Question 12 Marks
Suppose $(1+k x)^n=1-12 x+60 x^2-\ldots . .$. find $k$ and $n$.
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The 3 rd term of $(1+x)^n$ is $36 x^2$. Find 5 th term.
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Using the binomial theorem, find the value of $\sqrt[3]{995}$ upto four places of decimals.
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State, first four terms in the expansion of $\left(1-\frac{2 x}{3}\right)^{-1 / 2}$
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Show that there is no constant term in the expansion of $\left(2 x-\frac{x^2}{4}\right)^9$
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Show that there is no term containing $x^6$ in the expansion of $\left(x^2-\frac{3}{x}\right)^{11}$.
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If the constant term in the expansion of $\left(x^3+\frac{k}{x^8}\right)^{11}$ is 1320 , find $k$.
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If the coefficients of $x^2$ and $x^3$ in theexpansion of $(3+k x)^9$ are equal, find $k$.
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If the middle term in the expansion of $\left(x+\frac{b}{x}\right)^6$ is 160 , find $b$.
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Find the constant term in the expansion of$\left(2 x^2-\frac{1}{x}\right)^{12}$
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Find the constant term in the expansion of$\left(\frac{4 x^2}{3}+\frac{3}{2 x}\right)^9$
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Find the coefficients of $x^{60}$ in the expansion of $\left(\frac{1}{x^2}+x^4\right)^{18}$
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Find the coefficients of $x^6$ in the expantion of $\left(3 x^2-\frac{1}{3 x}\right)^9$
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Find the middle term(s) in the expansion of $\left(x^2+2 y^2\right)^7$
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Expand $\left(3 x^2+2 y\right)^5$
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Show that $C_0+2 C_1+3 C_2+4 C_3+\ldots . .+(n+1) C_n=(n+2) 2^{n-1}$
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Show that $C_0+C_2+C_4+C_6+C_8=C_1+C_3+C_5+C_7=128$
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Use the binomial theorem to evaluate the following upto four places of decimals.$(0.98)^{-3}$
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Use the binomial theorem to evaluate the following upto four places of decimals.$(1.02)^{-5}$
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Use the binomial theorem to evaluate the following upto four places of decimals.$\sqrt[3]{126}$
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Use the binomial theorem to evaluate the following upto four places of decimals.
√99
Question 222 Marks
Simplify the first three terms in the expansion of the following:$(5-3 x)^{-1 / 3}$
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Simplify the first three terms in the expansion of the following:$(5+4 x)^{-1 / 2}$
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State by writing first four terms, the expansion of the following, where |b| < |a|.$(a+b)^{-1 / 3}$
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State by writing first four terms, the expansion of the following, where |b| < |a|.$(a-b)^{-1 / 4}$
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State by writing first four terms, the expansion of the following, where |b| < |a|.$(a+b)^{1 / 4}$
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State by writing first four terms, the expansion of the following, where |b| < |a|.$(a+b)^{-4}$
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State by writing first four terms, the expansion of the following, where |b| < |a|.$(a-b)^{-3}$
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State, by writing the first four terms, the expansion of the following, where |x| < 1. $(1+x)^{-1 / 5}$
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State, by writing the first four terms, the expansion of the following, where |x| < 1. $(1-x)^{1 / 3}$
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The coefficient of $x^2$ in the expansion of $(1+2 x)^m$ is 112 . Find $m$.
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In the expansion of $(k+x)^8$, the coefficient of $x^5$ is 10 times the coefficient of $x^6$. Find the value of k.
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Find the middle terms in the expansion of$\left(\frac{x}{a}-\frac{a}{x}\right)^{10}$
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Find the middle terms in the expansion of$\left(x^2-\frac{2}{x}\right)^8$
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Find the middle terms in the expansion of$\left(\frac{x}{y}+\frac{y}{x}\right)^{12}$
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Find the constant term (term independent of x) in the expansion of$\left(2 x^2-\frac{5}{x}\right)^9$
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Find the constant term (term independent of x) in the expansion of$\left(x^2-\frac{1}{x}\right)^9$
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Find the constant term (term independent of x) in the expansion of$\left(\sqrt{x}-\frac{3}{x^2}\right)^{10}$
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In the following expansions, find the indicated term.In $\left(3 a+\frac{4}{a}\right)^{13}, 10$ th term
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In the following expansions, find the indicated term.In $\left(\frac{1}{3}+a^2\right)^{12}, 9$ th term
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In the following expansions, find the indicated term.$\left(\frac{4 x}{5}-\frac{5}{2 x}\right)^9, 7$ th term
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In the following expansions, find the indicated term.$\left(x^2-\frac{4}{x^3}\right)^{11}, 5$ th term
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In the following expansions, find the indicated term.$\left(2 x^2+\frac{3}{2 x}\right)^8, 3$ rd term
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Find the value of $(0.9)^6$, correct upto four places of decimals.
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Find the value of $(1.01)^5$, correct upto three places of decimals.
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Find the value of $(1.02)^6$, correct upto four places of decimals.
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Without expanding, find the value of$(2 x-1)^4+4(2 x-1)^3(3-2 x)+6(2 x-1)^2(3-2 x)^2+4(2 x-1)^1(3-2 x)^3+(3-2 x)^4$
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Without expanding, find the value of$(x+1)^4-4(x+1)^3(x-1)+6(x+1)^2(x-1)^2-4(x+1)(x-1)^3+(x-1)^4$
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Using binomial theorem, find the value of$(0.9)^4$
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Using binomial theorem, find the value of$(9.9)^3$
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