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
Show solution
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
Show solution
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 a = 8, b = 15, and c = 17, what is the perimeter?
Show solution
Solution
The perimeter of a triangle is the sum of its sides: a + b + c = 8 + 15 + 17 = 40.
Correct Answer:
A
— 30
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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
Show solution
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
Show solution
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
Show solution
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
Show solution
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
Show solution
Solution
Since 8^2 + 15^2 = 17^2, triangle XYZ is a right triangle.
Correct Answer:
A
— Yes
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Q. Solve the equation 2sin(x) + √3 = 0 for x in the interval [0, 2π].
A.
5π/3
B.
π/3
C.
2π/3
D.
4π/3
Show solution
Solution
Rearranging gives sin(x) = -√3/2, so x = 4π/3 and x = 5π/3.
Correct Answer:
A
— 5π/3
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Q. Solve the equation 2sin(x) - 1 = 0 for x in the interval [0, 2π].
A.
π/6
B.
5π/6
C.
π/2
D.
7π/6
Show solution
Solution
The solution is x = π/2.
Correct Answer:
C
— π/2
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Q. Solve the equation 3cos^2(x) - 1 = 0.
A.
x = π/3, 2π/3
B.
x = π/4, 3π/4
C.
x = 0, π
D.
x = π/6, 5π/6
Show solution
Solution
Rearranging gives cos^2(x) = 1/3, so x = π/3 and 2π/3.
Correct Answer:
A
— x = π/3, 2π/3
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Q. Solve the equation 3sin(x) - 4 = 0 for x in the interval [0, 2π].
A.
π/6
B.
π/3
C.
2π/3
D.
5π/6
Show solution
Solution
The solution is x = π/3.
Correct Answer:
B
— π/3
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Q. Solve the equation cos(x) + sin(x) = 1 for x in the interval [0, 2π].
A.
π/4
B.
π/2
C.
3π/4
D.
0
Show solution
Solution
The only solution is x = π/2.
Correct Answer:
B
— π/2
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Q. Solve the equation cos(x) = -1/2 for x in the interval [0, 2π].
A.
2π/3, 4π/3
B.
π/3, 5π/3
C.
π/2, 3π/2
D.
0, π
Show solution
Solution
The solutions are x = 2π/3 and x = 4π/3 in the interval [0, 2π].
Correct Answer:
A
— 2π/3, 4π/3
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Q. Solve the equation sin(2x) = 0 for x in the interval [0, 2π].
A.
0, π, 2π
B.
π/2, 3π/2
C.
π/4, 3π/4
D.
π/6, 5π/6
Show solution
Solution
The solutions are x = 0, π, 2π.
Correct Answer:
A
— 0, π, 2π
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Q. Solve the equation sin(2x) = 1 for x in the interval [0, 2π].
A.
π/4
B.
3π/4
C.
π/2
D.
5π/4
Show solution
Solution
The equation sin(2x) = 1 gives 2x = π/2 + 2nπ, hence x = π/4 + nπ/2. In [0, 2π], the solutions are π/4 and 5π/4.
Correct Answer:
C
— π/2
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Q. Solve the equation sin(2x) = √3/2 for x in the interval [0, 2π].
A.
π/12
B.
5π/12
C.
7π/12
D.
11π/12
Show solution
Solution
The solutions are x = π/12, 5π/12, 7π/12, and 11π/12.
Correct Answer:
A
— π/12
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Q. Solve the equation sin(3x) = 0 for x in the interval [0, 2π].
A.
0, π, 2π
B.
0, π/3, 2π/3
C.
0, π/2, π
D.
0, π/4, π/2
Show solution
Solution
The solutions are x = 0, π, 2π, and x = nπ/3 for n = 0, 1, 2, 3, 4, 5.
Correct Answer:
A
— 0, π, 2π
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Q. Solve the equation sin(x) = 0.5 for x in the interval [0, 2π].
A.
π/6
B.
5π/6
C.
7π/6
D.
11π/6
Show solution
Solution
The solutions are x = π/6 and x = 5π/6 in the interval [0, 2π].
Correct Answer:
A
— π/6
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Q. Solve the equation tan(x) = √3 for x in the interval [0, 2π].
A.
π/3
B.
2π/3
C.
4π/3
D.
5π/3
Show solution
Solution
The solutions are x = π/3 and x = 4π/3 in the interval [0, 2π].
