the same time, Q has also been running. Initially Q was ahead by 45°, i.e. arc length = 2πr × 45/360 = πr/4.
Since they meet when P has covered πr, Q must have covered πr − (πr/4) = (3πr/4).
So,
Distance covered by P : Distance covered by Q
= πr : 3πr/4
= 1 : 3/4
= 4 : 3So, the ratio of speeds of P and Q = 4 : 3
Hence, option (b) is correct.
Incorrect
Answer: B
Solution:
Given that P and Q are on a circular track and Q is ahead of P by 45°.
When P reaches the diametrically opposite point, P has covered half the circumference = πr.
In the same time, Q has also been running. Initially Q was ahead by 45°, i.e. arc length = 2πr × 45/360 = πr/4.
Since they meet when P has covered πr, Q must have covered πr − (πr/4) = (3πr/4).
So,
Distance covered by P : Distance covered by Q
= πr : 3πr/4
= 1 : 3/4
= 4 : 3So, the ratio of speeds of P and Q = 4 : 3
Hence, option (b) is correct.
-
Question 3 of 5
3. Question
A man started from his home at 14:30 hours and drove to a village. When he reached there, the village clock showed 15:15 hours. He stayed in the village for 25 minutes and then drove back home by a different route which was 1.25 times longer than the onward route. While returning, he drove at twice his onward speed and reached home at 16:00 hours (by his home clock). As compared to the clock at home, the village clock is
Correct
Answer: D
Solution:
Given:
Start from home = 14:30
Reached home again = 16:00
So total time (home clock) = 1 hour 30 minutes = 90 minutes.He stayed in the village for 25 minutes.
So total travelling time = 90 − 25 = 65 minutes.Let time taken from home to village = t minutes.
Then time taken from village to home = 65 − t minutes.Let the onward distance be D and onward speed be S.
Then onward time t = D/S.Return distance = 1.25D
Return speed = 2S
So return time = (1.25D)/(2S) = 0.625 × (D/S) = 0.625tSo,
t + 0.625t = 65
1.625t = 65
t = 65 / 1.625
t = 40 minutesSo, actual time taken from home to village = 40 minutes.
He started at 14:30, so actual arrival time = 14:30 + 40 minutes = 15:10.
But the village clock showed 15:15.
So the village clock was 5 minutes ahead of the correct time.
Hence, the village clock is 5 minutes fast.
Therefore, option (d) is correct.
Incorrect
Answer: D
Solution:
Given:
Start from home = 14:30
Reached home again = 16:00
So total time (home clock) = 1 hour 30 minutes = 90 minutes.He stayed in the village for 25 minutes.
So total travelling time = 90 − 25 = 65 minutes.Let time taken from home to village = t minutes.
Then time taken from village to home = 65 − t minutes.Let the onward distance be D and onward speed be S.
Then onward time t = D/S.Return distance = 1.25D
Return speed = 2S
So return time = (1.25D)/(2S) = 0.625 × (D/S) = 0.625tSo,
t + 0.625t = 65
1.625t = 65
t = 65 / 1.625
t = 40 minutesSo, actual time taken from home to village = 40 minutes.
He started at 14:30, so actual arrival time = 14:30 + 40 minutes = 15:10.
But the village clock showed 15:15.
So the village clock was 5 minutes ahead of the correct time.
Hence, the village clock is 5 minutes fast.
Therefore, option (d) is correct.
-
Question 4 of 5
4. Question
A car travels 45 km at a certain speed and then travels 40 km at a speed 3 km/h more than the original speed. If the total time taken for the journey is 3 hours, what is the original speed of the car?
Correct
Answer: B
Solution:
Let the original speed be x km/h.
Time for first 45 km = 45/x
Time for next 40 km = 40/(x + 3)
According to the question,
45/x + 40/(x + 3) = 3 ……(i)Take LCM x(x + 3):
45(x + 3) + 40x = 3x(x + 3)45x + 135 + 40x = 3x² + 9x
85x + 135 = 3x² + 9x
Bring all terms to one side:
3x² + 9x − 85x − 135 = 0
3x² − 76x − 135 = 0Factorising:
( x − 27 )( 3x + 5 ) = 0So x = 27 or x = −5/3 (not possible)
Therefore, x = 27 km/h
Hence, option (b) is correct.
Incorrect
Answer: B
Solution:
Let the original speed be x km/h.
Time for first 45 km = 45/x
Time for next 40 km = 40/(x + 3)
According to the question,
45/x + 40/(x + 3) = 3 ……(i)Take LCM x(x + 3):
45(x + 3) + 40x = 3x(x + 3)45x + 135 + 40x = 3x² + 9x
85x + 135 = 3x² + 9x
Bring all terms to one side:
3x² + 9x − 85x − 135 = 0
3x² − 76x − 135 = 0Factorising:
( x − 27 )( 3x + 5 ) = 0So x = 27 or x = −5/3 (not possible)
Therefore, x = 27 km/h
Hence, option (b) is correct.
-
Question 5 of 5
5. Question
A train 180 m long passes a pole in 15 seconds. How long will it take to pass a platform 420 m long?
Correct
Answer: C
Solution:
Length of train = 180 m
Time to pass pole = 15 s
So, speed of train = Distance/Time = 180/15 = 12 m/s
Length of platform = 420 m
Total distance to pass platform = 180 + 420 = 600 m
Time = Distance/Speed = 600/12 = 50 seconds
Hence, option (c) is correct.Incorrect
Answer: C
Solution:
Length of train = 180 m
Time to pass pole = 15 s
So, speed of train = Distance/Time = 180/15 = 12 m/s
Length of platform = 420 m
Total distance to pass platform = 180 + 420 = 600 m
Time = Distance/Speed = 600/12 = 50 seconds
Hence, option (c) is correct.
