Numerically Greatest Term

Q. The numerically greatest term in the expansion of $(3-5x{)}^{15}$ when $x=\frac{1}{5}$ is

1. $355\times 3^{12}$
2. $455\times 3^{11}$
3. $455\times 3^{12}$
4. $355\times 3^{11}$

Q. The sum of all those terms which are rational numbers in the expansion of ${(2^{1/3}+3^{1/4})}^{12}$ is

1. $43$
2. $27$
3. $35$
4. $89$

Q.

What does $\ln$ stands for?

Q.

If ${21}^{st}$ and ${22}^{nd}$ terms in the expansion of $(1+x{)}^{44}$ are equal, then $x$ is equal to

Q.

Find the numerically greatest term in the expansion of $(7-5x{)}^{11}$ when $x=\frac{2}{3}$.

1. 

2. 

3. 

4. 

Q.

$f\left(x\right)=x^5-5x^4+5x^3+1$ has

1. Two maximum and two minimum value

2. Two maximum and one minimum value

3. One maximum and one minimum value

4. None of the above

Q.

The term independent of $x$ in the expansion of ${\left[x^3-\frac{2}{x^2}\right]}^{15}$ is

1. ${\mathrm{T}}_7$

2. ${\mathrm{T}}_8$

3. ${\mathrm{T}}_9$

4. ${\mathrm{T}}_{10}$

Q.

The larger of ${99}^{50}+{100}^{50}and{101}^{50}$ is . . .

1. $(101{)}^{50}$

2. $(101{)}^{50}=(99{)}^{50}+(100{)}^{50}$

3. $(99{)}^{50}+(100{)}^{50}$

4. Can't be determined.

Q. If $4^{th}$ term in the expansion of ${(2+\frac{3}{8}x)}^{10}$ is numerically greatest term . Then the range of $x$ is

1. $[\frac{-64}{21},-2]\cup [2,\frac{64}{21}]$
2. $[\frac{-53}{21},-2]\cup [2,\frac{53}{21}]$
3. $[\frac{-64}{21},-1]\cup [1,\frac{64}{21}]$
4. $[\frac{-53}{21},-1]\cup [1,\frac{53}{21}]$

Q. Let A = {1, 2, 3, 4, 5} and $f:A\to A$ be an into function such that $f\left(i\right)\ne i\forall i\in A$ then number of such functions f are

1. 1024
2. 904
3. 980
4. 984

Q. The ${11}^{\text{th}}$ term in the expansion of ${(x+\frac{1}{\sqrt{x}})}^{14}$ is

1. $\frac{999}{x}$
2. $\frac{1001}{x}$
3. $i$
4. $\frac{x}{1001}$

Q.

The coefficient of ${\mathrm{x}}^{20}$ in the expansion of ${(1+3\mathrm{x}+3{\mathrm{x}}^2+{\mathrm{x}}^3)}^{20}$ is

1. ${}^{60}{\mathrm{C}}_{40}$

2. ${}^{30}{C}_{20}$

3. ${}^{15}{C}_2$

4. None of these

Q. For which of the following values of $x$, $5$th term will be the numerically greatest term in the expansion of ${(1+\frac{x}{3})}^{10}$.

1. $-2$
2. $1.8$
3. $2$
4. $-1.9$

Q.

The larger of ${99}^{50}+{100}^{50}and{101}^{50}$ is . . .

1. $(101{)}^{50}$

2. $(101{)}^{50}=(99{)}^{50}+(100{)}^{50}$

3. $(99{)}^{50}+(100{)}^{50}$

4. Can't be determined.

Q. Numerically greatest term in the expansion of $(2+3x{)}^9,$ where $x=\frac{3}{2}$ is

1. $3^{13}\cdot 7$
2. $\frac{3^{13}\cdot 7}{2}$
3. $3^{12}\cdot 7$
4. $\frac{3^{12}\cdot 7}{2}$

Q.

