Numerically Greatest Term

Q.

The largest interval for which $x^{12}-x^9+x^4-x+1>0$ is

1. $-4<x<0$

2. $0<x<1$

3. $-100<x<100$

4. $-\infty <x<\infty$

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.

Which term of the following sequences :

(a) $2,2\sqrt{2},4.....\text{is}128?$

(b) $\sqrt{3},3,3\sqrt{3},.....\text{is}729?$

c) $\frac{1}{3},\frac{1}{9},\frac{1}{27},.....\text{is}\frac{1}{19683}?$

Q.

Cube root of 217 is

1. None of these

2. 6.01

3. 6.04

4. 6.02

Q.

If the $(r+1{)}^{th}$ term in the expansion of ${(\sqrt[3]{3\frac{a}{\sqrt{b}}}+\sqrt{\frac{b}{\sqrt[3]{3a}}})}^{21}$ has the same power of a and b, then value of r is

1. 10

2. 6

3. 9

4. 8

Q.

In a conference of 8 persons, if each person shake hand with the other one only, then the total number of shake hands shall be

1. 49

2. 64

3. 56

4. 28

Q.

If s be the sum of the coefficients in the expansion of $(px+qy+rz{)}^n,p,q,r>0$, then ${lim}_{n\to \infty }\frac{S}{(S^{\frac{1}{n}}+1{)}^n}$=

1. pq/r

2. e ^pq/r

3. 0

4. None

Q.

Q.

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

1. 0

2. $2^{11}$

3. $2^{11}.{}^{11}{C}_5$

4. None

Q. Solve the inequality for real $x$.

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. Solve the inequality for real $x$.

Q.

k = $\underset{x\to \infty }{lim}\left(\frac{\sum _{k=1}^{1000}(x+k{)}^m}{x^m+{10}^{1000}}\right)$ is (m > 101)

1. 10²

2. 10³

3. 10⁴

4. 10

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

1. Can't be determined.

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

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

4. $(101{)}^{50}$

Q.

The number of students who joined the 'KEEP YOUR PLACE CLEAN' campaign are represented by 13th term in the expansion of ${(9x-\frac{1}{3\sqrt{x}})}^{18}$, Find the number of students.

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

Q. Solve the inequality for real $x$.

Q. Solve the inequality for real $x$.