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' (H) represent? (2020)
A.
Total energy of the system
B.
Energy required to break bonds
C.
Heat content of the system at constant pressure
D.
Work done by the system
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Solution
Enthalpy (H) represents the heat content of the system at constant pressure, defined as H = U + PV.
Correct Answer: C — Heat content of the system at constant pressure
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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 thin film interference, what happens to the colors observed when the thickness of the film increases?
A.
Colors become brighter
B.
Colors change
C.
Colors disappear
D.
Colors remain the same
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Solution
As the thickness of the film increases, the path difference changes, leading to a change in the observed colors due to interference.
Correct Answer: B — Colors change
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Q. In thin film interference, which of the following will cause a shift in the interference pattern? (2022)
A.
Change in wavelength
B.
Change in film thickness
C.
Change in angle of incidence
D.
All of the above
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Solution
All these factors can affect the path difference and thus shift the interference pattern in thin film interference.
Correct Answer: D — All of the above
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Q. In thin film interference, which of the following will not affect the interference pattern? (2022)
A.
Thickness of the film
B.
Wavelength of light
C.
Angle of incidence
D.
Color of the light source
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Solution
While thickness, wavelength, and angle of incidence affect the interference pattern, the color of the light source does not directly affect the pattern itself.
Correct Answer: D — Color of the light source
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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 = 30 degrees and angle B = 60 degrees, what is the measure of angle C? (2021)
A.
30 degrees
B.
60 degrees
C.
90 degrees
D.
120 degrees
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Solution
The sum of angles in a triangle is 180 degrees. Therefore, angle C = 180 - (30 + 60) = 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 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 angle A is 30 degrees and angle B is 60 degrees, what is the measure of angle C?
A.
30 degrees
B.
60 degrees
C.
90 degrees
D.
120 degrees
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Solution
Using the property that the sum of angles in a triangle is 180 degrees, angle C can be calculated as 180 - (30 + 60) = 90 degrees.
Correct Answer: C — 90 degrees
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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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