Q. A boat travels across a river with a speed of 4 m/s relative to the water. If the river flows at 3 m/s, what is the resultant speed of the boat relative to the riverbank?
Q. A boat travels across a river with a speed of 8 km/h relative to the water. If the river flows at 6 km/h, what is the speed of the boat relative to the riverbank?
A.8 km/h
B.10 km/h
C.14 km/h
D.6 km/h
Solution
Speed of boat relative to riverbank = √(8^2 + 6^2) = √(64 + 36) = √100 = 10 km/h.
Correct Answer: B — 10 km/h
Q. A body moves in a straight line with a uniform acceleration of 2 m/s². If its initial velocity is 5 m/s, what will be its velocity after 10 seconds?
A.25 m/s
B.20 m/s
C.15 m/s
D.10 m/s
Solution
Final velocity = initial velocity + acceleration * time = 5 + 2 * 10 = 25 m/s.
Correct Answer: A — 25 m/s
Q. A box contains 10 balls, 4 of which are red and 6 are blue. If one ball is drawn at random, what is the probability that it is not blue?
A.2/5
B.3/5
C.4/10
D.1/5
Solution
The probability of not drawing a blue ball = Number of red balls / Total balls = 4/10 = 2/5.
Correct Answer: A — 2/5
Q. A box contains 10 balls, 4 of which are red and 6 are blue. If one ball is drawn, what is the probability that it is blue?
A.2/5
B.3/5
C.4/10
D.6/10
Solution
The probability of drawing a blue ball is 6/10 = 3/5.
Correct Answer: B — 3/5
Q. A box contains 10 balls, 4 of which are white and the rest are black. If one ball is drawn at random, what is the probability that it is not white?
A.2/5
B.3/5
C.4/5
D.1/5
Solution
The total number of balls is 10. The number of non-white balls is 10 - 4 = 6. Thus, the probability of drawing a non-white ball is 6/10 = 3/5.
Correct Answer: B — 3/5
Q. A box contains 10 balls, 4 red and 6 green. If one ball is drawn at random, what is the probability that it is green given that it is not red?
A.1/2
B.3/5
C.2/5
D.4/5
Solution
If the ball is not red, it must be green. Therefore, P(Green | Not Red) = 1.
Correct Answer: B — 3/5
Q. A box contains 4 red, 3 green, and 2 blue balls. If a ball is drawn and it is green, what is the probability that the next ball drawn is red?
A.4/9
B.2/9
C.1/3
D.1/4
Solution
After drawing a green ball, there are 4 red, 2 green, and 2 blue balls left. The probability of drawing a red ball next is 4/8 = 1/2.
Correct Answer: A — 4/9
Q. A box contains 4 red, 3 green, and 5 blue balls. If a ball is drawn and it is blue, what is the probability that the next ball drawn is red?
A.4/11
B.3/11
C.5/11
D.1/3
Solution
After drawing a blue ball, there are 4 red, 3 green, and 4 blue left. The probability of drawing a red ball next is 4/11.
Correct Answer: A — 4/11
Q. A box contains 4 white and 6 black balls. If one ball is drawn and it is black, what is the probability that the next ball drawn is also black?
A.1/2
B.1/3
C.1/5
D.2/5
Solution
After drawing one black ball, there are 5 black and 4 white balls left. The probability of drawing another black ball is 5/9.
Correct Answer: D — 2/5
Q. A box contains 4 white and 6 black balls. If one ball is drawn at random, what is the probability that it is black given that it is not white?
A.2/5
B.3/5
C.4/5
D.1/5
Solution
The total number of balls is 10. The number of favorable outcomes (black balls) is 6. The probability that the ball is black given that it is not white is P(Black | Not White) = 6/6 = 1.
Correct Answer: C — 4/5
Q. A box contains 4 white and 6 black balls. If one ball is drawn at random, what is the probability that it is white given that it is not black?
A.2/5
B.1/5
C.1/2
D.1/3
Solution
If the ball is not black, it must be white. Therefore, P(White | Not Black) = 1.
Correct Answer: A — 2/5
Q. A box contains 5 red and 3 blue balls. What is the probability of drawing a red ball?
A.5/8
B.3/8
C.1/2
D.1/4
Solution
Total balls = 5 + 3 = 8. Probability of red = 5/8.
Correct Answer: A — 5/8
Q. A box contains 5 red and 3 green marbles. If one marble is drawn and it is red, what is the probability that the next marble drawn is green?
A.3/7
B.2/7
C.1/7
D.1/3
Solution
After drawing one red marble, there are 4 red and 3 green marbles left. The probability of drawing a green marble is 3/7.
Correct Answer: A — 3/7
Q. A box contains 5 red, 3 blue, and 2 green balls. If one ball is drawn at random, what is the probability that it is blue given that it is not red?
A.1/2
B.1/4
C.1/3
D.1/5
Solution
The total number of balls that are not red is 5 (3 blue + 2 green). The probability that the ball is blue given it is not red is P(Blue | Not Red) = 3/5.
Correct Answer: C — 1/3
Q. A box contains 5 red, 3 green, and 2 blue balls. What is the probability of drawing a green ball?
A.1/5
B.3/10
C.1/3
D.1/2
Solution
Total balls = 10. Probability of green = 3/10.
