Q. If the coordinates of a point P are (1, -1, 2), what is the x-coordinate of the point Q if it is reflected across the yz-plane? (2023)
Solution
Reflection across the yz-plane changes the sign of the x-coordinate. So, Q = (-1, -1, 2).
Correct Answer: B — -1
Learn More →
Q. If the coordinates of point A are (1, 2) and point B are (4, 6), what is the length of AB? (2023)
Solution
Length AB = √[(4-1)² + (6-2)²] = √[9 + 16] = √25 = 5.
Correct Answer: A — 5
Learn More →
Q. If the coordinates of point C are (5, 5) and point D are (5, 10), what is the distance CD? (2021)
Solution
Distance CD = |10 - 5| = 5.
Correct Answer: A — 5
Learn More →
Q. If the coordinates of point C are (5, 5) and point D are (5, 10), what is the length of CD? (2021)
Solution
Length CD = |10 - 5| = 5.
Correct Answer: A — 5
Learn More →
Q. If the coordinates of point C are (5, 5) and the slope of line AC is 1, what is the equation of line AC? (2021)
-
A.
y = x
-
B.
y = 5
-
C.
y = x + 5
-
D.
y = x - 5
Solution
Using point-slope form: y - 5 = 1(x - 5) => y = x
Correct Answer: A — y = x
Learn More →
Q. If the coordinates of point C are (5, 5) and the slope of the line is 1, what is the equation of the line? (2021) 2021
-
A.
y = x
-
B.
y = 5
-
C.
y = 2x - 5
-
D.
y = x + 5
Solution
Using point-slope form: y - 5 = 1(x - 5) => y = x.
Correct Answer: A — y = x
Learn More →
Q. If the cost function is C(x) = 3x^2 + 12x + 5, find the minimum cost. (2020)
Solution
The minimum cost occurs at x = -b/(2a) = -12/(2*3) = -2. C(-2) = 3(-2)^2 + 12(-2) + 5 = 8.
Correct Answer: B — 8
Learn More →
Q. If the cost function is C(x) = 3x^2 + 12x + 5, find the minimum cost. (2020) 2020
Solution
The minimum cost occurs at x = -b/(2a) = -12/(2*3) = -2. C(-2) = 3(-2)^2 + 12(-2) + 5 = 8.
Correct Answer: B — 8
Learn More →
Q. If the cost function is C(x) = 5x^2 + 20x + 100, find the minimum cost. (2020)
-
A.
100
-
B.
120
-
C.
140
-
D.
160
Solution
The minimum cost occurs at x = -b/(2a) = -20/(2*5) = -2. C(-2) = 5(-2)^2 + 20(-2) + 100 = 120.
Correct Answer: B — 120
Learn More →
Q. If the current in an AC circuit is given by I(t) = I0 cos(ωt), what is the RMS current? (2023)
-
A.
I0/√2
-
B.
I0
-
C.
2I0
-
D.
I0/2
Solution
RMS current I_rms = I0/√2 for a cosine function.
Correct Answer: A — I0/√2
Learn More →
Q. If the current in an AC circuit is I(t) = 5√2 sin(100t + π/4), what is the RMS current? (2021)
-
A.
5 A
-
B.
2.5 A
-
C.
7.07 A
-
D.
3.54 A
Solution
The RMS current is I_rms = I_peak / √2 = 5√2 / √2 = 5 A.
Correct Answer: B — 2.5 A
Learn More →
Q. If the current through a resistor is tripled, what happens to the power dissipated in the resistor? (2022)
-
A.
Increases by 3 times
-
B.
Increases by 9 times
-
C.
Remains the same
-
D.
Decreases by 3 times
Solution
Power is proportional to the square of the current (P = I²R). If I is tripled, P increases by 3² = 9 times.
Correct Answer: B — Increases by 9 times
Learn More →
Q. If the diameter of a circle is 20 cm, what is its circumference? (2022)
-
A.
62.83 cm
-
B.
31.42 cm
-
C.
20 cm
-
D.
40 cm
Solution
Circumference = πd; C = π * 20 ≈ 62.83 cm.
Correct Answer: A — 62.83 cm
Learn More →
Q. If the electric field at a point is 1000 N/C and the charge at that point is 5 µC, what is the force experienced by the charge?
-
A.
0.005 N
-
B.
0.05 N
-
C.
0.5 N
-
D.
5 N
Solution
F = E * q = 1000 N/C * 5 × 10^-6 C = 0.005 N.
Correct Answer: B — 0.05 N
Learn More →
Q. If the first term of a geometric series is 4 and the common ratio is 2, what is the 7th term?
-
A.
128
-
B.
256
-
C.
512
-
D.
1024
Solution
The nth term of a geometric series is given by a_n = ar^(n-1). Here, a = 4, r = 2, n = 7. So, a_7 = 4 * 2^(7-1) = 4 * 64 = 256.
Correct Answer: B — 256
Learn More →
Q. If the first term of an arithmetic series is 12 and the last term is 48, what is the common difference if there are 10 terms?
Solution
In an arithmetic series, the last term can be expressed as a + (n-1)d. Here, 48 = 12 + (10-1)d. Thus, 48 - 12 = 9d, giving d = 4.
