Mathematics (School) MCQ & Objective Questions
Mathematics is a crucial subject in school education, forming the foundation for various competitive exams. Mastering Mathematics (School) not only enhances problem-solving skills but also boosts confidence during exams. Practicing MCQs and objective questions is essential for effective exam preparation, as it helps students identify important questions and understand concepts clearly.
What You Will Practise Here
Number Systems and their properties
Algebraic Expressions and Equations
Geometry: Angles, Triangles, and Circles
Statistics and Probability concepts
Mensuration: Area, Volume, and Surface Area
Trigonometry basics and applications
Functions and Graphs
Exam Relevance
Mathematics (School) is a significant part of the curriculum for CBSE and State Boards, as well as competitive exams like NEET and JEE. Students can expect a variety of question patterns, including direct application of formulas, conceptual understanding, and problem-solving scenarios. Familiarity with MCQs in this subject can greatly enhance performance in both board and competitive examinations.
Common Mistakes Students Make
Misinterpreting the question, leading to incorrect answers.
Overlooking the importance of units in measurement-related problems.
Confusing similar formulas, especially in Geometry and Algebra.
Neglecting to check calculations, resulting in simple arithmetic errors.
Failing to understand the underlying concepts, which affects problem-solving ability.
FAQs
Question: How can I improve my speed in solving Mathematics (School) MCQs?Answer: Regular practice with timed quizzes and mock tests can significantly enhance your speed and accuracy.
Question: Are there any specific topics I should focus on for competitive exams?Answer: Focus on Algebra, Geometry, and Statistics, as these areas frequently appear in competitive exams.
Start your journey towards mastering Mathematics (School) today! Solve practice MCQs to test your understanding and prepare effectively for your exams. Remember, consistent practice leads to success!
Q. In triangle DEF, if angle D = 30° and angle E = 45°, what is angle F?
A.
105°
B.
90°
C.
75°
D.
60°
Show solution
Solution
Angle F = 180° - (30° + 45°) = 105°.
Correct Answer:
A
— 105°
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Q. In triangle DEF, if angle D = 30° and angle E = 45°, what is the measure of angle F?
A.
105°
B.
90°
C.
75°
D.
60°
Show solution
Solution
Angle F = 180° - (30° + 45°) = 105°.
Correct Answer:
A
— 105°
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Q. In triangle DEF, if angle D = 30° and angle E = 70°, what is the measure of angle F?
A.
80°
B.
70°
C.
60°
D.
50°
Show solution
Solution
Angle F = 180° - (30° + 70°) = 80°.
Correct Answer:
A
— 80°
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Q. In triangle DEF, if angle D = 40° and angle E = 70°, what is angle F?
A.
70°
B.
80°
C.
60°
D.
50°
Show solution
Solution
Angle F = 180° - (40° + 70°) = 70°.
Correct Answer:
B
— 80°
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Q. In triangle DEF, if angle D = 40° and angle E = 70°, what is the measure of angle F?
A.
70°
B.
80°
C.
90°
D.
100°
Show solution
Solution
Angle F = 180° - (40° + 70°) = 70°.
Correct Answer:
B
— 80°
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Q. In triangle DEF, if angle D = 45° and angle E = 45°, what is the type of triangle?
A.
Scalene
B.
Isosceles
C.
Equilateral
D.
Right
Show solution
Solution
Since two angles are equal, triangle DEF is an isosceles triangle.
Correct Answer:
B
— Isosceles
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Q. In triangle DEF, if angle D = 45° and angle E = 45°, what type of triangle is DEF?
A.
Scalene
B.
Isosceles
C.
Equilateral
D.
Right
Show solution
Solution
Since two angles are equal, triangle DEF is an isosceles triangle.
Correct Answer:
B
— Isosceles
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Q. In triangle DEF, if angle D = 45° and angle E = 45°, what type of triangle is it?
A.
Scalene
B.
Isosceles
C.
Equilateral
D.
Right
Show solution
Solution
A triangle with two equal angles is an isosceles triangle.
Correct Answer:
B
— Isosceles
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Q. In triangle DEF, if DE = 10 cm, DF = 15 cm, and angle E = 45 degrees, what is the length of EF using the Law of Cosines?
A.
5√2 cm
B.
10√2 cm
C.
15√2 cm
D.
