Binomial Expansion
« First Topic in Next Topic: General Terms and Middle Terms »
NEET DIGITAL LIBRARY
Binomial Theorem and its Simple Application

119563 If in the expansion of \(\left(2^x+\frac{1}{4^x}\right)^n, T_3=7 T_2\) and sum of the binomial coefficients of second and third terms is 36 , then the value of \(x\) is-

1 \(-1 / 3\)
2 \(-1 / 2\)
3 \(1 / 3\)
4 \(1 / 2\)
BITSAT-2009
Binomial Theorem and its Simple Application

119564 The coefficient of the middle term in the expansion of \((2+3 x)^4\) is :

1 6
2 5 !
3 8 !
4 216
CGPET-2010]
Binomial Theorem and its Simple Application

119565 If \(\mathrm{C}_0, \mathrm{C}_1, \mathrm{C}_2, \ldots . . \mathrm{C}_{\mathrm{n}}\) denote the binomial coefficients in the expansion of \((1+x)^n\), then the value of \(\mathbf{C}_0+\left(\mathbf{C}_0+\mathbf{C}_1\right)+\left(\mathbf{C}_0+\mathbf{C}_1+\mathbf{C}_2\right)+\) \(\ldots . .+\left(\mathbf{C}_0+\mathbf{C}_1+\ldots . .+\mathbf{C}_{\mathrm{n}-1}\right)\)

1 \(\mathrm{n} \cdot 2^{\mathrm{n}-1}\)
2 \(n .2^{\mathrm{n}}\)
3 \((\mathrm{n}-1) \cdot 2^{\mathrm{n}-1}\)
4 \((\mathrm{n}-1) \cdot 2^{\mathrm{n}}\)
BITSAT-2013
Binomial Theorem and its Simple Application

119566 The coefficient of \(x^{20}\) in the expansion of \(\left(1+x^2\right)^{40} \cdot\left(x^2+2+\frac{1}{x^2}\right)^{-5}\) is

1 \({ }^{30} \mathrm{C}_{10}\)
2 \({ }^{30} \mathrm{C}_{25}\)
3 1
4 None of these
BITSAT-2012
Join With Us for More Updates
Binomial Theorem and its Simple Application

119563 If in the expansion of \(\left(2^x+\frac{1}{4^x}\right)^n, T_3=7 T_2\) and sum of the binomial coefficients of second and third terms is 36 , then the value of \(x\) is-

1 \(-1 / 3\)
2 \(-1 / 2\)
3 \(1 / 3\)
4 \(1 / 2\)
BITSAT-2009
Binomial Theorem and its Simple Application

119564 The coefficient of the middle term in the expansion of \((2+3 x)^4\) is :

1 6
2 5 !
3 8 !
4 216
CGPET-2010]
Binomial Theorem and its Simple Application

119565 If \(\mathrm{C}_0, \mathrm{C}_1, \mathrm{C}_2, \ldots . . \mathrm{C}_{\mathrm{n}}\) denote the binomial coefficients in the expansion of \((1+x)^n\), then the value of \(\mathbf{C}_0+\left(\mathbf{C}_0+\mathbf{C}_1\right)+\left(\mathbf{C}_0+\mathbf{C}_1+\mathbf{C}_2\right)+\) \(\ldots . .+\left(\mathbf{C}_0+\mathbf{C}_1+\ldots . .+\mathbf{C}_{\mathrm{n}-1}\right)\)

1 \(\mathrm{n} \cdot 2^{\mathrm{n}-1}\)
2 \(n .2^{\mathrm{n}}\)
3 \((\mathrm{n}-1) \cdot 2^{\mathrm{n}-1}\)
4 \((\mathrm{n}-1) \cdot 2^{\mathrm{n}}\)
BITSAT-2013
Binomial Theorem and its Simple Application

119566 The coefficient of \(x^{20}\) in the expansion of \(\left(1+x^2\right)^{40} \cdot\left(x^2+2+\frac{1}{x^2}\right)^{-5}\) is

1 \({ }^{30} \mathrm{C}_{10}\)
2 \({ }^{30} \mathrm{C}_{25}\)
3 1
4 None of these
BITSAT-2012
For More Updates join with Us
NEET Test Series from KOTA - 10 Papers In MS WORD WhatsApp Here
Binomial Theorem and its Simple Application

