Welcome to Class 11 Maths MCQ – Limits and Derivatives chapter. Here, we’ve assembled 20 multiple-choice questions on Limits and Derivatives in Maths, each MCQ is followed by the correct answer and an explanation.

## 1. What is the limit of (x² – 4) / (x – 2) as x approaches 2?

### Answer:

### Explanation:

By factoring the numerator as (x+2)(x-2), and then canceling out (x-2), we get x+2. At x=2, this is 4.

## 2. The derivative of x³ with respect to x is:

### Answer:

### Explanation:

Using the power rule, the derivative is 3x².

## 3. If f(x) = x² + 4x + 4, then f'(x) is:

### Answer:

### Explanation:

Differentiating term-by-term, we get 2x + 4.

## 4. What is the limit of sin(x) / x as x approaches 0?

### Answer:

### Explanation:

This is a classic limit in calculus. As x approaches 0, sin(x)/x approaches 1.

## 5. The derivative of √x with respect to x is:

### Answer:

### Explanation:

Rewriting √x as x^(1/2) and differentiating using the power rule gives 1/2x^(-1/2), which is 1/2√x.

## 6. If f(x) = 1/x, then f'(x) is:

### Answer:

### Explanation:

Using the power rule on x^(-1) gives -x^(-2) or -1/x².

## 7. The derivative of ln(x) with respect to x is:

### Answer:

### Explanation:

The derivative of the natural logarithm, ln(x), is 1/x.

## 8. What is the limit of (x² – 9) / (x – 3) as x approaches 3?

### Answer:

### Explanation:

Factorizing the numerator as (x+3)(x-3), and then canceling out (x-3), we get x+3. At x=3, this is 6.

## 9. The limit of (1 + 1/x)^x as x approaches infinity is:

### Answer:

### Explanation:

This is a fundamental limit in calculus that defines the number e.

## 10. The derivative of a constant is:

### Answer:

### Explanation:

Constants don't change, so their rate of change (derivative) is 0.

## 11. What is the limit of x/x as x approaches 0?

### Answer:

### Explanation:

The function is always 1 for all x ≠ 0.

## 12. The derivative of e^x with respect to x is:

### Answer:

### Explanation:

The function e^x is its own derivative.

## 13. If f(x) = x^4, then f''(x) is:

### Answer:

### Explanation:

First derivative is 4x³, and the second derivative is 12x².

## 14. What is the limit of tan(x) as x approaches π/2 from the left?

### Answer:

### Explanation:

As x approaches π/2 from the left, tan(x) approaches infinity.

## 15. The derivative of cos(x) is:

### Answer:

### Explanation:

The rate of change of cos(x) is -sin(x).

## 16. What is the limit of (3x² + 2x – 5) as x approaches 2?

### Answer:

### Explanation:

Plugging in x = 2 into the polynomial gives 17.

## 17. The derivative of log(x) to the base 10 is:

### Answer:

### Explanation:

The derivative of log to the base 10 is 1/(x ln(10)).

## 18. The limit of 1/x as x approaches infinity is:

### Answer:

### Explanation:

As x grows larger, 1/x becomes closer to 0.

## 19. If f(x) = 2^x, its derivative is:

### Answer:

### Explanation:

The derivative of a^x is ln(a) * a^x.

## 20. The slope of the tangent to the curve y = x^2 at x = 2 is:

### Answer:

### Explanation:

The derivative of x^2 is 2x. At x=2, this is 4.