20 cm
Show solution
Solution
Using the Law of Cosines: EF² = DE² + DF² - 2 * DE * DF * cos(E). EF² = 10² + 15² - 2 * 10 * 15 * cos(45°) = 100 + 225 - 150√2. Thus, EF = 5√2 cm.
Correct Answer:
A
— 5√2 cm
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Q. In triangle DEF, if DE = 10, DF = 6, and EF = 8, which side is the longest?
A.
DE
B.
DF
C.
EF
D.
All are equal
Show solution
Solution
DE = 10 is the longest side since 10 > 8 and 10 > 6.
Correct Answer:
A
— DE
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Q. In triangle DEF, if DE = 5 cm, EF = 12 cm, and DF = 13 cm, is the triangle a right triangle?
A.
Yes
B.
No
C.
Not enough information
D.
Only if angles are known
Show solution
Solution
Using the Pythagorean theorem, 5² + 12² = 25 + 144 = 169 = 13², thus triangle DEF is a right triangle.
Correct Answer:
A
— Yes
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Q. In triangle DEF, if DE = 5, EF = 12, and DF = 13, what type of triangle is it?
A.
Equilateral
B.
Isosceles
C.
Right
D.
Scalene
Show solution
Solution
Since 5^2 + 12^2 = 13^2 (25 + 144 = 169), triangle DEF is a right triangle.
Correct Answer:
C
— Right
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Q. In triangle DEF, if DE = 6 cm, DF = 8 cm, and angle E = 90 degrees, what is the length of EF?
A.
10 cm
B.
12 cm
C.
14 cm
D.
16 cm
Show solution
Solution
Using the Pythagorean theorem, EF = √(DE^2 + DF^2) = √(6^2 + 8^2) = √(36 + 64) = √100 = 10 cm.
Correct Answer:
A
— 10 cm
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Q. In triangle DEF, if DE = 6 cm, DF = 8 cm, and EF = 10 cm, is triangle DEF a right triangle?
A.
Yes
B.
No
C.
Not enough information
D.
Only if DE is the longest side
Show solution
Solution
By the Pythagorean theorem, if DE^2 + DF^2 = EF^2, then it is a right triangle. 6^2 + 8^2 = 36 + 64 = 100 = 10^2.
Correct Answer:
A
— Yes
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Q. In triangle DEF, if DE = 6 cm, DF = 8 cm, and EF = 10 cm, what is the area of the triangle?
A.
24 cm²
B.
30 cm²
C.
48 cm²
D.
60 cm²
Show solution
Solution
Using Heron's formula, s = (6 + 8 + 10) / 2 = 12. Area = √[s(s-a)(s-b)(s-c)] = √[12(12-6)(12-8)(12-10)] = √[12*6*4*2] = √576 = 24 cm².
Correct Answer:
B
— 30 cm²
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Q. In triangle DEF, if DE = 6 cm, DF = 8 cm, and EF = 10 cm, what is the area of triangle DEF?
A.
24 cm²
B.
30 cm²
C.
48 cm²
D.
60 cm²
Show solution
Solution
Using Heron's formula, the semi-perimeter s = (6 + 8 + 10) / 2 = 12 cm. Area = √[s(s-a)(s-b)(s-c)] = √[12(12-6)(12-8)(12-10)] = √[12*6*4*2] = √576 = 24 cm².
Correct Answer:
B
— 30 cm²
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Q. In triangle DEF, if DE = 6 cm, EF = 8 cm, and DF = 10 cm, is triangle DEF a right triangle?
A.
Yes
B.
No
C.
Cannot be determined
D.
Only if angle D is 90 degrees
Show solution
Solution
Triangle DEF satisfies the Pythagorean theorem (6² + 8² = 10²), thus it is a right triangle.
Correct Answer:
A
— Yes
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Q. In triangle DEF, if DE = 6, DF = 8, and EF = 10, is triangle DEF a right triangle?
A.
Yes
B.
No
C.
Not enough information
D.
Only if DE is the hypotenuse
Show solution
Solution
Using the Pythagorean theorem, 6² + 8² = 36 + 64 = 100 = 10², so triangle DEF is a right triangle.
Correct Answer:
A
— Yes
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Q. In triangle DEF, if DE = 6, DF = 8, and EF = 10, what is the type of triangle?
A.
Acute
B.
Obtuse
C.
Right
D.
Equilateral
Show solution
Solution
Since 6² + 8² = 10², triangle DEF is a right triangle.
Correct Answer:
C
— Right
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Q. In triangle DEF, if DE = 6, DF = 8, and EF = 10, what type of triangle is it?
