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. If two triangles are similar, and the lengths of the sides of the first triangle are 3, 4, and 5, what are the lengths of the corresponding sides of the second triangle if the shortest side is 6?

A. 6, 8, 10
B. 9, 12, 15
C. 12, 16, 20
D. 15, 20, 25

Solution

The ratio of the sides of similar triangles is constant. If the shortest side of the first triangle (3) corresponds to 6, then the sides are scaled by a factor of 2. Thus, the other sides are 4*2=8 and 5*2=10.

Correct Answer: A — 6, 8, 10

Q. If two triangles are similar, and the lengths of the sides of the first triangle are 3 cm, 4 cm, and 5 cm, what are the lengths of the sides of the second triangle if the shortest side is 6 cm?

A. 6 cm, 8 cm, 10 cm
B. 6 cm, 9 cm, 12 cm
C. 6 cm, 7 cm, 8 cm
D. 6 cm, 10 cm, 12 cm

Solution

The ratio of the sides is 6/3 = 2. Therefore, the other sides are 4*2 = 8 cm and 5*2 = 10 cm.

Correct Answer: A — 6 cm, 8 cm, 10 cm

Q. If two triangles are similar, and the lengths of the sides of the first triangle are 3 cm, 4 cm, and 5 cm, what are the lengths of the corresponding sides of the second triangle if the ratio of similarity is 2:1?

A. 6 cm, 8 cm, 10 cm
B. 3 cm, 4 cm, 5 cm
C. 1.5 cm, 2 cm, 2.5 cm
D. 4 cm, 5 cm, 6 cm

Solution

If the ratio is 2:1, then the sides of the second triangle are 3*2, 4*2, and 5*2, which gives 6 cm, 8 cm, and 10 cm.

Correct Answer: A — 6 cm, 8 cm, 10 cm

Q. If two triangles are similar, what can be said about their areas?

A. They are equal
B. They are proportional to the square of the ratio of their corresponding sides
C. They are proportional to the ratio of their corresponding sides
D. They cannot be compared

Solution

The areas of similar triangles are proportional to the square of the ratio of their corresponding sides.

Correct Answer: B — They are proportional to the square of the ratio of their corresponding sides

Q. If two triangles are similar, what can be said about their corresponding angles?

A. They are equal
B. They are supplementary
C. They are complementary
D. They are unequal

Solution

In similar triangles, corresponding angles are equal.

Correct Answer: A — They are equal

Q. If two triangles are similar, what can be said about their corresponding sides?

A. They are equal.
B. They are proportional.
C. They are congruent.
D. They are not related.

Solution

In similar triangles, the corresponding sides are proportional.

Correct Answer: B — They are proportional.

Q. If two triangles are similar, what is the ratio of their areas if the ratio of their corresponding sides is 3:4?

A. 3:4
B. 9:16
C. 12:16
D. 1:1

Solution

The ratio of the areas of similar triangles is the square of the ratio of their corresponding sides. Therefore, (3/4)² = 9/16.

Correct Answer: B — 9:16

Q. If two triangles are similar, what is the ratio of their areas if the ratio of their corresponding sides is 3:5?

A. 3:5
B. 9:25
C. 15:25
D. 6:10

Solution

The ratio of the areas of similar triangles is the square of the ratio of their corresponding sides. Thus, (3/5)² = 9/25.

Correct Answer: B — 9:25

Q. If two triangles are similar, what is the ratio of their corresponding sides if the ratio of their areas is 9:16?

A. 3:4
B. 2:3
C. 4:3
D. 1:2

Solution

The ratio of the sides of similar triangles is the square root of the ratio of their areas. sqrt(9:16) = 3:4.

Correct Answer: A — 3:4

Q. If two triangles are similar, what is true about their corresponding angles?

A. They are equal
B. They are supplementary
C. They are complementary
D. They are different

Solution

In similar triangles, corresponding angles are equal.

Correct Answer: A — They are equal

Q. If two triangles are similar, what is true about their corresponding sides?

A. They are equal in length
B. They are proportional
C. They are perpendicular
D. They are congruent

Solution

In similar triangles, the lengths of corresponding sides are proportional.

Correct Answer: B — They are proportional

Q. If two triangles are similar, which of the following is true about their corresponding sides?

A. They are equal
B. They are proportional
C. They are congruent
D. They are perpendicular

Solution

In similar triangles, the corresponding sides are proportional to each other.

Correct Answer: B — They are proportional

Q. If two triangles have sides in the ratio 3:4, what can be said about their areas?

A. The areas are in the ratio 3:4.
B. The areas are in the ratio 9:16.
C. The areas are equal.
D. The areas are not related.

