Binomial Expansion
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Binomial Theorem and its Simple Application

119322 If \(\left(\mathbf{1}+\mathbf{x}-2 \mathbf{x}^2\right)^6=\mathbf{1}+\mathbf{C}_1 \mathbf{x}+\mathbf{C}_2 \mathbf{x}^2+\mathbf{C}_3 \mathbf{x}^3+\ldots \ldots\).
\(+\mathrm{C}_{12} \mathrm{x}^{12}\), then the value of \(\mathrm{C}_2+\mathrm{C}_4+\mathrm{C}_6+\ldots .\).
\(+\mathrm{C}_{12}\) is

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JCECE-2013]
Binomial Theorem and its Simple Application

119323 If \(x, y\) and \(r\) are positive integers, then \({ }^{\mathrm{x}} \mathrm{C}_{\mathrm{r}}+{ }^{\mathrm{x}} \mathrm{C}_{\mathrm{r}-1}{ }^{\mathrm{y}} \mathrm{C}_1+{ }^{\mathrm{x}} \mathrm{C}_{\mathrm{r}-2}{ }^{\mathrm{y}} \mathrm{C}_2+\ldots \ldots .+{ }^{\mathrm{y}} \mathrm{C}_{\mathrm{r}}\) is

1 \({ }^{(\mathrm{x}+\mathrm{y})} \mathrm{C}_{\mathrm{r}}\)
2 \(\frac{\mathrm{x} ! \mathrm{y} !}{\mathrm{r} !}\)
3 \(\frac{(\mathrm{x}+\mathrm{y}) !}{\mathrm{r} !}\)
4 \({ }^{x y} C_r\)
SRM JEEE-2011
Binomial Theorem and its Simple Application

119324 Expansion of \(\log \left(1+3 x+2 x^2\right)\) is

1 \(3 x-5 x^2 / 4+9 x^3 / 3-17 x^4 / 4+\) \(\qquad\)
2 \(4 x-5 x^2 / 4+9 x^3 / 3-17 x^4 / 4+\ldots \ldots \ldots \infty\)
3 \(3 x-5 x^2 / 2+9 x^3 / 3-17 x^4 / 4+\ldots \ldots \ldots \ldots\)
4 \(-3 x-5 x^2 / 2-9 x^3 / 3-17 x^4 / 4+\ldots \ldots \ldots \infty\)
SRM JEEE-2016
Binomial Theorem and its Simple Application

119325 \(\left(x+\sqrt{x^3-1}\right)^5+\left(x-\sqrt{x^3-1}\right)^5\) is a polynomial of the order of

1 5
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4 8
BITSAT-2007
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Binomial Theorem and its Simple Application

119322 If \(\left(\mathbf{1}+\mathbf{x}-2 \mathbf{x}^2\right)^6=\mathbf{1}+\mathbf{C}_1 \mathbf{x}+\mathbf{C}_2 \mathbf{x}^2+\mathbf{C}_3 \mathbf{x}^3+\ldots \ldots\).
\(+\mathrm{C}_{12} \mathrm{x}^{12}\), then the value of \(\mathrm{C}_2+\mathrm{C}_4+\mathrm{C}_6+\ldots .\).
\(+\mathrm{C}_{12}\) is

1 30
2 32
3 31
4 33
JCECE-2013]
Binomial Theorem and its Simple Application

119323 If \(x, y\) and \(r\) are positive integers, then \({ }^{\mathrm{x}} \mathrm{C}_{\mathrm{r}}+{ }^{\mathrm{x}} \mathrm{C}_{\mathrm{r}-1}{ }^{\mathrm{y}} \mathrm{C}_1+{ }^{\mathrm{x}} \mathrm{C}_{\mathrm{r}-2}{ }^{\mathrm{y}} \mathrm{C}_2+\ldots \ldots .+{ }^{\mathrm{y}} \mathrm{C}_{\mathrm{r}}\) is

1 \({ }^{(\mathrm{x}+\mathrm{y})} \mathrm{C}_{\mathrm{r}}\)
2 \(\frac{\mathrm{x} ! \mathrm{y} !}{\mathrm{r} !}\)
3 \(\frac{(\mathrm{x}+\mathrm{y}) !}{\mathrm{r} !}\)
4 \({ }^{x y} C_r\)
SRM JEEE-2011
Binomial Theorem and its Simple Application

119324 Expansion of \(\log \left(1+3 x+2 x^2\right)\) is

1 \(3 x-5 x^2 / 4+9 x^3 / 3-17 x^4 / 4+\) \(\qquad\)
2 \(4 x-5 x^2 / 4+9 x^3 / 3-17 x^4 / 4+\ldots \ldots \ldots \infty\)
3 \(3 x-5 x^2 / 2+9 x^3 / 3-17 x^4 / 4+\ldots \ldots \ldots \ldots\)
4 \(-3 x-5 x^2 / 2-9 x^3 / 3-17 x^4 / 4+\ldots \ldots \ldots \infty\)
SRM JEEE-2016
Binomial Theorem and its Simple Application

119325 \(\left(x+\sqrt{x^3-1}\right)^5+\left(x-\sqrt{x^3-1}\right)^5\) is a polynomial of the order of

1 5
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4 8
BITSAT-2007
NEET DIGITAL LIBRARY
Binomial Theorem and its Simple Application

