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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 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 type of triangle?
A.
Acute
B.
Obtuse
C.
Right
D.
Equilateral
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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 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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Q. In triangle ABC, if the lengths of the sides are 8, 15, and 17, what is the area of the triangle?
A.
60
B.
80
C.
120
D.
150
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Solution
Using Heron's formula, the semi-perimeter s = (8 + 15 + 17)/2 = 20. Area = √[s(s-a)(s-b)(s-c)] = √[20(20-8)(20-15)(20-17)] = √[20*12*5*3] = 60.
Correct Answer: A — 60
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Q. In triangle ABC, if the lengths of the sides are 8, 15, and 17, what is the type of triangle?
A.
Acute
B.
Obtuse
C.
Right
D.
Equilateral
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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 a = 5, b = 12, and c = 13, what is the perimeter of the triangle?
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Solution
The perimeter of a triangle is the sum of its sides. Therefore, 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 a = 8, b = 15, and c = 17, what is the value of cos A?
A.
0.5
B.
0.6
C.
0.8
D.
0.9
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Solution
Using the cosine rule, cos A = (b² + c² - a²) / (2bc) = (15² + 17² - 8²) / (2 * 15 * 17) = 0.8.
Correct Answer: C — 0.8
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Q. In triangle ABC, if the lengths of the sides are in the ratio 3:4:5, what type of triangle is it?
A.
Acute
B.
Obtuse
C.
Right
D.
Equilateral
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Solution
Since the sides are in the ratio of a Pythagorean triplet (3, 4, 5), triangle ABC is a right triangle.
Correct Answer: C — Right
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Q. In triangle ABC, if the sides are in the ratio 3:4:5, what is the nature of the triangle?
A.
Equilateral
B.
Isosceles
C.
Right
D.
Scalene
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Solution
The sides satisfy the Pythagorean theorem, hence it is a right triangle.
Correct Answer: C — Right
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Q. In triangle ABC, if the sides are in the ratio 3:4:5, what type of triangle is it?
A.
Acute
B.
Obtuse
C.
Right
D.
Equilateral
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Solution
A triangle with sides in the ratio 3:4:5 is a right triangle, as it satisfies the Pythagorean theorem.
Correct Answer: C — Right
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Q. In triangle MNO, if angle M = 45 degrees and angle N = 45 degrees, what is angle O?
A.
90 degrees
B.
45 degrees
C.
60 degrees
D.
30 degrees
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Solution
Angle O = 180 - (angle M + angle N) = 180 - (45 + 45) = 90 degrees.
Correct Answer: A — 90 degrees
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Q. In triangle PQR, if PQ = 10 cm, QR = 24 cm, and PR = 26 cm, what is the area of the triangle?
A.
120 cm²
B.
120√3 cm²
C.
240 cm²
D.
48 cm²
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Solution
Using Heron's formula, s = (10 + 24 + 26)/2 = 30. Area = √(30(30-10)(30-24)(30-26)) = √(30*20*6*4) = 120 cm².
Correct Answer: A — 120 cm²
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Q. In triangle XYZ, if XY = 8 cm, YZ = 15 cm, and XZ = 17 cm, is it a right triangle?
A.
Yes
B.
No
C.
Cannot be determined
D.
Only if XY is the hypotenuse
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Solution
Since 8^2 + 15^2 = 17^2, triangle XYZ is a right triangle.
Correct Answer: A — Yes
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Q. In which condition does a real gas behave most like an ideal gas?
A.
High pressure and low temperature
B.
Low pressure and high temperature
C.
High pressure and high temperature
D.
Low pressure and low temperature
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Solution
A real gas behaves most like an ideal gas under low pressure and high temperature conditions.
Correct Answer: B — Low pressure and high temperature
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Q. In which direction does the magnetic field point in relation to the current in a straight conductor?
A.
Parallel to the current
B.
Perpendicular to the current
C.
Opposite to the current
D.
In the same direction as the current
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Solution
The magnetic field around a straight conductor is always perpendicular to the direction of the current.
Correct Answer: B — Perpendicular to the current
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Q. In which direction does the magnetic field point inside a bar magnet?
A.
From south to north
B.
From north to south
C.
In a circular path
D.
It has no direction
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Solution
The magnetic field inside a bar magnet points from the north pole to the south pole.
Correct Answer: B — From north to south
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Q. In which direction does the magnetic field point inside a current-carrying loop?
A.
Out of the plane
B.
Into the plane
C.
Clockwise
D.
Counterclockwise
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Solution
Using the right-hand rule, the magnetic field inside a current-carrying loop points into the plane of the loop.
Correct Answer: B — Into the plane
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Q. In which medium does sound travel fastest?
A.
Air
B.
Water
C.
Steel
D.
Vacuum
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Solution
Sound travels fastest in solids like steel due to closely packed molecules.
Correct Answer: C — Steel
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Q. In which mode of heat transfer does the temperature difference drive the flow of heat?
A.
Conduction
B.
Convection
C.
Radiation
D.
Insulation
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Solution
Convection is the mode of heat transfer where the temperature difference causes the fluid to move, transferring heat.
Correct Answer: B — Convection
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Q. In which mode of heat transfer does the transfer of energy occur through electromagnetic waves?
A.
Conduction
B.
Convection
C.
Radiation
D.
Insulation
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Solution
Radiation is the mode of heat transfer that occurs through electromagnetic waves, such as infrared radiation.
Correct Answer: C — Radiation
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Q. In which of the following cases does a material exhibit plastic deformation?
A.
When the stress is below the yield point
B.
When the stress exceeds the yield point
C.
When the material is unloaded
D.
When the material is cooled
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Solution
Plastic deformation occurs when the stress exceeds the yield point.
Correct Answer: B — When the stress exceeds the yield point
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Q. In which of the following cases does the mesomeric effect dominate over the inductive effect?
A.
Aromatic compounds
B.
Aliphatic compounds
C.
Alkynes
D.
Alkenes
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Solution
In aromatic compounds, the mesomeric effect dominates due to resonance stabilization.
Correct Answer: A — Aromatic compounds
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Q. In which of the following cases is the magnetic field zero?
A.
At the center of a current-carrying loop
B.
Inside a solenoid with no current
C.
Near a straight wire carrying current
D.
At the midpoint between two parallel wires carrying equal currents in opposite directions
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Solution
The magnetic field is zero at the midpoint between two parallel wires carrying equal currents in opposite directions.
Correct Answer: D — At the midpoint between two parallel wires carrying equal currents in opposite directions
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