Correct Answer:
A
— π/3
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Q. Solve the equation tan^2(x) = 3 for x in the interval [0, 2π].
A.
π/3
B.
2π/3
C.
4π/3
D.
5π/3
Show solution
Solution
The solutions are x = π/3 and x = 4π/3.
Correct Answer:
A
— π/3
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Q. Solve the equation tan^2(x) = 3.
A.
x = π/3
B.
x = 2π/3
C.
x = 4π/3
D.
x = 5π/3
Show solution
Solution
The solutions are x = π/3 and x = 4π/3.
Correct Answer:
A
— x = π/3
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Q. The area of triangle ABC is 24 cm², and the base BC = 8 cm. What is the height from A to BC?
A.
6 cm
B.
8 cm
C.
4 cm
D.
3 cm
Show solution
Solution
Area = 1/2 * base * height => 24 = 1/2 * 8 * height => height = 6 cm.
Correct Answer:
A
— 6 cm
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Q. The area of triangle ABC is 30 square units, and the base BC is 10 units. What is the height from A to BC?
A.
3 units
B.
6 units
C.
5 units
D.
4 units
Show solution
Solution
Area = 1/2 * base * height => 30 = 1/2 * 10 * height => height = 6 units.
Correct Answer:
B
— 6 units
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Q. The lengths of the sides of triangle ABC are 7 cm, 24 cm, and 25 cm. What type of triangle is it?
A.
Acute
B.
Obtuse
C.
Right
D.
Equilateral
Show solution
Solution
Since 7^2 + 24^2 = 25^2, triangle ABC is a right triangle.
Correct Answer:
C
— Right
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Q. What are the solutions of the equation cos(x) + sin(x) = 1?
A.
x = 0
B.
x = π/4
C.
x = π/2
D.
x = π
Show solution
Solution
The only solution is x = 0.
Correct Answer:
A
— x = 0
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Q. What are the solutions of the equation cos(x) = -1/2 in the interval [0, 2π]?
A.
2π/3, 4π/3
B.
π/3, 5π/3
C.
π/2, 3π/2
D.
0, π
Show solution
Solution
The solutions are x = 2π/3 and 4π/3.
Correct Answer:
A
— 2π/3, 4π/3
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Q. What are the solutions of the equation cos(x) = -1/2?
A.
2π/3
B.
4π/3
C.
π/3
D.
5π/3
Show solution
Solution
The solutions are x = 2π/3 and x = 4π/3.
Correct Answer:
A
— 2π/3
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Showing 211 to 240 of 285 (10 Pages)
Trigonometry MCQ & Objective Questions
Trigonometry is a crucial branch of mathematics that plays a significant role in various school and competitive exams. Mastering this subject can enhance your problem-solving skills and boost your confidence. Practicing MCQs and objective questions is essential for effective exam preparation, as it helps you identify important questions and strengthens your understanding of key concepts.
What You Will Practise Here
Fundamental Trigonometric Ratios: Sine, Cosine, and Tangent
Inverse Trigonometric Functions and Their Applications
Trigonometric Identities and Equations
Graphs of Trigonometric Functions
Applications of Trigonometry in Real-Life Problems
Height and Distance Problems
Solving Triangles: Area and Perimeter Calculations
Exam Relevance
Trigonometry is a vital topic in the CBSE curriculum and is frequently tested in State Boards, NEET, and JEE exams. Students can expect questions that assess their understanding of trigonometric ratios, identities, and real-world applications. Common question patterns include solving equations, proving identities, and applying concepts to practical scenarios.
Common Mistakes Students Make
Confusing the values of trigonometric ratios in different quadrants.
Neglecting to apply the correct identities while simplifying expressions.
Misinterpreting the angle measures, especially in height and distance problems.
Overlooking the importance of unit circle concepts in graphing functions.
FAQs
Question: What are some important Trigonometry MCQ questions for exams?Answer: Important questions often include finding the values of trigonometric ratios, solving trigonometric equations, and applying identities to simplify expressions.
Question: How can I effectively prepare for Trigonometry objective questions?Answer: Regular practice of MCQs, understanding key concepts, and reviewing mistakes can significantly improve your preparation.
Now is the time to enhance your Trigonometry skills! Dive into our practice MCQs and test your understanding to excel in your exams.