A.
Acute
B.
Obtuse
C.
Right
D.
Equilateral
Show solution
Solution
Using the Pythagorean theorem, since 6² + 8² = 36 + 64 = 100 = 10², triangle DEF is a right triangle.
Correct Answer:
C
— Right
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Q. In triangle DEF, if DE = 6, EF = 8, and DF = 10, is triangle DEF a right triangle?
A.
Yes
B.
No
C.
Not enough information
D.
Only if angle D is 90 degrees
Show solution
Solution
Using the Pythagorean theorem, 6² + 8² = 36 + 64 = 100 = 10², thus triangle DEF is a right triangle.
Correct Answer:
A
— Yes
Learn More →
Q. In triangle DEF, if DE = 8 cm, EF = 6 cm, and DF = 10 cm, is triangle DEF a right triangle?
A.
Yes
B.
No
C.
Cannot be determined
D.
Only if angle D is 90 degrees
Show solution
Solution
Using the Pythagorean theorem: 8² + 6² = 64 + 36 = 100 = 10², so triangle DEF is a right triangle.
Correct Answer:
A
— Yes
Learn More →
Q. In triangle DEF, if DE = 8 cm, EF = 6 cm, and DF = 10 cm, what is the area of the triangle?
A.
24 cm²
B.
30 cm²
C.
36 cm²
D.
48 cm²
Show solution
Solution
Using Heron's formula, s = (8 + 6 + 10) / 2 = 12 cm. Area = √[s(s-a)(s-b)(s-c)] = √[12(12-8)(12-6)(12-10)] = √[12*4*6*2] = √144 = 12 cm².
Correct Answer:
B
— 30 cm²
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Q. In triangle DEF, if DE = 8 cm, EF = 6 cm, and DF = 10 cm, what type of triangle is DEF?
A.
Equilateral
B.
Isosceles
C.
Scalene
D.
Right
Show solution
Solution
Since all sides are of different lengths, triangle DEF is a scalene triangle.
Correct Answer:
C
— Scalene
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Q. In triangle GHI, if angle G = 30 degrees and angle H = 60 degrees, what is the length of side GH if side GI = 10 cm?
A.
5 cm
B.
8.66 cm
C.
10 cm
D.
12 cm
Show solution
Solution
Using the sine rule: GH/sin(30) = GI/sin(60). Therefore, GH = 10 * sin(30)/sin(60) = 10 * 0.5/(√3/2) = 10 * 1/√3 = 10/√3 ≈ 8.66 cm.
Correct Answer:
B
— 8.66 cm
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Q. In triangle GHI, if angle G = 30° and angle H = 45°, what is the measure of angle I?
A.
105°
B.
90°
C.
75°
D.
60°
Show solution
Solution
The sum of angles in a triangle is 180°. Therefore, angle I = 180° - (30° + 45°) = 105°.
Correct Answer:
A
— 105°
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Q. In triangle GHI, if angle G = 30° and angle H = 60°, what is the length of side g opposite angle G if side h opposite angle H is 10 units?
Show solution
Solution
Using the sine rule: g/h = sin(G)/sin(H) => g/10 = sin(30°)/sin(60°) => g = 10 * (1/2) / (√3/2) = 10/√3 = 8.66.
Correct Answer:
B
— 8.66
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Q. In triangle GHI, if angle G = 30° and angle H = 70°, what is the measure of angle I?
A.
80°
B.
60°
C.
50°
D.
40°
Show solution
Solution
The sum of angles in a triangle is 180°. Therefore, angle I = 180° - (30° + 70°) = 80°.
Correct Answer:
B
— 60°
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Q. In triangle GHI, if angle G = 45 degrees and angle H = 45 degrees, what type of triangle is it?
A.
Scalene
B.
Isosceles
C.
Equilateral
D.
Right
Show solution
Solution
A triangle with two equal angles is an isosceles triangle.
Correct Answer:
B
— Isosceles
Learn More →
Q. In triangle GHI, if angle G = 50 degrees and angle H = 70 degrees, what is the length of side GH if side GI = 10 cm?
A.
5 cm
B.
10 cm
C.
15 cm
D.
20 cm
Show solution
Solution
Using the Law of Sines, GH / sin(I) = GI / sin(G). Since angles sum to 180, angle I = 60 degrees. Thus, GH = 10 * sin(60) / sin(50).
Correct Answer:
B
— 10 cm
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