119322 If \(\left(\mathbf{1}+\mathbf{x}-2 \mathbf{x}^2\right)^6=\mathbf{1}+\mathbf{C}_1 \mathbf{x}+\mathbf{C}_2 \mathbf{x}^2+\mathbf{C}_3 \mathbf{x}^3+\ldots \ldots\).
\(+\mathrm{C}_{12} \mathrm{x}^{12}\), then the value of \(\mathrm{C}_2+\mathrm{C}_4+\mathrm{C}_6+\ldots .\).
\(+\mathrm{C}_{12}\) is

1 30
2 32
3 31
4 33
JCECE-2013]
Binomial Theorem and its Simple Application

119323 If \(x, y\) and \(r\) are positive integers, then \({ }^{\mathrm{x}} \mathrm{C}_{\mathrm{r}}+{ }^{\mathrm{x}} \mathrm{C}_{\mathrm{r}-1}{ }^{\mathrm{y}} \mathrm{C}_1+{ }^{\mathrm{x}} \mathrm{C}_{\mathrm{r}-2}{ }^{\mathrm{y}} \mathrm{C}_2+\ldots \ldots .+{ }^{\mathrm{y}} \mathrm{C}_{\mathrm{r}}\) is

1 \({ }^{(\mathrm{x}+\mathrm{y})} \mathrm{C}_{\mathrm{r}}\)
2 \(\frac{\mathrm{x} ! \mathrm{y} !}{\mathrm{r} !}\)
3 \(\frac{(\mathrm{x}+\mathrm{y}) !}{\mathrm{r} !}\)
4 \({ }^{x y} C_r\)
SRM JEEE-2011
Binomial Theorem and its Simple Application

119324 Expansion of \(\log \left(1+3 x+2 x^2\right)\) is

1 \(3 x-5 x^2 / 4+9 x^3 / 3-17 x^4 / 4+\) \(\qquad\)
2 \(4 x-5 x^2 / 4+9 x^3 / 3-17 x^4 / 4+\ldots \ldots \ldots \infty\)
3 \(3 x-5 x^2 / 2+9 x^3 / 3-17 x^4 / 4+\ldots \ldots \ldots \ldots\)
4 \(-3 x-5 x^2 / 2-9 x^3 / 3-17 x^4 / 4+\ldots \ldots \ldots \infty\)
SRM JEEE-2016
Binomial Theorem and its Simple Application

119325 \(\left(x+\sqrt{x^3-1}\right)^5+\left(x-\sqrt{x^3-1}\right)^5\) is a polynomial of the order of

1 5
2 6
3 7
4 8
BITSAT-2007
Join With Us for More Updates
Binomial Theorem and its Simple Application

119322 If \(\left(\mathbf{1}+\mathbf{x}-2 \mathbf{x}^2\right)^6=\mathbf{1}+\mathbf{C}_1 \mathbf{x}+\mathbf{C}_2 \mathbf{x}^2+\mathbf{C}_3 \mathbf{x}^3+\ldots \ldots\).
\(+\mathrm{C}_{12} \mathrm{x}^{12}\), then the value of \(\mathrm{C}_2+\mathrm{C}_4+\mathrm{C}_6+\ldots .\).
\(+\mathrm{C}_{12}\) is

1 30
2 32
3 31
4 33
JCECE-2013]
Binomial Theorem and its Simple Application

119323 If \(x, y\) and \(r\) are positive integers, then \({ }^{\mathrm{x}} \mathrm{C}_{\mathrm{r}}+{ }^{\mathrm{x}} \mathrm{C}_{\mathrm{r}-1}{ }^{\mathrm{y}} \mathrm{C}_1+{ }^{\mathrm{x}} \mathrm{C}_{\mathrm{r}-2}{ }^{\mathrm{y}} \mathrm{C}_2+\ldots \ldots .+{ }^{\mathrm{y}} \mathrm{C}_{\mathrm{r}}\) is

1 \({ }^{(\mathrm{x}+\mathrm{y})} \mathrm{C}_{\mathrm{r}}\)
2 \(\frac{\mathrm{x} ! \mathrm{y} !}{\mathrm{r} !}\)
3 \(\frac{(\mathrm{x}+\mathrm{y}) !}{\mathrm{r} !}\)
4 \({ }^{x y} C_r\)
SRM JEEE-2011
Binomial Theorem and its Simple Application

119324 Expansion of \(\log \left(1+3 x+2 x^2\right)\) is

1 \(3 x-5 x^2 / 4+9 x^3 / 3-17 x^4 / 4+\) \(\qquad\)
2 \(4 x-5 x^2 / 4+9 x^3 / 3-17 x^4 / 4+\ldots \ldots \ldots \infty\)
3 \(3 x-5 x^2 / 2+9 x^3 / 3-17 x^4 / 4+\ldots \ldots \ldots \ldots\)
4 \(-3 x-5 x^2 / 2-9 x^3 / 3-17 x^4 / 4+\ldots \ldots \ldots \infty\)
SRM JEEE-2016
Binomial Theorem and its Simple Application

119325 \(\left(x+\sqrt{x^3-1}\right)^5+\left(x-\sqrt{x^3-1}\right)^5\) is a polynomial of the order of

1 5
2 6
3 7
4 8
BITSAT-2007
For More Updates join with Us