CBSE Mathematics MCQs Quiz

Study Notes

CBSE Important Mathematics Multiple Choice Questions (MCQs)

In your preparations for the Central Board of Secondary Education (CBSE) exams, it's crucial to hone your problem-solving skills and familiarize yourself with the types of questions that may appear. Here, we'll delve into some important Mathematics multiple-choice questions, which will help you strengthen your conceptual understanding and boost your confidence.

1. Integer and Rational Numbers

Question: Which of the following is not a rational number?

A) 2 B) 1.3 C) 0.6 D) -7

Answer: A) 2

Explanation: A rational number can be expressed as a fraction or an integer divided by another integer that is not zero. However, A) 2 is simply an integer—not a fraction or a division of integers—and thus is not a rational number.

2. Algebra

Question: Which of the following is equal to x² + 3x + 2?

A) x + 2 B) 2x + 1 C) x² + 1 D) x² + 3

Answer: D) x² + 3

Explanation: To solve for the expression that is equal to x² + 3x + 2, we can factor out the common term x: (x + 2)(x + 1) ⟹ x² + 3x + 2. However, other options do not factor out x: A) x + 2 = x + 2x + 0, B) 2x + 1 = 2x + 2 + (-1), and C) x² + 1 = x² + 2x + 1 – 1. Thus, D) x² + 3 is the only correct answer.

3. Geometry

Question: Which of the following is an exterior angle of a triangle?

A) 180 degrees B) 90 degrees C) 360 degrees D) 45 degrees

Answer: A) 180 degrees

Explanation: An exterior angle of a triangle is formed by drawing a line from a vertex of the triangle outside the triangle, extending to the line containing the opposite side. The sum of the three exterior angles of a triangle is equal to 360 degrees, while each interior angle of a triangle adds up to 180 degrees. Therefore, exterior angles are always greater than 180 degrees, and the answer D) 45 degrees is incorrect.

4. Trigonometry

Question: If sin(θ) = √3/2, then what is cos(θ)?

A) √3/2 B) 1/√3 C) √2/2 D) 1/2

Answer: B) 1/√3

Explanation: To find the cosine of an angle when we know the sine, we can use the Pythagorean identity: sin²(θ) + cos²(θ) = 1. Plugging in the given value of sin(θ): (√3/2)² + cos²(θ) = 1, so cos²(θ) = 1 - (√3/2)² = 1 - 3/4 = 1/4. The square root of 1/4 is 1/√3. Since cosine is positive in the first and fourth quadrants, and θ is in the first quadrant, the answer is B) 1/√3.

5. Coordinate Geometry

Question: Which of the following points lies on the x-axis?

A) (2, 5) B) (0, 7) C) (-4, 4) D) (3, 4)

Answer: B) (0, 7)

Explanation: The x-axis is a horizontal line, and its equation is y = 0. To determine if a point lies on the x-axis, substitute its y-coordinate into the equation of the x-axis: y = 0. Only B) (0, 7) satisfies this equation.

6. Data Analysis

Question: What is the mode of the data set {2, 2, 3, 4, 4}?

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

Answer: B) 2

Explanation: The mode is the value in the data set that occurs most frequently. In this case, the value 2 appears twice while the other values appear only once. Therefore, the mode is B) 2.

7. Probability

Question: What is the probability of rolling a number greater than 4 on a six-sided die?

A) 1/2 B) 1/3 C) 3/4 D) 2/3

Answer: B) 1/3

Explanation: To find the probability of rolling a number greater than 4, consider the favorable outcomes (rolling a 5 or a 6). There are 2 favorable outcomes (rolling a 5 or a 6) and 6 possible outcomes (rolling a 1, 2, 3, 4, 5, or 6). Thus, the probability is the ratio of favorable outcomes to possible outcomes: (2/6) = 1/3.

8. Calculus

Question: Which of the following functions has a positive derivative at x = 0?

A) f(x) = 2x² + 3x – 5 B) f(x) = x³ – 3x C) f(x) = 4x – x² D) f(x) = x + 4

Answer: C) f(x) = 4x – x²

Explanation: To determine the sign of the derivative at x = 0, find the derivative of each function:

A) f'(x) = 4x + 3 B) f'(x) = 3x² – 3 C) f'(x) = 4 – 2x D) f'(x) = 1

Now, evaluate the derivative at x = 0:

A) f'(0) = 3 B) f'(0) = -

Description

Test your knowledge with these multiple-choice questions covering topics like integers, algebra, geometry, trigonometry, coordinate geometry, data analysis, probability, and calculus to prepare for CBSE exams.