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# Lecture - 3 Chapter 8 Binomial Theorem

Total number of terms in a Binomial Expansion, General Term of Binomial Expansion, Finding Term in a Binomial Expansion

NCERT Exercise 8.2 |

Find the coefficient of

**Question 1. **\( x^5 \) in \((x+3)^8\)

**Question 2. **\( a^5b^7\) in \( (a-2b)^{12}\)

Write the general term in the expansion of

**Question 3. **\( (x^2-y)^6 \)

**Question 4. **\( (x^2-yx)^{12}, x \ne 0\)

**Question 5.** Find the 4^{th} term in the expansion of \( (x-2y)^{12}\).

**Question 6. **Find the 13^{th} term in the expansion of \( \left ( 9x – \frac{1}{3 \sqrt{x}} \right )^{18}, x \ne 0 \)

**Question 9.** In the expansion of \((1+a)^{m+n}\), prove that coefficients of *a ^{m}* and

*a*are equal.

^{n}**Question 12.** Find a positive value of *m* for which the coefficient of *x*^{2} in the expansion \((1+x)^m\) is 6.