Mathematics (School)

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Mathematics (School)

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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!

Algebra (Secondary) Arithmetic (Primary) Geometry Statistics & Probability Trigonometry

Q. In triangle PQR, if angle P = 30 degrees and angle Q = 60 degrees, what is the length of side PR if PQ = 10 cm?

A. 5 cm
B. 8.66 cm
C. 10 cm
D. 12 cm

Solution

Using the sine rule: PR/sin(30) = PQ/sin(60) => PR = 10 * sin(30)/sin(60) = 10 * 0.5/√3/2 = 10 * 0.5 * 2/√3 = 10/√3 ≈ 8.66 cm.

Correct Answer: B — 8.66 cm

Q. In triangle PQR, if angle P = 30 degrees and angle Q = 90 degrees, what is angle R?

A. 60 degrees
B. 30 degrees
C. 90 degrees
D. 120 degrees

Solution

Angle R = 180 - (30 + 90) = 60 degrees.

Correct Answer: A — 60 degrees

Q. In triangle PQR, if angle P = 30 degrees and angle Q = 90 degrees, what is the length of side PR if PQ = 10 cm?

A. 5 cm
B. 10 cm
C. 15 cm
D. 20 cm

Solution

In a right triangle, the side opposite the 30-degree angle is half the hypotenuse. Therefore, PR = PQ = 10 cm.

Correct Answer: B — 10 cm

Q. In triangle PQR, if angle P = 45 degrees and angle Q = 45 degrees, what is the type of triangle?

A. Scalene
B. Isosceles
C. Equilateral
D. Right

Solution

Since two angles are equal, triangle PQR is an isosceles triangle.

Correct Answer: B — Isosceles

Q. In triangle PQR, if angle P = 90 degrees and PQ = 6 cm, PR = 8 cm, what is the length of QR?

A. 10 cm
B. 12 cm
C. 14 cm
D. 16 cm

Solution

Using the Pythagorean theorem, QR = √(PQ² + PR²) = √(6² + 8²) = √(36 + 64) = √100 = 10 cm.

Correct Answer: A — 10 cm

Q. In triangle PQR, if PQ = 12 cm, PR = 16 cm, and QR = 20 cm, is triangle PQR similar to triangle ABC with sides 3 cm, 4 cm, and 5 cm?

A. Yes
B. No
C. Only if angles are equal
D. Not enough information

Solution

The sides of triangle PQR are in the ratio 12:16:20 = 3:4:5, which matches triangle ABC, confirming similarity.

Correct Answer: A — Yes

Q. In triangle PQR, if PQ = 12 cm, PR = 9 cm, and QR = 15 cm, which criterion can be used to prove that triangle PQR is not congruent to triangle STU with sides ST = 12 cm, SU = 9 cm, and TU = 14 cm?

A. SSS
B. SAS
C. ASA
D. AAS

Solution

Triangle PQR cannot be congruent to triangle STU by SSS since the third side QR (15 cm) is not equal to TU (14 cm).

Correct Answer: A — SSS

Q. In triangle PQR, if PQ = 5 cm, QR = 12 cm, and PR = 13 cm, is triangle PQR a right triangle?

A. Yes
B. No
C. Cannot be determined
D. Only if angle P is 90 degrees

Solution

Using the Pythagorean theorem, 5^2 + 12^2 = 25 + 144 = 169 = 13^2, so triangle PQR is a right triangle.

Correct Answer: A — Yes

Q. In triangle PQR, if PQ = 5 cm, QR = 12 cm, and PR = 13 cm, what type of triangle is it?

A. Acute
B. Obtuse
C. Right
D. Equilateral

Solution

Using the Pythagorean theorem, 5^2 + 12^2 = 25 + 144 = 169, which equals 13^2. Therefore, triangle PQR is a right triangle.

