MHT-CET
Q. A ball is thrown horizontally from a height of 20 m. How long does it take to hit the ground? (2019)
A.
1 s
B.
2 s
C.
3 s
D.
4 s
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Solution
Using the equation of motion for free fall: h = (1/2)gt². 20 m = (1/2)(9.8)t². Solving gives t ≈ 2 s.
Correct Answer: B — 2 s
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Q. A ball is thrown upwards with a speed of 20 m/s. How long will it take to reach the maximum height? (Take g = 10 m/s²) (2023)
A.
1 s
B.
2 s
C.
3 s
D.
4 s
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Solution
Time to reach maximum height = initial velocity / g = 20 / 10 = 2 s.
Correct Answer: B — 2 s
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Q. A ball is thrown upwards with a velocity of 20 m/s. How high will it go before coming to rest? (2023)
A.
10 m
B.
20 m
C.
30 m
D.
40 m
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Solution
Using the formula h = v²/(2g), where g = 10 m/s², h = (20 m/s)² / (2 * 10 m/s²) = 20 m.
Correct Answer: C — 30 m
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Q. A ball is thrown vertically upwards with a speed of 15 m/s. How high will it rise before coming to a stop? (2023)
A.
11.25 m
B.
15 m
C.
22.5 m
D.
30 m
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Solution
Using the formula: height = (initial velocity^2) / (2 * g), where g = 9.8 m/s². Height = (15^2) / (2 * 9.8) = 11.25 m.
Correct Answer: A — 11.25 m
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Q. A ball is thrown vertically upwards with a speed of 20 m/s. How high will it go? (g = 10 m/s²) (2023)
A.
10 m
B.
20 m
C.
30 m
D.
40 m
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Solution
Using the formula h = v²/(2g), we have h = (20 m/s)² / (2 * 10 m/s²) = 20 m.
Correct Answer: B — 20 m
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Q. A beam of light passes through a narrow slit and produces a diffraction pattern. What happens to the width of the central maximum if the slit width is decreased? (2019)
A.
It increases
B.
It decreases
C.
It remains the same
D.
It becomes zero
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Solution
According to the diffraction principle, as the slit width decreases, the width of the central maximum increases.
Correct Answer: A — It increases
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Q. A block of mass 2 kg is placed on a frictionless surface and is pushed with a force of 10 N. What is its acceleration?
A.
2 m/s²
B.
5 m/s²
C.
10 m/s²
D.
20 m/s²
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Solution
Using Newton's second law, F = ma. Here, F = 10 N and m = 2 kg. Therefore, a = F/m = 10/2 = 5 m/s².
Correct Answer: B — 5 m/s²
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Q. A block of mass 2 kg is sliding down a frictionless incline of height 5 m. What is its speed at the bottom?
A.
5 m/s
B.
10 m/s
C.
15 m/s
D.
20 m/s
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Solution
Using conservation of energy, potential energy at the top (mgh) converts to kinetic energy at the bottom (1/2 mv²). Thus, v = sqrt(2gh) = sqrt(2 * 9.8 * 5) ≈ 10 m/s.
Correct Answer: B — 10 m/s
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Q. A block of mass 2 kg is sliding down a frictionless incline of height 5 m. What is its speed at the bottom of the incline?
A.
10 m/s
B.
5 m/s
C.
20 m/s
D.
15 m/s
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Solution
Using conservation of energy, potential energy at the top = kinetic energy at the bottom. mgh = 0.5mv². Thus, v = sqrt(2gh) = sqrt(2 * 9.81 * 5) = 10 m/s.
Correct Answer: A — 10 m/s
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Q. A block of mass 5 kg is pulled on a horizontal surface with a force of 20 N. If the frictional force is 5 N, what is the acceleration of the block? (2020)
A.
2 m/s²
B.
3 m/s²
C.
4 m/s²
D.
5 m/s²
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Solution
Net force = Applied force - Frictional force = 20 N - 5 N = 15 N. Using F = ma, a = F/m = 15 N / 5 kg = 3 m/s².
Correct Answer: B — 3 m/s²
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Q. A block of mass 5 kg is resting on a frictionless surface. A force of 10 N is applied to it. What will be its acceleration? (2020)
A.
2 m/s²
B.
5 m/s²
C.
10 m/s²
D.
20 m/s²
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Solution
Using Newton's second law, F = ma, acceleration (a) = F/m = 10 N / 5 kg = 2 m/s².
Correct Answer: B — 5 m/s²
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Q. A box contains 4 white and 6 black balls. What is the probability of drawing a black ball? (2023)
A.
2/5
B.
3/5
C.
4/5
D.
1/5
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Solution
Total balls = 4 + 6 = 10. Probability of black ball = 6/10 = 3/5.
Correct Answer: B — 3/5
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Q. A box contains 4 white and 6 black balls. What is the probability of picking a black ball?
A.
2/5
B.
3/5
C.
4/5
D.
1/5
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Solution
Total balls = 4 + 6 = 10. Probability of black ball = 6/10 = 3/5.
Correct Answer: B — 3/5
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Q. A box contains 5 white and 3 black balls. What is the probability of drawing a black ball?
A.
3/8
B.
5/8
C.
1/2
D.
1/3
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Solution
Total balls = 5 + 3 = 8. Probability of black ball = 3/8.
Correct Answer: A — 3/8
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Q. A box contains 5 white and 3 black balls. What is the probability of picking a black ball? (2021)
A.
3/8
B.
5/8
C.
1/2
D.
1/3
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Solution
Total balls = 5 + 3 = 8. Probability of black ball = 3/8.
