Class 11 Binomial Theorem Basic Worksheet

Q1. Expand $(x + 2)^3$.

Worked Solution:
$x^3 + 3x^2(2) + 3x(2^2) + 2^3 = x^3 + 6x^2 + 12x + 8$.
Q2. Find the number of terms in the expansion of $(2x + 3y)^8$.

Worked Solution:
Number of terms = $n + 1 = 8 + 1 = 9$.
Q3. What is the general term of $(a+b)^n$?

Worked Solution:
$T_{r+1} = ^nC_r a^{n-r} b^r$.
Q4. Find the coefficient of $x^3$ in $(1+x)^5$.

Worked Solution:
$^5C_3 = \frac{5 \times 4}{2} = 10$.
Q5. Evaluate $(98)^2$ using binomial theorem.

Worked Solution:
$(100-2)^2 = 10000 - 400 + 4 = 9604$.
Q6. Expand $(1 - x)^4$.

Worked Solution:
$1 - 4x + 6x^2 - 4x^3 + x^4$.
Q7. Find the middle term in the expansion of $(x + y)^6$.

Worked Solution:
$n=6$ (even), so middle term is $(6/2 + 1) = 4$th term.
$T_4 = ^6C_3 x^3 y^3 = 20x^3y^3$.
Q8. Value of $^nC_0 + ^nC_n$.

Worked Solution:
$1 + 1 = 2$.
Q9. Write the first 2 terms of $(1+x)^{10}$.

Worked Solution:
$^1\!0C_0 + ^1\!0C_1 x = 1 + 10x$.
Q10. Find $^7C_4$.

Worked Solution:
$^7C_4 = ^7C_3 = \frac{7 \times 6 \times 5}{6} = 35$.

Standard Worksheet HOTS Worksheet

Chapter 7: Binomial Theorem