Engineering & Architecture Admissions
Q. In thermodynamics, what does the first law of thermodynamics state?
A.
Energy cannot be created or destroyed
B.
Entropy always increases
C.
Heat flows from cold to hot
D.
Work done is independent of path
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Solution
The first law of thermodynamics states that energy cannot be created or destroyed, only transformed from one form to another.
Correct Answer: A — Energy cannot be created or destroyed
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Q. In thermodynamics, what does the first law state?
A.
Energy cannot be created or destroyed
B.
Entropy always increases
C.
Pressure and volume are inversely related
D.
Heat flows from cold to hot
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Solution
The first law of thermodynamics states that energy cannot be created or destroyed, only transformed from one form to another.
Correct Answer: A — Energy cannot be created or destroyed
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Q. In thermodynamics, what does the term 'enthalpy' refer to?
A.
Internal energy plus pressure times volume
B.
Internal energy minus pressure times volume
C.
Heat content of a system
D.
Work done by a system
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Solution
Enthalpy is defined as H = U + PV, where U is internal energy, P is pressure, and V is volume.
Correct Answer: A — Internal energy plus pressure times volume
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Q. In thin film interference, if the refractive index of the film is greater than that of the surrounding medium, what happens to the phase of the reflected wave?
A.
No phase change
B.
Phase change of π
C.
Phase change of 2π
D.
Phase change of λ
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Solution
When light reflects off a denser medium, it undergoes a phase change of π (180 degrees).
Correct Answer: B — Phase change of π
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Q. In thin film interference, what causes a phase change of π?
A.
Reflection from a denser medium
B.
Reflection from a rarer medium
C.
Transmission through a denser medium
D.
Transmission through a rarer medium
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Solution
A phase change of π occurs when a wave reflects off a denser medium.
Correct Answer: A — Reflection from a denser medium
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Q. In triangle ABC, if a = 7, b = 24, and c = 25, what is the area of the triangle?
A.
84
B.
96
C.
120
D.
144
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Solution
Using Heron's formula, s = (7 + 24 + 25)/2 = 28. Area = √[s(s-a)(s-b)(s-c)] = √[28(28-7)(28-24)(28-25)] = √[28*21*4*3] = 84.
Correct Answer: A — 84
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Q. In triangle ABC, if AB = 10 cm, AC = 6 cm, and angle A = 30°, what is the length of side BC?
A.
8 cm
B.
7 cm
C.
5 cm
D.
4 cm
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Solution
Using the Law of Cosines: BC² = AB² + AC² - 2 * AB * AC * cos(A) = 10² + 6² - 2 * 10 * 6 * (√3/2) = 100 + 36 - 60√3. BC = √(100 + 36 - 60√3) ≈ 7 cm.
Correct Answer: B — 7 cm
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Q. In triangle ABC, if AB = 7 cm, AC = 24 cm, and BC = 25 cm, is triangle ABC a right triangle?
A.
Yes
B.
No
C.
Cannot be determined
D.
Only if angle A is 90°
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Solution
Using the Pythagorean theorem, 7^2 + 24^2 = 49 + 576 = 625 = 25^2, so triangle ABC is a right triangle.
Correct Answer: A — Yes
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Q. In triangle ABC, if AB = 7 cm, AC = 24 cm, and BC = 25 cm, what is the area of the triangle?
A.
84 cm²
B.
96 cm²
C.
120 cm²
D.
140 cm²
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Solution
Using Heron's formula, the semi-perimeter s = (7 + 24 + 25)/2 = 28. Area = √[s(s-a)(s-b)(s-c)] = √[28(28-7)(28-24)(28-25)] = √[28*21*4*3] = 84 cm².
Correct Answer: B — 96 cm²
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Q. In triangle ABC, if AB = 8, AC = 6, and BC = 10, what is the semi-perimeter?
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Solution
Semi-perimeter s = (AB + AC + BC) / 2 = (8 + 6 + 10) / 2 = 12.
Correct Answer: B — 14
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Q. In triangle ABC, if angle A = 45 degrees and angle B = 45 degrees, what is angle C?
A.
45 degrees
B.
60 degrees
C.
90 degrees
D.
135 degrees
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Solution
The sum of angles in a triangle is 180 degrees. Therefore, angle C = 180 - (45 + 45) = 90 degrees.
Correct Answer: C — 90 degrees
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Q. In triangle ABC, if angle A = 45 degrees and angle B = 45 degrees, what is the relationship between sides a, b, and c?
A.
a = b
B.
a > b
C.
a < b
D.
a + b = c
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Solution
In an isosceles triangle with angles A and B equal, the sides opposite those angles are equal, hence a = b.
Correct Answer: A — a = b
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Q. In triangle ABC, if angle A = 45 degrees and angle B = 45 degrees, what is the type of triangle?
A.
Scalene
B.
Isosceles
C.
Equilateral
D.
Right
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Solution
Since two angles are equal, triangle ABC is isosceles.
Correct Answer: B — Isosceles
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Q. In triangle ABC, if angle A = 45 degrees and side a = 10 cm, what is the length of side b if angle B = 60 degrees?
A.
8.66 cm
B.
10 cm
C.
12.25 cm
D.
15 cm
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Solution
Using the Law of Sines: a/sin(A) = b/sin(B). Therefore, b = a * (sin(B)/sin(A)) = 10 * (sin(60)/sin(45)) = 10 * (√3/2)/(√2/2) = 10 * √3/√2 = 10 * √(3/2) = 8.66 cm.
Correct Answer: A — 8.66 cm
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Q. In triangle ABC, if angle A = 45° and angle B = 45°, what is angle C?