Correct Answer: A — 3/8
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Q. A car accelerates from rest at a constant rate of 2 m/s². How far does it travel in 5 seconds? (2021)
A.
10 m
B.
20 m
C.
25 m
D.
50 m
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Solution
Using the equation of motion: s = ut + (1/2)at². Here, u = 0, a = 2 m/s², t = 5 s. So, s = 0 + (1/2)(2)(5²) = 25 m.
Correct Answer: C — 25 m
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Q. A car accelerates from rest at a rate of 2 m/s². What is its speed after 5 seconds? (2023)
A.
5 m/s
B.
10 m/s
C.
15 m/s
D.
20 m/s
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Solution
Using the formula v = u + at, where u = 0, a = 2 m/s², and t = 5 s, we get v = 0 + 2 * 5 = 10 m/s.
Correct Answer: B — 10 m/s
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Q. A car accelerates from rest to a speed of 20 m/s in 5 seconds. What is its acceleration?
A.
2 m/s²
B.
4 m/s²
C.
5 m/s²
D.
10 m/s²
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Solution
Acceleration is calculated using the formula a = (final velocity - initial velocity) / time. Here, a = (20 m/s - 0 m/s) / 5 s = 4 m/s².
Correct Answer: B — 4 m/s²
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Q. A car accelerates from rest to a speed of 30 m/s in 10 seconds. What is the acceleration of the car? (2022)
A.
3 m/s²
B.
2 m/s²
C.
1 m/s²
D.
4 m/s²
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Solution
Acceleration (a) = (final velocity - initial velocity) / time = (30 m/s - 0) / 10 s = 3 m/s².
Correct Answer: A — 3 m/s²
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Q. A car moving at 30 m/s applies brakes and comes to a stop in 6 seconds. What is the distance covered during braking? (2023)
A.
90 m
B.
120 m
C.
150 m
D.
180 m
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Solution
Using the formula: distance = initial velocity * time + 0.5 * acceleration * time^2. Here, acceleration = (0 - 30) / 6 = -5 m/s². Distance = 30 * 6 + 0.5 * (-5) * 6^2 = 180 - 90 = 90 m.
Correct Answer: B — 120 m
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Q. A car of mass 1000 kg accelerates from rest to a speed of 20 m/s. What is the kinetic energy gained?
A.
200,000 J
B.
100,000 J
C.
50,000 J
D.
20,000 J
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Solution
Kinetic Energy = 0.5 * m * v² = 0.5 * 1000 kg * (20 m/s)² = 200,000 J.
Correct Answer: B — 100,000 J
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Q. A card is drawn from a standard deck of 52 cards. What is the probability of drawing a heart?
A.
1/4
B.
1/13
C.
1/2
D.
1/52
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Solution
Number of hearts = 13. Probability = 13/52 = 1/4.
Correct Answer: A — 1/4
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Q. A charge of +4 µC is placed in a uniform electric field of strength 500 N/C. What is the work done in moving the charge 0.2 m in the direction of the field?
A.
400 J
B.
200 J
C.
100 J
D.
50 J
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Solution
W = F * d = (E * q) * d = (500 N/C * 4 × 10^-6 C) * 0.2 m = 0.4 J.
Correct Answer: B — 200 J
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Q. A charged particle moves in a magnetic field. What is the path of the particle if it enters the field perpendicularly? (2023)
A.
Straight line
B.
Circular path
C.
Elliptical path
D.
Parabolic path
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Solution
A charged particle moving perpendicularly to a magnetic field experiences a magnetic force that acts as a centripetal force, causing it to move in a circular path.
Correct Answer: B — Circular path
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Q. A charged particle moves in a magnetic field. What is the path of the particle? (2019)
A.
Straight line
B.
Circular
C.
Elliptical
D.
Parabolic
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Solution
A charged particle moving in a magnetic field experiences a force that is perpendicular to its velocity, resulting in circular motion.
Correct Answer: B — Circular
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Q. A chord of a circle is 12 cm long and is 5 cm away from the center. What is the radius of the circle? (2020)
A.
10 cm
B.
13 cm
C.
15 cm
D.
12 cm
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Solution
Using Pythagoras theorem: r² = (5)² + (6)² = 25 + 36 = 61; r = √61 ≈ 7.81 cm.
Correct Answer: B — 13 cm
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Q. A circle has a diameter of 20 cm. What is its circumference? (2022)
A.
62.8 cm
B.
40 cm
C.
31.4 cm
D.
20 cm
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Solution
Circumference = πd = π * 20 = 62.8 cm.
Correct Answer: A — 62.8 cm
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Q. A circle has a radius of 10 cm. What is the diameter? (2020)
A.
5 cm
B.
10 cm
C.
15 cm
D.
20 cm
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Solution
Diameter = 2 * radius = 2 * 10 cm = 20 cm.
Correct Answer: D — 20 cm
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Q. A circle has a radius of 5 cm. What is the length of an arc that subtends a central angle of 60 degrees? (2021)
A.
5.24 cm
B.
10.47 cm
C.
3.14 cm
D.
6.28 cm
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Solution
Arc length = (θ/360) * 2πr; = (60/360) * 2π * 5 = 10.47 cm.
Correct Answer: B — 10.47 cm
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Q. A circle has a radius of 5 cm. What is the length of an arc that subtends an angle of 60 degrees at the center? (2020)
A.
5.24 cm
B.
3.14 cm
C.
5.00 cm
D.
10.47 cm
Show solution
Solution
Arc length = (θ/360) * 2πr = (60/360) * 2 * π * 5 = 5.24 cm.
Correct Answer: A — 5.24 cm
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