Correct Answer: C — Right

Q. In triangle PQR, if PQ = 6 cm, PR = 8 cm, and QR = 10 cm, is triangle PQR a right triangle?

A. Yes
B. No
C. Cannot be determined
D. Only if angle P is 90°

Solution

Using the Pythagorean theorem, if QR² = PQ² + PR², then 10² = 6² + 8², which gives 100 = 36 + 64 = 100. Therefore, triangle PQR is a right triangle.

Correct Answer: A — Yes

Q. In triangle PQR, if PQ = 6 cm, QR = 8 cm, and PR = 10 cm, what type of triangle is it?

A. Acute
B. Obtuse
C. Right
D. Equilateral

Solution

It is a right triangle because 6^2 + 8^2 = 36 + 64 = 100 = 10^2.

Correct Answer: C — Right

Q. In triangle PQR, if PQ = 7 cm, PR = 24 cm, and QR = 25 cm, what type of triangle is it?

A. Acute
B. Obtuse
C. Right
D. Equilateral

Solution

Using the Pythagorean theorem, 7² + 24² = 49 + 576 = 625 = 25², thus triangle PQR is a right triangle.

Correct Answer: C — Right

Q. In triangle PQR, if PQ = 8 cm, PR = 6 cm, and angle P = 90 degrees, what is the length of QR?

A. 10 cm
B. 12 cm
C. 14 cm
D. 16 cm

Solution

Using the Pythagorean theorem, QR = √(PQ² + PR²) = √(8² + 6²) = √(64 + 36) = √100 = 10 cm.

Correct Answer: A — 10 cm

Q. In triangle PQR, if PQ = 8 cm, PR = 6 cm, and QR = 10 cm, is triangle PQR a right triangle?

A. Yes
B. No
C. Cannot be determined
D. Only if angle P is 90 degrees

Solution

Using the Pythagorean theorem, if PQ² + PR² = QR², then it is a right triangle. 8² + 6² = 64 + 36 = 100 = 10².

Correct Answer: A — Yes

Q. In triangle PQR, if PQ = 8 cm, QR = 6 cm, and PR = 10 cm, what type of triangle is it?

A. Equilateral
B. Isosceles
C. Scalene
D. Right

Solution

Since all sides are of different lengths, triangle PQR is a scalene triangle.

Correct Answer: C — Scalene

Q. In triangle RST, if RS = 10 cm, ST = 24 cm, and RT = 26 cm, what is the perimeter of triangle RST?

A. 50 cm
B. 60 cm
C. 70 cm
D. 80 cm

Solution

The perimeter is the sum of all sides: 10 + 24 + 26 = 60 cm.

Correct Answer: A — 50 cm

Q. In triangle RST, if RS = 5 cm, ST = 12 cm, and RT = 13 cm, is triangle RST a right triangle?

A. Yes
B. No
C. Only if angle R is 90 degrees
D. Only if angle S is 90 degrees

Solution

Using the Pythagorean theorem, check if 5^2 + 12^2 = 13^2. 25 + 144 = 169, which is true. Therefore, triangle RST is a right triangle.

Correct Answer: A — Yes

Q. In triangle STU, if angle S = 30 degrees and angle T = 45 degrees, what is the measure of angle U?

A. 45 degrees
B. 30 degrees
C. 105 degrees
D. 75 degrees

Solution

The sum of angles in a triangle is 180 degrees. Therefore, angle U = 180 - (30 + 45) = 105 degrees.

Correct Answer: D — 75 degrees

Q. In triangle STU, if angle S = 30 degrees and angle T = 60 degrees, what is the measure of angle U?

A. 30 degrees
B. 60 degrees
C. 90 degrees
D. 120 degrees

Solution

The sum of angles in a triangle is 180 degrees. Therefore, angle U = 180 - (30 + 60) = 90 degrees.

Correct Answer: C — 90 degrees

Q. In triangle STU, if angle S = 30 degrees and angle T = 70 degrees, what is the length of side SU if ST = 10 cm and TU = 15 cm?

