Q. What is the absolute error if the true value is 50 and the measured value is 48? (2022)
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Solution
Absolute error is calculated as the absolute difference between the true value and the measured value, which is |50 - 48| = 2.
Correct Answer:
A
— 2
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Q. What is the absolute error in a measurement of 50.0 cm if the true value is 48.0 cm? (2022)
A.
2.0 cm
B.
1.0 cm
C.
3.0 cm
D.
4.0 cm
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Solution
Absolute error = |Measured value - True value| = |50.0 cm - 48.0 cm| = 2.0 cm.
Correct Answer:
A
— 2.0 cm
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Q. What is the absolute error in a measurement of 50.0 cm if the true value is 52.0 cm? (2022)
A.
2.0 cm
B.
1.0 cm
C.
0.5 cm
D.
3.0 cm
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Solution
Absolute error = |Measured value - True value| = |50.0 cm - 52.0 cm| = 2.0 cm.
Correct Answer:
A
— 2.0 cm
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Q. What is the absolute error in a measurement? (2021)
A.
The difference between the measured value and the true value
B.
The average of all measurements
C.
The maximum value in a set of measurements
D.
The minimum value in a set of measurements
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Solution
Absolute error is defined as the difference between the measured value and the true value.
Correct Answer:
A
— The difference between the measured value and the true value
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Q. What is the absolute value of -12? (2023)
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Solution
The absolute value of -12 is 12.
Correct Answer:
C
— 12
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Q. What is the absolute value of -7? (2023)
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Solution
The absolute value of -7 is 7.
Correct Answer:
C
— 7
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Q. What is the acceleration due to gravity at a height equal to the radius of the Earth?
A.
g/2
B.
g/3
C.
g/4
D.
g/5
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Solution
At height equal to radius, g' = g / (1 + h/R)² = g / (2)² = g/4.
Correct Answer:
C
— g/4
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Q. What is the acceleration due to gravity at the surface of the Earth? (2022)
A.
9.81 m/s²
B.
10 m/s²
C.
9.8 m/s²
D.
8.9 m/s²
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Solution
The standard acceleration due to gravity at the surface of the Earth is approximately 9.81 m/s².
Correct Answer:
A
— 9.81 m/s²
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Q. What is the acceleration due to gravity on Earth? (2022)
A.
9.8 m/s²
B.
10 m/s²
C.
9.81 m/s²
D.
8.9 m/s²
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Solution
The standard acceleration due to gravity on Earth is approximately 9.8 m/s².
Correct Answer:
A
— 9.8 m/s²
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Q. What is the acceleration due to gravity on the surface of the Earth? (2018)
A.
9.8 m/s²
B.
10 m/s²
C.
9.81 m/s²
D.
8.9 m/s²
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Solution
The standard acceleration due to gravity on the surface of the Earth is approximately 9.81 m/s².
Correct Answer:
C
— 9.81 m/s²
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Q. What is the acceleration of a rolling object down an incline if the incline angle is θ?
A.
g sin(θ)
B.
g sin(θ)/2
C.
g sin(θ)/3
D.
g sin(θ)/4
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Solution
The acceleration of a rolling object down an incline is given by g sin(θ)/2, considering both translational and rotational motion.
Correct Answer:
B
— g sin(θ)/2
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Q. What is the adverb in the sentence: He quickly finished his homework. (2023)
A.
He
B.
quickly
C.
finished
D.
homework
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Solution
'Quickly' is the adverb that describes how he finished his homework.
Correct Answer:
B
— quickly
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Q. What is the aim of the Pradhan Mantri Ujjwala Yojana? (2016)
A.
To provide free education
B.
To provide clean cooking fuel
C.
To promote digital literacy
D.
To enhance agricultural productivity
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Solution
The Pradhan Mantri Ujjwala Yojana aims to provide clean cooking fuel to women from below poverty line households.
Correct Answer:
B
— To provide clean cooking fuel
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Q. What is the angle between a tangent to a circle and a chord drawn to the point of contact?
A.
0 degrees
B.
45 degrees
C.
90 degrees
D.
The angle is equal to the angle in the alternate segment
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Solution
The angle between a tangent and a chord through the point of contact is equal to the angle in the alternate segment.
Correct Answer:
D
— The angle is equal to the angle in the alternate segment
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Q. What is the angle between a tangent to a circle and a radius drawn to the point of tangency?
A.
0 degrees
B.
45 degrees
C.
90 degrees
D.
180 degrees
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Solution
The angle between a tangent and a radius at the point of tangency is always 90 degrees.
Correct Answer:
C
— 90 degrees
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Q. What is the angle between Magnetic North and True North called? (2023)
A.
Declination
B.
Inclination
C.
Azimuth
D.
Elevation
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Solution
The angle between Magnetic North and True North is known as Declination.
Correct Answer:
A
— Declination
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Q. What is the angle between the lines 2x + 3y - 6 = 0 and 4x - y + 1 = 0?
A.
45 degrees
B.
60 degrees
C.
90 degrees
D.
30 degrees
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Solution
The slopes of the lines are -2/3 and 4. The angle θ can be found using tan(θ) = |(m1 - m2) / (1 + m1*m2)|.
