Numerically Greatest Term

Q.

Find the degree measure of $\frac{1}{4}\mathrm{radian}$.

Q.

For a positive integer $n$, ${\left(1+\frac{1}{x}\right)}^n$ is expanded in increasing powers of $x$.

If three consecutive coefficients in this expansion are in the ratio, $2:5:12$, then $n$ is equal to

Q. If $(5.6{)}^x=(0.0056{)}^y={10}^5$, then the value of $\frac{1}{x}-\frac{1}{y}$ is

1. $\frac{1}{5}$
2. $\frac{3}{5}$
3. $\frac{5}{6}$
4. $\frac{5}{3}$

Q.

What is the difference between $\log$ and $\ln$?

Q. Range of the function $f\left(x\right)=x^2+\frac{1}{x^2+1}$, is

1. $[\frac{3}{2},\infty )$
2. $[1,\infty )$
3. $(-\infty ,\infty )$
4. $[2,\infty )$

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.

Find the numerical value of the following expression:

$3x^{2}y-4x{y}^2$ if $x=8$ and $y=3$

Q.

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

1. ${}^{12}{C}_7{5}^5.4$

2. ${}^{12}{C}_8\frac{5^8}{2^4}$

3. ${}^{12}{C}_7(\frac{5}{2}{)}^7{.2}^5$

4. None of these

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.

If $6^{th}$ term in the expansion of $(\frac{3}{2}+\frac{x}{3}{)}^n$ is the numerically greatest term when x=3, then find the sum of all possible values of n

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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. If the interval in which $x(>0)$ must lie so that the greatest term in the expansion of $(1+x{)}^{100}$ has the greatest coefficient in $(a,b)$ then $2ab=$

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. $\frac{{}^{20}{C}_9}{27}$
4. $\frac{{}^{20}{C}_6}{27}$