The numerically greatest term in the expansion of $(2+3x{)}^{12}$ when $x=\frac{5}{6}$ is:

1. 

2. 

3. 

4. 

Q. If $4^{th}$ term in the expansion of ${(2+\frac{3}{8}x)}^{10}$ is numerically greatest term . Then the range of $x$ is

1. $[\frac{-64}{21},-2]\cup [2,\frac{64}{21}]$
2. $[\frac{-53}{21},-2]\cup [2,\frac{53}{21}]$
3. $[\frac{-64}{21},-1]\cup [1,\frac{64}{21}]$
4. $[\frac{-53}{21},-1]\cup [1,\frac{53}{21}]$

Q.

Numerically greatest term in the expansion of $(x-\frac{1}{x}{)}^{11}$ when x=2 is given by

1. 0

2. None

3. 2¹¹.¹¹C₅

4. 2¹¹

Q. What is simphson rule ?

Q. The greatest term in the expansion of $\sqrt{3}{(1+\frac{1}{\sqrt{3}})}^{20}$ is

1. $\frac{25840}{9}$
2. $\frac{24840}{9}$
3. $\frac{26840}{9}$
4. None of these

Q. If the coefficients of the three successive terms in the binomial expansion of $(1+x{)}^n$ are in the ratio $1:7:42$, then the first of these terms in the expansion is

1. $6$th
2. $7$th
3. $8$th
4. $9$th

Q. Given sequence $15,30,60,120,240$ is in G.P.

1. True
2. False

Q. Numerically greatest term in the expansion of $(2+3x{)}^9,$ where $x=\frac{3}{2}$ is

1. $3^{13}\cdot 7$
2. $\frac{3^{12}\cdot 7}{2}$
3. $\frac{3^{13}\cdot 7}{2}$
4. $3^{12}\cdot 7$

Q. If $\frac{a_{k+1}}{a_k}$ is constant for every $k\ge 1$. If $n>m\Rightarrow a_n>a_m$ and $a_1+a_n=66,a_2{a}_{n-1}=128$ and $\sum _{i=1}^n{a}_i=126$, then

1. $n=6$
2. $n=5$
3. $\frac{a_{k+1}}{a_k}=2$
4. $\frac{a_{k+1}}{a_k}=4$

Q. Solve the inequality $\frac{3(x-2)}{5}\le \frac{5(2-x)}{3}$

Q. The greatest term in the expansion of $\sqrt{3}{(1+\frac{1}{\sqrt{3}})}^{20}$ is

1. $\frac{{}^{20}{C}_8}{27}$
2. $\frac{{}^{20}{C}_7}{27}$
3. $\frac{{}^{20}{C}_6}{27}$
4. $\frac{{}^{20}{C}_9}{27}$

Q.

Given that the $4^{th}$ term in the expansion of $(2+\frac{3}{8}a{)}^{10}$ has the maximum numerical value, then

1. 

2. 

3. 

4. 

Q. The number of distinct terms in the expansion of ${(\sqrt{x}+\frac{1}{\sqrt{x}}+x^{\frac{3}{2}}+\frac{1}{x^{\frac{3}{2}}})}^{40}$ is/are (with respect to different power of $x$)

1. $120$
2. $121$
3. $60$
4. $31$

Q. Which term in the expansion of ${[\sqrt[3]{3\left(\frac{a}{\sqrt{b}}\right)}+\sqrt{\left(\frac{b}{\sqrt[3]{3a}}\right)}]}^{21}$ contains $a$ and $b$ to one and same power.

1. $8^{th}$ term
2. $9^{th}$ term
3. ${14}^{th}$ term
4. ${15}^{th}$ term

Q. For which of the following values of $x$, $7^{\text{th}}$ term is the numerically greatest term in the expansion of ${(1+\frac{2x}{5})}^{12}$

1. $\frac{9}{4}$
2. $\frac{5}{2}$
3. $\frac{11}{4}$
4. $\frac{13}{4}$