119563 If in the expansion of \(\left(2^x+\frac{1}{4^x}\right)^n, T_3=7 T_2\) and sum of the binomial coefficients of second and third terms is 36 , then the value of \(x\) is-

1 \(-1 / 3\)
2 \(-1 / 2\)
3 \(1 / 3\)
4 \(1 / 2\)
BITSAT-2009
Binomial Theorem and its Simple Application

119564 The coefficient of the middle term in the expansion of \((2+3 x)^4\) is :

1 6
2 5 !
3 8 !
4 216
CGPET-2010]
Binomial Theorem and its Simple Application

119565 If \(\mathrm{C}_0, \mathrm{C}_1, \mathrm{C}_2, \ldots . . \mathrm{C}_{\mathrm{n}}\) denote the binomial coefficients in the expansion of \((1+x)^n\), then the value of \(\mathbf{C}_0+\left(\mathbf{C}_0+\mathbf{C}_1\right)+\left(\mathbf{C}_0+\mathbf{C}_1+\mathbf{C}_2\right)+\) \(\ldots . .+\left(\mathbf{C}_0+\mathbf{C}_1+\ldots . .+\mathbf{C}_{\mathrm{n}-1}\right)\)

1 \(\mathrm{n} \cdot 2^{\mathrm{n}-1}\)
2 \(n .2^{\mathrm{n}}\)
3 \((\mathrm{n}-1) \cdot 2^{\mathrm{n}-1}\)
4 \((\mathrm{n}-1) \cdot 2^{\mathrm{n}}\)
BITSAT-2013
Binomial Theorem and its Simple Application

119566 The coefficient of \(x^{20}\) in the expansion of \(\left(1+x^2\right)^{40} \cdot\left(x^2+2+\frac{1}{x^2}\right)^{-5}\) is

1 \({ }^{30} \mathrm{C}_{10}\)
2 \({ }^{30} \mathrm{C}_{25}\)
3 1
4 None of these
BITSAT-2012
NEET DIGITAL LIBRARY
Binomial Theorem and its Simple Application

119563 If in the expansion of \(\left(2^x+\frac{1}{4^x}\right)^n, T_3=7 T_2\) and sum of the binomial coefficients of second and third terms is 36 , then the value of \(x\) is-

1 \(-1 / 3\)
2 \(-1 / 2\)
3 \(1 / 3\)
4 \(1 / 2\)
BITSAT-2009
Binomial Theorem and its Simple Application

119564 The coefficient of the middle term in the expansion of \((2+3 x)^4\) is :

1 6
2 5 !
3 8 !
4 216
CGPET-2010]
Binomial Theorem and its Simple Application

119565 If \(\mathrm{C}_0, \mathrm{C}_1, \mathrm{C}_2, \ldots . . \mathrm{C}_{\mathrm{n}}\) denote the binomial coefficients in the expansion of \((1+x)^n\), then the value of \(\mathbf{C}_0+\left(\mathbf{C}_0+\mathbf{C}_1\right)+\left(\mathbf{C}_0+\mathbf{C}_1+\mathbf{C}_2\right)+\) \(\ldots . .+\left(\mathbf{C}_0+\mathbf{C}_1+\ldots . .+\mathbf{C}_{\mathrm{n}-1}\right)\)

1 \(\mathrm{n} \cdot 2^{\mathrm{n}-1}\)
2 \(n .2^{\mathrm{n}}\)
3 \((\mathrm{n}-1) \cdot 2^{\mathrm{n}-1}\)
4 \((\mathrm{n}-1) \cdot 2^{\mathrm{n}}\)
BITSAT-2013
Binomial Theorem and its Simple Application

119566 The coefficient of \(x^{20}\) in the expansion of \(\left(1+x^2\right)^{40} \cdot\left(x^2+2+\frac{1}{x^2}\right)^{-5}\) is

1 \({ }^{30} \mathrm{C}_{10}\)
2 \({ }^{30} \mathrm{C}_{25}\)
3 1
4 None of these
BITSAT-2012
Join With Us for More Updates