Class 12 Binomial Theorem Exercise 2.1 Solutions | Basic Mathematics Sukunda Pustak Bhawan

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1) Expand each of the following by the binomial theorem and simplify:

Question 1 a)

Class 12 Binomial Theorem Exercise 2.1 Solutions | Basic Mathematics Sukunda Pustak Bhawan

1) Expand each of the following by the binomial theorem and simplify:

Expand by binomial theorem and simplify.$\rm (a + b)^7 $

Expand by binomial theorem and simplify.$\rm (2x - 3y)^4 $

Expand by binomial theorem and simplify.$\rm (2x + y^2)^5 $

Expand by binomial theorem and simplify.$\rm (\frac{x}{2} + \frac{2}{y})^5 $

Expand by binomial theorem and simplify.$\rm (x^2 + \frac {2}{y})^{5} $

2) Find the stated terms in the following cases:

Find seven term of $\rm (2x^2 + \frac {1}{x})^8 $.

Find seven term of $\rm (2x + y)^{12} $

Find seven term of $\rm (x - \frac {2}{x})^7 $

3) Find the general terms of the following:

Find the general term of $\rm (x^2 + \frac {1}{x})^6 $

Find the general term of $(\rm\frac {a}{b} + \frac {b}{a})^{2n + 1} $

4) Find the coefficients of:

Find the coefficient of $\rm x^5 $ in the expansion of $(\rm x + \frac {1}{2x})^7 $

Find the coefficient of $\rm x^2 $ in the expansion of $(\rm x^3 + \frac {a}{x})^{10} $

Find the coefficient of $\rm x^6 $ in the expansion of $(\rm 3x^2 - \frac {1}{3x})^9 $

5) Find the term independent (free) of x in the expansions of:

Find the term independent (free) of $\rm x$ in the expansion of $(\rm x^2 + \frac {1}{x})^{12} $.

Find the term independent (free) of $\rm x$ in the expansion of $(\rm 2x + \frac {1}{3x^2})^9$.

Find the term independent (free) of $\rm x$ in the expansion of $ (\rm x + \frac {1}{x})^{2n} $.

Find the term independent (free) of $\rm x$ in the expansion of $(\rm \frac {3x^2}{2} - \frac {1}{3x})^9 $.

Write down the fourth term in the expansion of $(\rm px + \frac {1}{x})^n$. If this term is independent of $\rm x$, find the value of $\rm n$. With this value of n, calculate the value of $\rm p $ given that the fourth term is $\rm \frac {5}{2}$.

If the coefficient of $\rm x^{-1}$ in the expansion of $(\rm x + \frac {k}{x^2})^5$ is 90, find the value of k.

7) Find the middle term or terms in the expansion of:

Find the middle term or terms in the expansion of $(\rm x + \frac {1}{x})^{18} $.

Find the middle term or terms in the expansion of $(\rm 2x + \frac {1}{x})^{17} $.

Find the middle term or terms in the expansion of $(\rm \frac {x}{a} - \frac {a}{x})^{2n + 1} $.

Find the middle term or terms in the expansion of $(\rm ax - \frac {1}{ax})^{2n} $.

Expand by binomial theorem and simplify.
$\rm (a + b)^7 $

Expand by binomial theorem and simplify.
$\rm (2x - 3y)^4 $

Expand by binomial theorem and simplify.
$\rm (2x + y^2)^5 $

Expand by binomial theorem and simplify.
$\rm (\frac{x}{2} + \frac{2}{y})^5 $

Expand by binomial theorem and simplify.
$\rm (x^2 + \frac {2}{y})^{5} $