Correct Answer:
C
— 90 degrees
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Q. What is the angle between the lines 2x + 3y = 6 and 4x - y = 5?
A.
45 degrees
B.
60 degrees
C.
90 degrees
D.
30 degrees
Show solution
Solution
The slopes of the lines are -2/3 and 4. The angle θ can be found using tan(θ) = |(m1 - m2) / (1 + m1*m2)|.
Correct Answer:
B
— 60 degrees
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Q. What is the angle between the lines represented by the equation 2x^2 + 3xy - 2y^2 = 0?
A.
45 degrees
B.
60 degrees
C.
90 degrees
D.
30 degrees
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Solution
Using the formula for the angle between two lines, we find that the angle is 90 degrees.
Correct Answer:
C
— 90 degrees
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Q. What is the angle between the lines represented by the equation x^2 - 2xy + y^2 = 0?
A.
0 degrees
B.
45 degrees
C.
90 degrees
D.
135 degrees
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Solution
The angle can be calculated using the slopes derived from the equation, leading to 90 degrees.
Correct Answer:
C
— 90 degrees
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Q. What is the angle between the lines represented by the equation x^2 - 6x + y^2 - 8y + 9 = 0?
A.
0 degrees
B.
45 degrees
C.
90 degrees
D.
135 degrees
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Solution
By completing the square, we can find the slopes of the lines and calculate the angle between them.
Correct Answer:
C
— 90 degrees
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Q. What is the angle between the lines represented by the equations y = 2x + 1 and y = -1/2x + 3? (2021)
A.
90 degrees
B.
45 degrees
C.
60 degrees
D.
30 degrees
Show solution
Solution
The slopes are m1 = 2 and m2 = -1/2. The angle θ between the lines is given by tan(θ) = |(m1 - m2) / (1 + m1*m2)|, which results in 90 degrees.
Correct Answer:
A
— 90 degrees
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Q. What is the angle between the lines y = 2x + 1 and y = -0.5x + 3?
A.
90 degrees
B.
60 degrees
C.
45 degrees
D.
30 degrees
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Solution
The slopes are m1 = 2 and m2 = -0.5. The angle θ is given by tan(θ) = |(m1 - m2) / (1 + m1*m2)| = |(2 + 0.5) / (1 - 1)|, which is undefined, indicating 90 degrees.
Correct Answer:
A
— 90 degrees
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Q. What is the angle between the lines y = 2x + 1 and y = -1/2x + 3?
A.
90 degrees
B.
60 degrees
C.
45 degrees
D.
30 degrees
Show solution
Solution
The slopes are m1 = 2 and m2 = -1/2. The angle θ = tan^(-1) |(m1 - m2) / (1 + m1*m2)| = tan^(-1)(5/4) which is approximately 60 degrees.
Correct Answer:
B
— 60 degrees
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Q. What is the angle between the lines y = 2x + 3 and y = -1/2x + 1?
A.
90 degrees
B.
45 degrees
C.
60 degrees
D.
30 degrees
Show solution
Solution
The slopes are m1 = 2 and m2 = -1/2. The angle θ = tan^(-1) |(m1 - m2) / (1 + m1*m2)| = tan^(-1)(5/0) = 90 degrees.
Correct Answer:
A
— 90 degrees
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Q. What is the angle between the lines y = 3x + 2 and y = -1/3x + 1? (2021)
A.
90 degrees
B.
45 degrees
C.
60 degrees
D.
30 degrees
Show solution
Solution
The slopes are m1 = 3 and m2 = -1/3. The angle θ = tan⁻¹(|(m1 - m2) / (1 + m1*m2)|) = tan⁻¹(10/8) = 90 degrees.
Correct Answer:
A
— 90 degrees
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Q. What is the angle between the vectors (1, 0) and (0, 1)?
A.
0 degrees
B.
90 degrees
C.
45 degrees
D.
180 degrees
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Solution
The angle between (1, 0) and (0, 1) is 90 degrees.
Correct Answer:
B
— 90 degrees
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Q. What is the angle between the vectors (1, 2, 2) and (2, 1, 2)?
A.
90 degrees
B.
60 degrees
C.
45 degrees
D.
30 degrees
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Solution
Cosine of angle θ = (u · v) / (|u| |v|). Calculate to find θ = 60 degrees.
Correct Answer:
B
— 60 degrees
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Q. What is the angle between the vectors a = (1, 2, 2) and b = (2, 0, 2)?
A.
0 degrees
B.
45 degrees
C.
90 degrees
D.
60 degrees
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Solution
cos(θ) = (a · b) / (|a| |b|). Calculate a · b = 1*2 + 2*0 + 2*2 = 6, |a| = √(1^2 + 2^2 + 2^2) = 3, |b| = √(2^2 + 0^2 + 2^2) = 2√2. Thus, cos(θ) = 6 / (3 * 2√2) = 1/√2, θ = 45 degrees.
Correct Answer:
D
— 60 degrees
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Q. What is the angle between the vectors A = 2i + 2j and B = 2i - 2j?
A.
0 degrees
B.
45 degrees
C.
90 degrees
D.
180 degrees
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Solution
cos(θ) = (A · B) / (|A||B|) = (8) / (√8 * √8) = 1, θ = 0 degrees.
Correct Answer:
C
— 90 degrees
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