Term Independent of x

Q.

If $\sin \left(\theta \right)=\frac{12}{13},\left(0<\theta <\frac{\mathrm{\pi }}{2}\right)$ and $\cos \left(\phi \right)=-\frac{3}{5},\left(\mathrm{\pi }<\mathrm{\phi }<\frac{3\mathrm{\pi }}{2}\right)$, then $\sin \left(\theta +\phi \right)$ will be

1. $\frac{-56}{61}$

2. $\frac{-56}{65}$

3. $\frac{1}{65}$

4. $-56$

Q.

If $3(se{c}^2\theta +{\tan }^2\theta )=5$, then the general value of $\theta$ is

1. $2n\pi +\frac{\pi }{6}$

2. $2n\pi \pm \frac{\pi }{6}$

3. $n\pi \pm \frac{\pi }{6}$

4. $n\pi \pm \frac{\pi }{3}$

Q.

If the expansion of ${\left[\frac{3\sqrt{x}}{7}-\frac{5}{2x\sqrt{x}}\right]}^{13n}$contains a term independent of $x$ in ${14}^{th}$ term, then $n$ should be

1. $10$

2. $5$

3. $6$

4. $4$

5. $11$

Q.

How do you write $x^{\frac{1}{2}}$ in radical form.

Q. The term independent of $x$ in the expansion of $(1+x+2x^3){(\frac{3x^2}{2}-\frac{1}{3x})}^9$ is

1. $\frac{17}{54}$
2. $\frac{17}{52}$
3. $\frac{19}{54}$
4. $\frac{19}{52}$

Q. The term independent of $x$ in the expansion ${(\frac{\sqrt{x}}{\sqrt{3}}+\frac{\sqrt{3}}{2x^2})}^{10}$ is equal to:

1. $\frac{7}{12}$
2. $\frac{1}{3}$
3. $\frac{4}{7}$
4. $\frac{5}{12}$

Q. If the term independent of $x$ in the expansion of ${(\sqrt{x}-\frac{m}{x^2})}^{10}$ is $405$, then

1. $m=2$
2. $m=-2$
3. $m=3$
4. $m=-3$

Q. The term independent of x in the expansion of $(1+x{)}^n{(1+\frac{1}{x})}^n$ is

1. $C_0^2+2C_1^2+3C_2^2+....+(n+1)C_n^2$
2. $(C_0+c_1+....+c_n{)}^2$
3. $c_0^2+C_1^2+.....+c_n^2$
4. $Noneoftheabove$

Q. The term independent of x expansion of ${(\frac{x+1}{x^{\frac{2}{3}}-x^{\frac{1}{3}}+1}-\frac{x-1}{x-x^{\frac{1}{2}}})}^{10}$ is

1. 4
2. 120
3. 210
4. 310

Q. Let $g:N\to N$ be defined as
$g(3n+1)=3n+2$,
$g(3n+2)=3n+3$,
$g(3n+3)=3n+1$, for all $n\ge 0$.
Then which of the following statements is true?

1. $gogog=g$
2. There exists a one-one function $f:N\to N$ such that $fog=f$
3. There exists a function $f:N\to N$ such that $gof=f$
4. There exists an onto function $f:N\to N$ such that $fog=f$

Q. The term independent of $x$ in the expansion of $(1+x+2x^3){(\frac{3x^2}{2}-\frac{1}{3x})}^9$ is

1. $\frac{17}{54}$
2. $\frac{17}{52}$
3. $\frac{19}{54}$
4. $\frac{19}{52}$

Q. The ratio of coefficient of $x^{15}$ to the term independent of $x$ in the expansion of ${(x^2+\frac{1}{2x})}^{15}$ is

1. $16:1$
2. $1:32$
3. $1:16$
4. $32:1$

Q. If the term independent of $x$ in the expansion of ${(\sqrt{x}-\frac{k}{x^2})}^{10}$ is $405$, then the value(s) of $k$ can be

1. $-3$
2. $-2$
3. $3$
4. $2$

Q. If the term independent of $x$ in the expansion of ${(\sqrt{x}-\frac{k}{x^2})}^{10}$ is $405$, then the value(s) of $k$ can be

1. $-3$
2. $-2$
3. $3$
4. $2$

Q. In the expansion of ${(x+\frac{2}{x^2})}^{15}$, the term independent of x is

1. ${}^{15}{C}_6{2}^6$
2. ${}^{15}{C}_5{2}^5$
3. ${}^{15}{C}_4{2}^4$
4. ${}^{15}{C}_8{2}^8$

Q. If sum of the coefficients of first, second and third terms in the expansion of ${(x^2+\frac{1}{x})}^m$ is $46,$ then coefficient of the term that is independent of $x$ is

1. $96$
2. $84$
3. $78$
4. $88$

Q. In the expansion of ${(x+\frac{2}{x^2})}^{15}$, the term independent of x is

1. ${}^{15}{C}_6{2}^6$
2. ${}^{15}{C}_5{2}^5$
3. ${}^{15}{C}_4{2}^4$
4. ${}^{15}{C}_8{2}^8$

Q. The term independent of $x$ in expansion of ${(\frac{x+1}{x^{2/3}-x^{1/3}+1}-\frac{x-1}{x-x^{1/2}})}^{10}$ is :

1. $4$
2. $120$
3. $210$
4. $310$