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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?
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A.
Acute
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B.
Obtuse
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C.
Right
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D.
Equilateral
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?
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?
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A.
30 cm
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B.
40 cm
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C.
50 cm
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D.
60 cm
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 cm, 15 cm, and 17 cm, what is the type of triangle?
-
A.
Acute
-
B.
Obtuse
-
C.
Right
-
D.
Equilateral
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, 15, and 17, what is the area of the triangle?
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A.
60
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B.
80
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C.
120
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D.
150
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
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?
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?
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A.
0.5
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B.
0.6
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C.
0.8
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D.
0.9
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?
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A.
Acute
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B.
Obtuse
-
C.
Right
-
D.
Equilateral
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?
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A.
Equilateral
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B.
Isosceles
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C.
Right
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D.
Scalene
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?
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A.
Acute
-
B.
Obtuse
-
C.
Right
-
D.
Equilateral
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?
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A.
90 degrees
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B.
45 degrees
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C.
60 degrees
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D.
30 degrees
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?
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A.
120 cm²
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B.
120√3 cm²
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C.
240 cm²
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D.
48 cm²
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?
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A.
Yes
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B.
No
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C.
Cannot be determined
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D.
Only if XY is the hypotenuse
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?
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A.
High pressure and low temperature
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B.
Low pressure and high temperature
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C.
High pressure and high temperature
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D.
Low pressure and low temperature
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?
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A.
Parallel to the current
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B.
Perpendicular to the current
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C.
Opposite to the current
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D.
In the same direction as the current
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?
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A.
From south to north
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B.
From north to south
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C.
In a circular path
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D.
It has no direction
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?
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A.
Out of the plane
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B.
Into the plane
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C.
Clockwise
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D.
Counterclockwise
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?
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A.
Air
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B.
Water
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C.
Steel
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D.
Vacuum
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?
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A.
Conduction
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B.
Convection
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C.
Radiation
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D.
Insulation
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?
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A.
Conduction
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B.
Convection
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C.
Radiation
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D.
Insulation
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?
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A.
When the stress is below the yield point
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B.
When the stress exceeds the yield point
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C.
When the material is unloaded
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D.
When the material is cooled
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?
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A.
Aromatic compounds
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B.
Aliphatic compounds
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C.
Alkynes
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D.
Alkenes
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?
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A.
At the center of a current-carrying loop
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B.
Inside a solenoid with no current
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C.
Near a straight wire carrying current
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D.
At the midpoint between two parallel wires carrying equal currents in opposite directions
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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Q. In which of the following compounds does the central atom exhibit dsp3 hybridization?
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A.
PCl5
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B.
SF6
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C.
XeF4
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D.
NH3
Solution
In PCl5, phosphorus exhibits dsp3 hybridization, forming five P-Cl bonds.
Correct Answer: A — PCl5
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Q. In which of the following compounds does the central atom exhibit sp hybridization?
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A.
C2H4
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B.
N2
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C.
HCl
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D.
C2H2
Solution
In C2H2, the carbon atoms are sp hybridized, forming a triple bond between them.
Correct Answer: D — C2H2
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Q. In which of the following compounds does the central atom have sp3d hybridization?
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A.
PCl5
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B.
SiCl4
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C.
XeF4
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D.
NH4Cl
Solution
In PCl5, the phosphorus atom is sp3d hybridized, allowing it to form five P-Cl bonds.
Correct Answer: A — PCl5
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Q. In which of the following compounds does the inductive effect play a significant role?
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A.
Benzene
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B.
Acetic acid
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C.
Cyclohexane
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D.
Ethylene
Solution
In acetic acid, the inductive effect of the –COOH group influences the acidity of the compound.
Correct Answer: B — Acetic acid
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Q. In which of the following compounds is the bond order equal to 1?
Solution
H2 has a bond order of 1, indicating a single bond between the two hydrogen atoms.
Correct Answer: C — H2
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Q. In which of the following conditions does a gas deviate most from ideal behavior?
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A.
High temperature and low pressure
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B.
Low temperature and high pressure
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C.
High temperature and high pressure
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D.
Low temperature and low pressure
Solution
A gas deviates most from ideal behavior at low temperatures and high pressures due to increased intermolecular forces.
Correct Answer: B — Low temperature and high pressure
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