A. 7.5 cm
B. 10 cm
C. 12.5 cm
D. 15 cm

Solution

Using the Law of Sines: SU / sin(80) = 10 / sin(30). Therefore, SU = 10 * sin(80) / sin(30) = 10 * 0.9848 / 0.5 = 19.696 cm.

Correct Answer: C — 12.5 cm

Q. In triangle STU, if angle S = 45 degrees and angle T = 45 degrees, what is the type of triangle STU?

A. Acute
B. Obtuse
C. Right
D. Isosceles

Solution

Since two angles are equal, triangle STU is isosceles.

Correct Answer: D — Isosceles

Q. In triangle STU, if ST = 12 cm, TU = 16 cm, and SU = 20 cm, what is the perimeter of triangle STU?

A. 28 cm
B. 36 cm
C. 40 cm
D. 48 cm

Solution

The perimeter of triangle STU is ST + TU + SU = 12 + 16 + 20 = 48 cm.

Correct Answer: B — 36 cm

Q. In triangle STU, if ST = 7 cm, TU = 24 cm, and SU = 25 cm, is triangle STU a right triangle?

A. Yes
B. No
C. Only if angle S is 90 degrees
D. Only if angle T is 90 degrees

Solution

Using the Pythagorean theorem, 7^2 + 24^2 = 49 + 576 = 625, which equals 25^2. Therefore, triangle STU is a right triangle.

Correct Answer: A — Yes

Q. In triangle UVW, if angle U = 45 degrees and angle V = 45 degrees, what type of triangle is it?

A. Equilateral
B. Isosceles
C. Scalene
D. Right

Solution

Since two angles are equal (45 degrees each), triangle UVW is an isosceles triangle.

Correct Answer: B — Isosceles

Q. In triangle XYZ, if angle X = 45 degrees and angle Y = 45 degrees, what type of triangle is it?

A. Scalene
B. Isosceles
C. Equilateral
D. Right

Solution

Since two angles are equal, triangle XYZ is an isosceles triangle.

Correct Answer: B — Isosceles

Q. In triangle XYZ, if angle X = 90 degrees, angle Y = 45 degrees, and side XY = 10 units, what is the length of side XZ?

A. 10√2 units
B. 5√2 units
C. 10 units
D. 5 units

Solution

In a 45-45-90 triangle, the sides opposite the 45-degree angles are equal, and the hypotenuse is √2 times the length of each leg. Thus, XZ = XY√2 = 10√2 units.

Correct Answer: A — 10√2 units

Q. In triangle XYZ, if angle X is 30 degrees and angle Y is 60 degrees, what is angle Z?

A. 30 degrees
B. 60 degrees
C. 90 degrees
D. 120 degrees

Solution

The sum of the angles in a triangle is 180 degrees. Therefore, angle Z = 180 - (30 + 60) = 90 degrees.

Correct Answer: C — 90 degrees

Q. In triangle XYZ, if XY = 5 cm, YZ = 12 cm, and XZ = 13 cm, is triangle XYZ a right triangle?

A. Yes
B. No
C. Not enough information
D. Only if XY is the longest side

Solution

Triangle XYZ is a right triangle because 5² + 12² = 25 + 144 = 169 = 13².

Correct Answer: A — Yes

Q. In triangle XYZ, if XY = 7 cm, YZ = 24 cm, and XZ = 25 cm, is triangle XYZ a right triangle?

A. Yes
B. No
C. Only if angle Y is 90 degrees
D. Only if angle Z is 90 degrees

Solution

Using the Pythagorean theorem, 7^2 + 24^2 = 49 + 576 = 625 = 25^2, thus triangle XYZ is a right triangle.

Correct Answer: A — Yes

Q. In triangle XYZ, if XY = 8 cm, XZ = 6 cm, and YZ = 10 cm, what type of triangle is it?

A. Equilateral
B. Isosceles
C. Scalene
D. Right

Solution

Triangle XYZ is scalene because all sides have different lengths.

Correct Answer: C — Scalene

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