Correct Answer: A — 4
Learn More →
Q. If the frequency of a vibrating tuning fork is 440 Hz, what is the time period of the vibration? (2023)
-
A.
0.00227 s
-
B.
0.005 s
-
C.
0.01 s
-
D.
0.0227 s
Solution
The time period T is the reciprocal of frequency f, T = 1/f. Therefore, T = 1/440 ≈ 0.00227 s.
Correct Answer: A — 0.00227 s
Learn More →
Q. If the frequency of a wave is halved, what happens to its wavelength? (2015)
-
A.
Halves
-
B.
Doubles
-
C.
Remains the same
-
D.
Increases by four times
Solution
Wavelength is inversely proportional to frequency. If frequency is halved, wavelength doubles.
Correct Answer: B — Doubles
Learn More →
Q. If the frequency of an AC source is doubled, how does the inductive reactance change? (2020)
-
A.
Doubles
-
B.
Halves
-
C.
Remains the same
-
D.
Quadruples
Solution
Xl = 2πfL; if f is doubled, Xl also doubles.
Correct Answer: B — Halves
Learn More →
Q. If the frequency of an AC source is doubled, what happens to the inductive reactance? (2014)
-
A.
It doubles
-
B.
It halves
-
C.
It remains the same
-
D.
It quadruples
Solution
Inductive reactance XL = 2πfL, so if frequency f is doubled, XL halves.
Correct Answer: B — It halves
Learn More →
Q. If the frequency of an AC source is doubled, what happens to the reactance of a capacitor? (2023)
-
A.
It doubles
-
B.
It halves
-
C.
It remains the same
-
D.
It quadruples
Solution
The capacitive reactance Xc = 1/(2πfC) halves when the frequency f is doubled.
Correct Answer: B — It halves
Learn More →
Q. If the inductance of a coil is 0.5H and the frequency is 60Hz, what is the inductive reactance? (2023)
-
A.
31.42 ohms
-
B.
18.85 ohms
-
C.
37.70 ohms
-
D.
25.13 ohms
Solution
Xl = 2πfL = 2π × 60 × 0.5 = 31.42 ohms.
Correct Answer: A — 31.42 ohms
Learn More →
Q. If the inductive reactance of a coil is 30Ω and the resistance is 10Ω, what is the total impedance? (2018)
-
A.
10Ω
-
B.
30Ω
-
C.
33.33Ω
-
D.
40Ω
Solution
Total impedance Z = √(R² + (XL)²) = √(10² + 30²) = √(100 + 900) = √1000 = 31.62Ω.
Correct Answer: C — 33.33Ω
Learn More →
Q. If the latent heat of fusion of ice is 334 J/g, how much heat is required to melt 50 g of ice? (2019)
-
A.
1670 J
-
B.
3340 J
-
C.
5000 J
-
D.
1000 J
Solution
Heat required = mass × latent heat = 50 g × 334 J/g = 16700 J.
Correct Answer: A — 1670 J
Learn More →
Q. If the line 2x + 3y = 6 intersects the x-axis, what is the point of intersection?
-
A.
(3, 0)
-
B.
(0, 2)
-
C.
(0, 3)
-
D.
(2, 0)
Solution
Setting y = 0 gives 2x = 6, thus x = 3. The point of intersection is (3, 0).
Correct Answer: A — (3, 0)
Learn More →
Q. If the line 2x + 3y = 6 intersects the x-axis, what is the x-coordinate of the intersection point?
Solution
Setting y = 0 gives 2x = 6, thus x = 3. The x-coordinate of the intersection point is 3.
Correct Answer: B — 2
Learn More →
Q. If the line 3x + 4y = 12 intersects the y-axis, what is the point of intersection? (2021)
-
A.
(0, 3)
-
B.
(0, 4)
-
C.
(0, 2)
-
D.
(0, 1)
Solution
Setting x = 0 gives 4y = 12, thus y = 3. The point of intersection is (0, 3).
Correct Answer: A — (0, 3)
Learn More →
Q. If the line 3x - 4y + 12 = 0 intersects the y-axis, what is the point of intersection?
-
A.
(0, 3)
-
B.
(0, -3)
-
C.
(0, 4)
-
D.
(0, -4)
Solution
Setting x = 0 gives -4y + 12 = 0, thus y = -3. The point of intersection is (0, -3).
Correct Answer: D — (0, -4)
Learn More →
Q. If the line 3x - 4y + 12 = 0 is parallel to another line, what is the slope of the parallel line?
-
A.
3/4
-
B.
-3/4
-
C.
4/3
-
D.
-4/3
Solution
Rearranging gives y = (3/4)x + 3. The slope of the line is 3/4, so the slope of the parallel line is -3/4.
Correct Answer: B — -3/4
Learn More →
Q. If the line 3x - 4y + 12 = 0 is parallel to which of the following lines?
-
A.
6x - 8y + 24 = 0
-
B.
3x + 4y - 12 = 0
-
C.
x + 2y - 5 = 0
-
D.
2x - 3y + 6 = 0
Solution
Parallel lines have the same slope. The slope of the given line is 3/4, which is the same as the slope of 6x - 8y + 24 = 0.
Correct Answer: A — 6x - 8y + 24 = 0
Learn More →
Showing 841 to 870 of 2235 (75 Pages)
