Q. If the peak voltage of an AC source is 200 V, what is the RMS voltage?
-
A.
100 V
-
B.
141.42 V
-
C.
200 V
-
D.
282.84 V
Solution
The RMS voltage (V_rms) is given by V_rms = V_peak / √2. Therefore, V_rms = 200 V / √2 = 141.42 V.
Correct Answer: B — 141.42 V
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Q. If the peak voltage of an AC source is 220 V, what is the RMS voltage?
-
A.
110 V
-
B.
154 V
-
C.
220 V
-
D.
311 V
Solution
The RMS voltage (V_rms) is given by V_rms = V_peak / √2. Therefore, V_rms = 220 V / √2 = 110 V.
Correct Answer: A — 110 V
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Q. If the perimeter of a rectangle is 30 cm and the length is 10 cm, what is the width?
-
A.
5 cm
-
B.
10 cm
-
C.
7.5 cm
-
D.
15 cm
Solution
Perimeter P = 2(length + width). So, 30 = 2(10 + width). Dividing by 2 gives 15 = 10 + width. Thus, width = 15 - 10 = 5 cm.
Correct Answer: A — 5 cm
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Q. If the perimeter of a rectangle is 50 cm and the length is 15 cm, what is the width? (2020)
-
A.
10 cm
-
B.
12.5 cm
-
C.
15 cm
-
D.
20 cm
Solution
Perimeter = 2(length + width). So, 50 = 2(15 + width). Solving gives width = 10 cm.
Correct Answer: B — 12.5 cm
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Q. If the perimeter of a regular hexagon is 72 cm, what is the length of each side?
-
A.
10 cm
-
B.
12 cm
-
C.
14 cm
-
D.
8 cm
Solution
The perimeter of a regular hexagon is the sum of the lengths of its 6 equal sides. Therefore, each side is 72 cm / 6 = 12 cm.
Correct Answer: B — 12 cm
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Q. If the perimeter of a square is 40 cm, what is the length of one side? (2018)
-
A.
10 cm
-
B.
15 cm
-
C.
20 cm
-
D.
25 cm
Solution
Perimeter = 4 × side, so side = 40/4 = 10 cm.
Correct Answer: A — 10 cm
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Q. If the perimeter of a triangle is 30 cm and the lengths of two sides are 10 cm and 12 cm, what is the length of the third side? (2020)
-
A.
8 cm
-
B.
10 cm
-
C.
12 cm
-
D.
14 cm
Solution
Let the third side be x. Then, 10 + 12 + x = 30, so x = 30 - 22 = 8 cm.
Correct Answer: A — 8 cm
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Q. If the perimeter of an equilateral triangle is 36 cm, what is the length of each side?
-
A.
9 cm
-
B.
12 cm
-
C.
15 cm
-
D.
18 cm
Solution
In an equilateral triangle, all sides are equal. Therefore, if the perimeter is 36 cm, each side is 36/3 = 12 cm.
Correct Answer: B — 12 cm
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Q. If the period of a satellite in a circular orbit is T, what is the relationship between T and the radius r of the orbit?
-
A.
T ∝ r
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B.
T ∝ r²
-
C.
T ∝ √r
-
D.
T ∝ 1/√r
Solution
T = 2π√(r³/GM), thus T ∝ √r.
Correct Answer: C — T ∝ √r
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Q. If the pH of a river is measured to be 7.5, what type of water is it considered? (2020)
-
A.
Acidic
-
B.
Neutral
-
C.
Alkaline
-
D.
Distilled
Solution
A pH greater than 7 is considered alkaline.
Correct Answer: C — Alkaline
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Q. If the pH of a solution is 3, what is the concentration of H+ ions? (2023)
-
A.
0.001 M
-
B.
0.01 M
-
C.
0.1 M
-
D.
0.0001 M
Solution
pH = 3 means [H+] = 10^-3 M = 0.001 M.
Correct Answer: B — 0.01 M
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Q. If the photoelectric effect is observed, what can be inferred about the incident light?
-
A.
It has a frequency below the threshold
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B.
It has a frequency equal to the threshold
-
C.
It has a frequency above the threshold
-
D.
It has any frequency
Solution
The photoelectric effect occurs only when the frequency of the incident light is above the threshold frequency.
Correct Answer: C — It has a frequency above the threshold
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Q. If the pKa of acetic acid is 4.76, what is the pH of a 0.1 M solution?
-
A.
4.76
-
B.
5.76
-
C.
6.76
-
D.
3.76
Solution
For a weak acid, pH ≈ pKa for a 0.1 M solution, so pH ≈ 4.76.
Correct Answer: A — 4.76
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Q. If the point (x, y) lies on the line 4x - 5y = 20, what is the value of y when x = 0?
Solution
Substituting x = 0: 4(0) - 5y = 20 => -5y = 20 => y = -4.
Correct Answer: B — 5
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Q. If the points (1, 2), (3, 4), and (5, 6) are collinear, what is the slope of the line?
-
A.
1
-
B.
2
-
C.
