CBSE Mathematics MCQs Quiz

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) = -