Correct Answer: B — 3/10
Q. A box contains 5 red, 3 green, and 2 blue marbles. If a marble is drawn at random, what is the probability that it is green given that it is not red?
A.1/2
B.1/3
C.1/4
D.1/5
Solution
The total number of non-red marbles is 5 (3 green + 2 blue). Therefore, P(Green | Not Red) = 3/5.
Correct Answer: B — 1/3
Q. A box contains 5 red, 3 green, and 2 blue marbles. If one marble is drawn at random, what is the probability that it is green given that it is not red?
A.1/2
B.1/3
C.1/4
D.1/5
Solution
The total number of non-red marbles is 5 (3 green + 2 blue). The probability that the marble is green given that it is not red is P(Green | Not Red) = 3/5.
Correct Answer: B — 1/3
Q. A box contains 5 red, 3 green, and 2 blue marbles. What is the probability of drawing a green marble given that the marble drawn is not blue?
A.3/10
B.1/3
C.1/5
D.1/2
Solution
The total number of marbles that are not blue is 8 (5 red + 3 green). The probability of drawing a green marble is 3/8.
Correct Answer: A — 3/10
Q. A box contains 5 white and 3 black balls. If a ball is drawn and it is black, what is the probability that the next ball drawn is white?
A.5/8
B.3/8
C.1/2
D.1/3
Solution
After drawing a black ball, there are 5 white and 2 black balls left. The probability of drawing a white ball next is 5/7.
Correct Answer: A — 5/8
Q. A box contains 5 white and 3 black balls. If one ball is drawn and it is black, what is the probability that the next ball drawn is white?
A.5/7
B.3/8
C.5/8
D.1/2
Solution
After drawing a black ball, there are 5 white and 2 black balls left. The probability of drawing a white ball next is 5/7.
Correct Answer: A — 5/7
Q. A box contains 5 white and 3 black balls. If one ball is drawn at random, what is the probability that it is not black?
A.3/8
B.5/8
C.1/2
D.7/8
Solution
The probability of not drawing a black ball is the probability of drawing a white ball, which is 5/8.
Correct Answer: B — 5/8
Q. A box contains 5 white and 3 black balls. If two balls are drawn at random, what is the probability that both are white?
A.1/28
B.5/28
C.15/28
D.3/28
Solution
The probability of drawing 2 white balls = (5/8) * (4/7) = 20/56 = 5/14.
Correct Answer: B — 5/28
Q. A box is pushed with a force of 50 N on a surface with a coefficient of kinetic friction of 0.4. What is the acceleration of the box if its mass is 10 kg?
A.1 m/s²
B.2 m/s²
C.3 m/s²
D.4 m/s²
Solution
Net force = applied force - frictional force. Frictional force = μ_k * N = 0.4 * 10 kg * 9.8 m/s² = 39.2 N. Net force = 50 N - 39.2 N = 10.8 N. Acceleration = F/m = 10.8 N / 10 kg = 1.08 m/s², approximately 1 m/s².
Correct Answer: B — 2 m/s²
Q. A box is pushed with a force of 50 N on a surface with a coefficient of kinetic friction of 0.3. If the normal force is 100 N, what is the net force acting on the box?
A.20 N
B.30 N
C.50 N
D.70 N
Solution
Frictional force = μk * N = 0.3 * 100 N = 30 N. Net force = applied force - frictional force = 50 N - 30 N = 20 N.
Correct Answer: B — 30 N
Q. A building is 30 meters tall. From a point 40 meters away from the base of the building, what is the angle of elevation to the top of the building?
A.30 degrees
B.36.87 degrees
C.45 degrees
D.60 degrees
Solution
Using tan(θ) = height/distance, we have tan(θ) = 30/40 = 0.75. Therefore, θ = tan⁻¹(0.75) ≈ 36.87 degrees.
Correct Answer: B — 36.87 degrees
Q. A building is 40 m high. From a point on the ground, the angle of elevation to the top of the building is 60 degrees. What is the distance from the point to the base of the building?
A.20√3 m
B.40 m
C.30 m
D.10√3 m
Solution
Using tan(60°) = height/distance, we have distance = height/tan(60°) = 40/√3 = 20√3 m.
Correct Answer: A — 20√3 m
Q. A capacitor has a capacitance of 4μF and is charged to 12V. What is the charge on the capacitor?
A.48μC
B.12μC
C.4μC
D.3μC
Solution
Charge (Q) on a capacitor is given by Q = C * V. Thus, Q = 4μF * 12V = 48μC.
Correct Answer: A — 48μC
Q. A capacitor in an AC circuit has a capacitive reactance of 50 ohms. If the frequency of the AC source is increased, what happens to the capacitive reactance?
A.Increases
B.Decreases
C.Remains the same
D.Becomes infinite
Solution
Capacitive reactance (X_C) is given by X_C = 1/(2πfC). If the frequency (f) increases, X_C decreases.
Correct Answer: B — Decreases
Q. A capacitor in an AC circuit has a capacitive reactance of 50 ohms. What is the frequency if the capacitance is 10 microfarads?
A.1 kHz
B.10 kHz
C.100 Hz
D.1000 Hz
Solution
Capacitive reactance (X_C) is given by X_C = 1 / (2πfC). Rearranging gives f = 1 / (2πX_CC). Substituting X_C = 50 ohms and C = 10 x 10^-6 F gives f = 318.31 Hz, approximately 1 kHz.