A.
45°
B.
60°
C.
75°
D.
90°
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Solution
Angle C = 180° - (angle A + angle B) = 180° - (45° + 45°) = 90°.
Correct Answer: D — 90°
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Q. In triangle ABC, if angle A = 45° and side a = 10, what is the length of side b if angle B = 60°?
A.
8.66
B.
7.5
C.
5
D.
10
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Solution
Using the Law of Sines: b/a = sin(B)/sin(A) => b = a * (sin(B)/sin(A)) = 10 * (√3/2)/(√2/2) = 10 * √3/√2 = 10 * 8.66/10 = 8.66.
Correct Answer: A — 8.66
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Q. In triangle ABC, if angle A = 60 degrees and angle B = 70 degrees, what is angle C?
A.
50 degrees
B.
60 degrees
C.
70 degrees
D.
80 degrees
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Solution
Angle C = 180 - (angle A + angle B) = 180 - (60 + 70) = 50 degrees.
Correct Answer: A — 50 degrees
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Q. In triangle ABC, if angle A = 60 degrees and angle B = 70 degrees, what is the measure of angle C?
A.
50 degrees
B.
60 degrees
C.
70 degrees
D.
80 degrees
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Solution
The sum of angles in a triangle is 180 degrees. Therefore, angle C = 180 - (60 + 70) = 50 degrees.
Correct Answer: A — 50 degrees
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Q. In triangle ABC, if angle A = 60° and angle B = 70°, what is angle C?
A.
50°
B.
60°
C.
70°
D.
80°
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Solution
Angle C = 180° - (angle A + angle B) = 180° - (60° + 70°) = 50°.
Correct Answer: A — 50°
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Q. In triangle ABC, if the angles are in the ratio 2:3:4, what is the measure of the largest angle?
A.
60 degrees
B.
80 degrees
C.
90 degrees
D.
120 degrees
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Solution
Let the angles be 2x, 3x, and 4x. Then, 2x + 3x + 4x = 180 => 9x = 180 => x = 20. The largest angle = 4x = 80 degrees.
Correct Answer: B — 80 degrees
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Q. In triangle ABC, if the coordinates of A, B, and C are (1, 2), (4, 6), and (7, 2) respectively, what is the length of side AB?
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Solution
Length of AB = √[(4-1)² + (6-2)²] = √[3² + 4²] = √[9 + 16] = √25 = 5.
Correct Answer: B — 5
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Q. In triangle ABC, if the coordinates of A, B, and C are (1, 2), (4, 6), and (7, 2) respectively, what is the area of triangle ABC?
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Solution
Using the formula for the area of a triangle given vertices, Area = 1/2 | x1(y2-y3) + x2(y3-y1) + x3(y1-y2) | = 1/2 | 1(6-2) + 4(2-2) + 7(2-6) | = 1/2 | 4 + 0 - 28 | = 12.
Correct Answer: A — 12
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Q. In triangle ABC, if the lengths of sides a = 10, b = 24, and angle C = 60 degrees, find the length of side c.
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Solution
Using the cosine rule: c^2 = a^2 + b^2 - 2ab*cos(C) = 10^2 + 24^2 - 2*10*24*(1/2) = 100 + 576 - 240 = 436. Thus, c = √436 = 20.
Correct Answer: A — 20
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Q. In triangle ABC, if the lengths of sides a, b, and c are 5, 12, and 13 respectively, what is the perimeter of the triangle?
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Solution
Perimeter = a + b + c = 5 + 12 + 13 = 30.
Correct Answer: B — 25
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Q. In triangle ABC, if the lengths of sides a, b, and c are 7, 24, and 25 respectively, what type of triangle is it?
A.
Acute
B.
Obtuse
C.
Right
D.
Equilateral
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Solution
Since 7² + 24² = 49 + 576 = 625 = 25², triangle ABC is a right triangle.
Correct Answer: C — Right
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Q. In triangle ABC, if the lengths of sides a, b, and c are 7, 24, and 25 respectively, what is the area of the triangle?
A.
84
B.
96
C.
120
D.
168
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Solution
Using Heron's formula, s = (7 + 24 + 25)/2 = 28. Area = √[s(s-a)(s-b)(s-c)] = √[28(28-7)(28-24)(28-25)] = √[28*21*4*3] = 84.
Correct Answer: B — 96
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Q. In triangle ABC, if the lengths of sides a, b, and c are 8, 15, and 17 respectively, what is the type of triangle?
A.
Acute
B.
Obtuse
C.
Right
D.
Equilateral
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Solution
Since 8² + 15² = 17², triangle ABC is a right triangle.
Correct Answer: C — Right
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Q. In triangle ABC, if the lengths of sides are 8 cm, 15 cm, and 17 cm, what is the type of triangle?
A.
Acute
B.
Obtuse
C.
Right
D.
Isosceles
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Solution
Since 8² + 15² = 64 + 225 = 289 = 17², triangle ABC is a right triangle.
Correct Answer: C — Right
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Q. In triangle ABC, if the lengths of the sides are 5, 12, and 13, what is the perimeter?
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Solution
Perimeter = a + b + c = 5 + 12 + 13 = 30.
Correct Answer: B — 25
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Q. In triangle ABC, if the lengths of the sides are 8 cm, 15 cm, and 17 cm, what is the perimeter?
A.
30 cm
B.
40 cm
C.
50 cm
D.
60 cm
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Solution
Perimeter = 8 + 15 + 17 = 40 cm.
Correct Answer: A — 30 cm
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