0
-
D.
undefined
Solution
Slope = (4-2)/(3-1) = 1, and it remains the same for other points.
Correct Answer: A — 1
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Q. If the points A(1, 2), B(3, 4), and C(5, 6) are collinear, what is the area of triangle ABC?
Solution
Area = 1/2 | x1(y2-y3) + x2(y3-y1) + x3(y1-y2) | = 0.
Correct Answer: A — 0
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Q. If the polynomial P(x) = x^2 + bx + c has roots 3 and -2, what is the value of b?
Solution
Using Vieta's formulas, the sum of the roots (3 + (-2)) = 1, hence b = -1.
Correct Answer: B — 5
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Q. If the polynomial P(x) = x^3 - 3x^2 + 4 has a local maximum at x = 1, what is the value of P(1)?
Solution
Calculating P(1) gives 1^3 - 3(1^2) + 4 = 1 - 3 + 4 = 2.
Correct Answer: A — 2
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Q. If the polynomial P(x) = x^3 - 6x^2 + 11x - 6 has a root at x = 1, what is P(2)?
Solution
P(2) = 2^3 - 6(2^2) + 11(2) - 6 = 8 - 24 + 22 - 6 = 0.
Correct Answer: D — 3
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Q. If the population of a city increases by 10% every year, what will be the population after 2 years if the current population is 1000? (2021)
-
A.
1210
-
B.
1100
-
C.
1020
-
D.
1200
Solution
Population after 1 year = 1000 * 1.10 = 1100. Population after 2 years = 1100 * 1.10 = 1210.
Correct Answer: A — 1210
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Q. If the population of a country increases by 5% every year, what will be the population after 2 years if the current population is 100,000?
-
A.
110,250
-
B.
105,000
-
C.
120,000
-
D.
102,500
Solution
Population after 2 years = 100,000 * (1 + 0.05)^2 = 100,000 * 1.1025 = 110,250.
Correct Answer: A — 110,250
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Q. If the population of a town increases by 10% every year, what will be the population after 2 years if the current population is 1000? (2021)
-
A.
1210
-
B.
1100
-
C.
1020
-
D.
1200
Solution
Population after 1 year = 1000 * 1.10 = 1100. Population after 2 years = 1100 * 1.10 = 1210.
Correct Answer: A — 1210
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Q. If the position vector of a point is (5, 12), what is its distance from the origin?
Solution
Distance = √(5^2 + 12^2) = √(25 + 144) = √169 = 13
Correct Answer: A — 13
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Q. If the position vector of a point is given by r = (2t, 3t, 4t), what is the velocity vector?
-
A.
(2, 3, 4)
-
B.
(4, 6, 8)
-
C.
(2t, 3t, 4t)
-
D.
(0, 0, 0)
Solution
Velocity vector = dr/dt = (2, 3, 4)
Correct Answer: A — (2, 3, 4)
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Q. If the position vector of a point P is (2, 3, 4), what is the distance from the origin to point P?
Solution
Distance = √(2^2 + 3^2 + 4^2) = √(4 + 9 + 16) = √29 ≈ 5.385.
Correct Answer: B — 6
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Q. If the position vector of a point P is (x, y, z) and the vector a = (1, 2, 3), what is the projection of P onto a?
-
A.
(1, 2, 3)
-
B.
(2, 4, 6)
-
C.
(0, 0, 0)
-
D.
(x, y, z)
Solution
Projection of P onto a = ((P · a) / |a|^2) * a.
Correct Answer: D — (x, y, z)
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Q. If the position vector of a point P is given by r = (2t, 3t, 4t), find the coordinates of P when t = 1.
-
A.
(2, 3, 4)
-
B.
(1, 1, 1)
-
C.
(0, 0, 0)
-
D.
(2, 4, 6)
Solution
Substituting t = 1, r = (2*1, 3*1, 4*1) = (2, 3, 4).
Correct Answer: A — (2, 3, 4)
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Q. If the position vector of point P is (3, -2) and Q is (1, 4), what is the vector PQ?
-
A.
(-2, 6)
-
B.
(2, -6)
-
C.
(4, -6)
-
D.
(6, 2)
Solution
Vector PQ = Q - P = (1 - 3, 4 - (-2)) = (-2, 6).
Correct Answer: A — (-2, 6)
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Q. If the position vector of point P is (3, 4) and Q is (1, 2), what is the vector PQ?
-
A.
(2, 2)
-
B.
(4, 6)
-
C.
(2, 4)
-
D.
(1, 1)
Solution
Vector PQ = Q - P = (1 - 3, 2 - 4) = (-2, -2).
Correct Answer: A — (2, 2)
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Q. If the potential difference across a capacitor is halved, what happens to the energy stored in the capacitor? (2019)
-
A.
Halved
-
B.
Doubled
-
C.
Remains the same
-
D.
Quadrupled
Solution
The energy stored in a capacitor is given by U = 1/2 CV^2. If V is halved, the energy becomes U' = 1/2 C(V/2)^2 = 1/8 CV^2, which is halved.
Correct Answer: A — Halved
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