Welcome to Class 11 Maths MCQ – Binomial Theorem. Here, we curated a set of 20 multiple-choice questions to test your knowledge of the Binomial Theorem in Maths.

## 1. The binomial expansion of (a + b)^2 is:

### Answer:

### Explanation:

Using the Binomial theorem, (a + b)^2 = a^2 + 2ab + b^2.

## 2. The coefficient of x^2 in the expansion of (1 + x)^5 is:

### Answer:

### Explanation:

Using the formula nCk, we get 5C2 = 10.

## 3. In the expansion of (x + y)^n, the number of terms is:

### Answer:

### Explanation:

There are n+1 terms in the expansion.

## 4. The middle term in the expansion of (a + b)^6 is:

### Answer:

### Explanation:

The middle term is 6C3 * a^3 * b^3 = 20a^3b^3.

## 5. The term independent of x in the expansion of (2x + 3/x)^5 is:

### Answer:

### Explanation:

The term is 5C2 * (2x)^3 * (3/x)^2 = 243.

## 6. In the expansion of (1 + x)^n, the rth term is:

### Answer:

### Explanation:

Using the general term formula.

## 7. The coefficient of x^4 in (1 – x^2)^5 is:

### Answer:

### Explanation:

The term is 5C2 * (x^2)^2 = -10x^4.

## 8. The 3rd term in the expansion of (x^2 + 3/x)^6 is:

### Answer:

### Explanation:

6C2 * (x^2)^4 * (3/x)^2 = 540x^4.

## 9. In the binomial expansion of (a + b)^n, if the fifth term is four times the fourth term, then n is:

### Answer:

### Explanation:

Using the relationship of terms and simplifying, we get n = 8.

## 10. The general term of (x + y)^n is given by:

### Answer:

### Explanation:

It's derived from the binomial theorem's expansion.

## 11. If the coefficients of 2nd and 3rd terms in the expansion of (1 + x)^n are equal, then n is:

### Answer:

### Explanation:

For 2nd and 3rd terms to be equal, nC1 = nC2. This gives n = 5.

## 12. The coefficient of x^5 in the expansion of (1 + x)^9 is:

### Answer:

### Explanation:

It's given by 9C5 = 84.

## 13. The term independent of x in the expansion of (x + 1/x)^6 is:

### Answer:

### Explanation:

It's given by 6C3 * x^3 * (1/x)^3 = 15.

## 14. The binomial expansion of (a – b)^3 is:

### Answer:

### Explanation:

Using the binomial expansion formula.

## 15. The sum of the coefficients in the expansion of (x – y)^7 is:

### Answer:

### Explanation:

If we put x = 1 and y = 1, the sum becomes 2^7. Each term's coefficient when added gives 128, but half are subtracted out.

## 16. The coefficient of x^2 in (1 + x)^7 – (1 – x)^7 is:

### Answer:

### Explanation:

From (1 + x)^7, coefficient of x^2 is 7C2 and from (1 – x)^7 it's -7C2. The difference is 2*7C2 = 70.

## 17. In the expansion of (a + b)^8, the ratio of the 7th term to the 8th term is:

### Answer:

### Explanation:

Using the formula for the rth term, the ratio can be derived as 8:7.

## 18. The constant term in the expansion of (x + 3/x)^7 is:

### Answer:

### Explanation:

It's given by 7C3 * x^3 * (3/x)^4 = 2187.

## 19. The expansion of (x + y)^0 is:

### Answer:

### Explanation:

Any non-zero number raised to the power of 0 is 1.

## 20. The coefficient of the 4th term in the expansion of (x + y)^9 is:

### Answer:

### Explanation:

It's given by 9C3 = 84.