Solution

The areas of similar triangles are in the ratio of the squares of their corresponding sides. Therefore, (3:4)² = 9:16.

Correct Answer: B — The areas are in the ratio 9:16.

Q. If two triangles have sides in the ratio 3:4, what is the ratio of their areas?

A. 3:4
B. 9:16
C. 12:16
D. 6:8

Solution

The ratio of the areas of two similar triangles is the square of the ratio of their corresponding sides. Therefore, (3:4)² = 9:16.

Correct Answer: B — 9:16

Q. If two triangles have sides in the ratio 3:4:5, what can be said about their similarity?

A. They are similar
B. They are congruent
C. They are not similar
D. Not enough information

Solution

Triangles with sides in the same ratio are similar.

Correct Answer: A — They are similar

Q. If two triangles have sides in the ratio 3:4:5, what type of triangle are they?

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

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

Q. If x^2 + 6x + 9 = 0, what are the roots?

A. -3
B. 3
C. 0
D. 6

Solution

The polynomial can be factored as (x + 3)(x + 3) = 0, giving the root x = -3.

Correct Answer: A — -3

Q. If x^2 - 4x + 4 = 0, what is the repeated root?

A. 2
B. 4
C. 0
D. 1

Solution

Factoring gives (x - 2)(x - 2) = 0, so the repeated root is x = 2.

Correct Answer: A — 2

Q. If x^2 - 4x + k has a double root, what is the value of k?

A. 4
B. 0
C. 8
D. 16

Solution

For a double root, the discriminant must be zero: b^2 - 4ac = 0. Here, 4^2 - 4(1)(k) = 0. Thus, 16 - 4k = 0, leading to k = 4.

Correct Answer: A — 4

Q. If x^2 - 6x + 9 = 0, what is the repeated root?

A. 3
B. 6
C. 9
D. 0

Solution

The polynomial can be factored as (x - 3)(x - 3) = 0, giving a repeated root of x = 3.

Correct Answer: A — 3

Q. If you divide 1/2 by 1/4, what do you get?

A. 1/2
B. 1
C. 2
D. 4

Solution

1/2 ÷ 1/4 = 1/2 x 4/1 = 2.

Correct Answer: C — 2

Q. If you eat 1/4 of a pizza and there are 3 pizzas, how much pizza is left?

A. 2.25
B. 2.5
C. 2
D. 1.75

Solution

3 pizzas - (3 * 1/4) = 3 - 0.75 = 2.25 pizzas left.

Correct Answer: B — 2.5

Q. If you eat 1/4 of a pizza and there are 4 slices, how many slices are left?

A. 3
B. 2
C. 1
D. 4

Solution

4 slices - 1 slice (1/4 of 4) = 3 slices left.

Correct Answer: A — 3

Q. If you eat 1/4 of a pizza and your friend eats 1/4 of the same pizza, how much of the pizza is left?

A. 1/2
B. 1/4
C. 3/4
D. 1/8

Solution

1 - (1/4 + 1/4) = 1/2 of the pizza is left.

Correct Answer: A — 1/2

Q. If you flip a fair coin three times, what is the probability of getting exactly two heads?

A. 1/8
B. 3/8
C. 3/4
D. 1/2

Solution

The probability of getting exactly 2 heads in 3 flips = C(3,2) * (1/2)^2 * (1/2)^1 = 3/8.

Correct Answer: B — 3/8

Q. If you have 0.75 of a pizza and eat 0.25, how much is left?

A. 0.25
B. 0.5
C. 0.75
D. 1.0

Solution

0.75 - 0.25 = 0.5

Correct Answer: B — 0.5

Q. If you have 0.8 of a pizza and eat 0.3, how much is left?

A. 0.3
B. 0.4
C. 0.5
D. 0.6

Solution

0.8 - 0.3 = 0.5

Correct Answer: B — 0.4

Q. If you have 1.2 liters of juice and pour out 0.2 liters, how much juice is left?

A. 0.8
B. 1.0
C. 1.2
D. 1.4

Solution

1.2 - 0.2 = 1.0

Correct Answer: A — 0.8

Q. If you have 1.2 liters of juice and pour out 0.7 liters, how much juice is left?

A. 0.3
B. 0.4
C. 0.5
D. 0.6

Solution

1.2 - 0.7 = 0.5

Correct Answer: D — 0.6

Q. If you have 1.2 liters of juice and you drink 0.5 liters, how much juice is left?

A. 0.7 liters
B. 0.6 liters
C. 0.5 liters
D. 0.8 liters

Solution

1.2 - 0.5 = 0.7 liters

Correct Answer: A — 0.7 liters

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